A Hybrid Mathematical-Simulation Approach to Hospital Beds Capacity Optimization for COVID-19 Pandemic Conditions

A Hybrid Mathematical-Simulation Approach to Hospital Beds Capacity Optimization for COVID-19 Pandemic Conditions | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A Hybrid Mathematical-Simulation Approach to Hospital Beds Capacity Optimization for COVID-19 Pandemic Conditions Reza Maleki, Mohammadreza Taghizadeh-Yazdi, Rohollah Ghasemi, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4515650/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 14 Nov, 2024 Read the published version in Operations Research Forum → Version 1 posted 11 You are reading this latest preprint version Abstract The Covid-19 pandemic was an unforeseen threat to human survival, and the efficiency of the health sector faced a severe challenge. The lack of hospital beds was one of the most critical concerns, and optimizing the capacity of hospital beds was considered one of the key issues. Due to the ageing of the population and the occasional occurrence of environmental and health crises, the demand for health services and the need for improved planning and administration are increasing daily. Therefore, the optimal allocation of hospital resources, particularly the number of beds, the essential criterion for a medical center’s capacity, can substantially reduce patient waiting time and treatment costs and improve services. An ideal multi-objective integer programming problem is presented in this study for optimizing the number of hospital beds and reducing costs of the length of stay and length of hospital stay. The problem also considers constraints relating to critical circumstances, given the Corona's prevalence. Moreover, the optimal answer is obtained using a simulation model, mathematical optimization, and a simulation-based optimization approach. For this purpose, mathematical modelling was used to minimize patients' waiting time, hospitalizations, and maintenance costs of existing beds and purchasing a new bed. Following that, real-world conditions were introduced into the problem using the simulation model and information acquired from one month of hospitalization of patients during the Coronavirus outbreak at Imam Hussein Hospital in Tehran. After comparing mathematical and simulated models, the OptQuest simulation-based optimization technique revealed the ideal number of hospital beds. Hospital beds capacity COVID-19 pandemic Simulation-based optimization Discrete event simulation Mathematical modeling Figures Figure 1 Figure 2 Highlights Hospital bed optimization improves patient care, wait times, and costs • Hospital bed allocation is crucial, especially during pandemics like COVID-19 • Financial constraints and bed capacity limit the mathematical framework • Simulation-based optimization serves as a supplement to mathematical modeling • Real-world conditions aid mathematical modeling for healthcare resource allocation 1 Introduction Capacity design is one of the operational managers' most significant strategic decisions (Sazvar et al. 2021 ). There are two concerns in capacity design; the first concern is the cost of shortages when demand exceeds supply, and the second concern is the cost of lost opportunities for available capacity that occur in situations where demand is less than supply (Kalvig and Machacek 2018 ; Shurrab et al. 2022 ; Wu et al. 2022 ). The Coronavirus pandemic is one of the main challenges of the healthcare industry in the current century, which has involved the entire human population in a short period (Abd-Alrazaq et al. 2021 ; Menhat et al. 2021 ). This unanticipated disaster left many industries with supply and demand uncertainty (Grida et al. 2020 ). Even industries such as hotels, airlines, and others experienced a decline in demand (Denizci Guillet and Chu 2021 ; Dey Tirtha et al. 2022 ); However, this situation showed its other side in the health sector, and the demand for using hospital services (Rees et al. 2020 ; Izadi et al. 2023 ) was met with such a growth that the lack of hospital beds followed (Delgado et al. 2022 ). According to the evidence, global healthcare systems were under tremendous pressure even before the pandemic due to a lack of proper planning to use 100% of hospital bed capacity (Andersen et al. 2017 ; German et al. 2018 ). A high level of bed occupancy can adversely affect patient care because it becomes more challenging to direct the most appropriate bed for patient care. Additionally, the lack of beds can increase the infection rate (Zhou et al. 2020 ), improper patient placement in the clinic (Song et al. 2020 ), and pressure on the staff (Tengilimoğlu et al. 2021 ). In addition, many countries consider hospital overcrowding a global and national crisis (Quarto et al. 2020 ). One of the main factors of over-occupancy is the poor planning of required bed capacity (Makarem et al. 2020 ). On average, hospitals with bed occupancy rates above 85% are subject to bed shortages, frequent capacity crises, contagion, and infection (Bosque-Mercader and Siciliani 2023 ). The number of available beds falls whenever the demand for urgent care rises. Thus, the hospital's ability to treat patients is weakened, and the delay in treatment is increased due to a lack of resources and medical staff. Overcrowding in hospitals is the result of four key factors; equipment (including lack of beds, lack of restrooms, and lack of used tools), lack of human resources (lack of doctors, nurses, treatment staff, and administrative personnel), inappropriate procedures (caused by unfavorable planning and lack of appropriate executive instructions), and the hospital's physical environment (Makarem et al. 2020 ). Inefficient hospital bed management causes countless problems for patients, managers, doctors, and nurses. Increased patient waiting time, delays in the discharge process, the need for unplanned changes in the number of employees, lack of resources, and misallocation of patients all result from inefficient bed management planning (Makarem et al. 2020 ). In addition to the lengthy wait time for patients, which causes inappropriate planning by doctors and nurses, one should also add the lack of proper treatment by treating doctors (Nowak et al. 2012 ). However, when the patient is finally allocated a bed, the hospital faces a blocked transfer situation (Affleck et al. 2013 ). For instance, the patient's condition is determined by moving from one bed to another, and each hospital department is classified with different treatment methods. A patient suffering from a stroke should be transferred to the appropriate ward and bed. Due to a lack of prior planning, this bottleneck occurs, preventing the patient from being placed in a suitable bed (Kim et al. 2020 ). The spread of Corona has caused concern that the hospitalization of critically ill patients may face problems due to the lack of beds in the ICU department. In such circumstances, in all countries affected by the disease, beds in other departments may also be transferred to the intensive care unit (Zangrillo et al. 2020 ). Making facility changes on this scale can take significant time and cause severe disruption when these resources are most needed. Compared to most big countries affected by this disease, Iran faced a significant shortage of hospital beds in proportion to its population (Halpern and Tan 2020 ). Therefore, a novel approach to health care is presented in this article to maximize the use of resources and reduce costs in a dynamic and unpredictable environment, such as a hospital facing a bed shortage due to the critical situation of the spread of Coronavirus. The methods of discrete event simulation and ideal multi-objective optimization based on simulation have been combined to solve the problem. According to Fig. 1 , the research implementation process consists of 10 steps. 2 Theorical Background 2.1 Hospital capacity planning The COVID-19 pandemic has made hospital capacity planning a crucial aspect of healthcare management, as it plays a significant role in controlling healthcare expenses and maintaining high standards of patient care (Sen-Crowe et al. 2021 ). Recent studies highlight the importance of hospital bed capacity in the face of increased demand for medical services during the pandemic (Sen-Crowe et al. 2021 ). It is founded that hospital bed capacity significantly impacts the spread of COVID-19, emphasizing the need for efficient bed planning and capacity analysis (Kokudo and Sugiyama 2021 ). The COVID-19 pandemic has considerably influenced hospital bed capacity, staffing, and (Moghadas et al. 2020 ). Effective planning is essential to manage the demand for medical services during the pandemic, and dynamic modeling and optimization of hospital bed allocation have been suggested as a solution (Kokudo and Sugiyama 2021 ). Amidst the COVID-19 outbreak, an intelligent decision support system (DSS) has been developed to aid in planning physician shifts (Güler and Geçici 2020 ). This system aims to facilitate efficient and effective capacity planning. Contemporary research consistently emphasizes the importance of effective hospital bed management and capacity evaluation in pandemics, offering various methodologies. Recent research has focused on the modeling, analysis, and optimization framework for allocating hospital beds during the spread of the coronavirus (Sarkar et al. 2021 ). The utilization of reinforcement learning has facilitated the implementation of a technique for the dynamic allocation of hospital beds (Zong and Luo 2022 ) and introduced a deep reinforcement learning approach for dynamic hospital bed allocation. Using a methodology grounded in a fuzzy rule-based approach (Jena et al. 2022 ) and a dynamic programming model for the allocation of beds (Ma et al. 2022 ) has facilitated the healthcare sector in delivering optimal patient care. 2.2 Capacity design methods and models in hospital Application of mathematical modeling for hospital capacity design . In recent years, hospital capacity management has relied heavily on optimal planning. Utilizing the multi-objective optimization method to allocate hospital beds in real-world conditions by factoring in bed utilization rate, patient waiting time, and hospital revenue are prevalent in the healthcare literature (Behnamian and Gharabaghli 2023 ). In addition, a decision-support tool with a stochastic demand model for bed allocation has been developed (Fernandez et al. 2021 ). This tool has demonstrated its ability to increase bed utilization and decrease patient wait times. The mixed integer linear programming (MILP) model contributes significantly to optimizing hospital resources (Chouba et al. 2020 ). This model can evaluate and demonstrate various restrictions, such as admission criteria and personnel requirements, to increase bed utilization and decrease patient waiting time. Moreover, the optimal allocation of human resources in therapeutic environments is a rapidly growing field of research in optimal planning (Hafezalkotob et al. 2022 ). The application of Data Envelopment Analysis (DEA) has assisted healthcare organizations with strategic planning and bed allocation (Soroush et al. 2022 ) Additionally, reducing resource consumption in the health industry by establishing goals using the goal programming methodology is possible. In order to minimize network cost, maximize network coverage, and maximize network reliability in a health network and the overall framework, the deviation between the three objectives was optimized (Hasani and Sheikh 2023 ). Application of simulation in hospital capacity design . Several contemporary research works have demonstrated that simulation in hospital capacity design can enhance patient flow, diminish wait times, and elevate healthcare efficiency and satisfaction (Barros et al. 2021 ). These studies continue to explore the application of simulation in healthcare, focusing on optimizing patient flow, reducing wait times, and augmenting overall efficiency and contentment (Kovalchuk et al. 2018 ). Numerous academics have simulated patient flow in the emergency room using simulation approaches, and they have then suggested viable solutions to eliminate bottlenecks and boost operational effectiveness (Peng et al. 2020 ). In order to determine how triage methods affect patient wait times, simulation has also been used (Kobayashi et al. 2017 ). This technique has helped to define specific protocols that will drastically cut down on wait times. Researchers are now looking into how simulation might be combined with other tools and processes to improve healthcare quality. Machine learning, artificial intelligence (AI), and simulation algorithms have been combined in recent studies to maximize the use of hospital resources, particularly in the emergency department (Olave-Rojas and Nickel 2021 ; Ortiz-Barrios et al. 2023 ). Investigations into the impact of telemedicine on patient flow and wait times also use simulation approaches (Nikolaeva et al. 2021 ). Research shows that telemedicine can significantly decrease waiting times and boost patient satisfaction. The COVID-19 pandemic has highly strained healthcare systems globally, leading to overwhelming hospital capacities. Simulation techniques have been increasingly utilized in the design of hospital capacity during the COVID-19 pandemic, incorporating intricate systems and processes (Currie et al. 2020 ). The Covid-19 pandemic has brought to light particular bottlenecks and inefficiencies in hospital simulation procedures (Zeinalnezhad et al. 2020 ). Researchers have employed discrete event simulation to determine the most effective staffing and resource allocation strategies for mitigating the impact of COVID-19 patient care in emergency departments (Melman et al. 2021 ). Simulation has been instrumental in enhancing the safety of human resources in the healthcare sector amidst the ongoing pandemic. The researchers have used simulation techniques to investigate the potential for COVID-19 transmission among medical center employees utilizing personal protective equipment (PPE) (Mosher et al. 2022 ). The simulation of hospital capacity design is subject to variation as the epidemic progresses and presents novel challenges. Application of Simulation-based optimization in hospital capacity design . Simulation-based optimization is an effective method for decision-making in hospital capacity design, as it blends the advantages of simulation and optimization (Aboueljinane and Frichi 2022 ). This powerful tool helps to understand complex systems, evaluate their performance under uncertainty, and find the best solutions from a broader range of options. The medical field and resource allocation have seen numerous recent studies that have utilized simulation-based optimization, including hospital bed allocation (Daldoul et al. 2022 ; Fattahi et al. 2023 ). Overcrowding, particularly in emergency departments, can result from insufficient resource allocation and increase the risk of death (Nahhas et al. 2017 ). The significance of simulation-based optimization in hospital capacity design has been made clear by the COVID-19 pandemic. Hospital selection in emergency medical service systems has been researched, with proximity, hospital treatment capabilities, and the shortest line or most available beds as the primary selection factors (Rolón and Cadavid 2021 ). Queuing models, discrete event simulation, and mixed linear integer programming are examples of solution methods (Rolón and Cadavid 2021 ). Hospital capacity command centers, which feature multidisciplinary teams managing patient flow operations using real-time data, have also been investigated (Franklin et al. 2022 ). However, peer-reviewed research on their layout and efficacy is still in infancy. During the COVID-19 pandemic, these methods can be modified to optimize hospital capacity design, resulting in effective resource allocation and enhanced patient care. 3 Research methodology In this study, the presentation of the simulation model and comparison of its outcomes using the Arena software's OptQuest optimization tool will aid in drawing conclusions and offering suggestions for the future. 3.1 Research limitations The current model is subject to data limitations, which limit its capacity to accommodate more than one inter-departmental transfer per patient. Additionally, the model lacks information in incorporating data about multiple transfers among various departments within the hospital. In reality, individuals necessitating intensive care or encountering frequent fluctuations in their medical condition may undergo numerous hospital transfers throughout their hospitalization period. The model is restricted to emergency patients as it lacks access to patients' information with appointments, precluding individuals treated with a prior appointment from being included. The proposed model operates under the assumption of resource homogeneity, whereby resources are considered to be uniform and devoid of any variation. Including crucial resources, such as healthcare professionals and hospital beds, within a simulation model can provide a more accurate and all-encompassing depiction. This study is based on the premise that all patients adhere to their scheduled appointments on time. In the context of clinical settings, it is a frequent occurrence for patients to arrive late for their scheduled appointments, despite having a predetermined time slot. 3.2 Presentation of optimization/mathematical model This section is presented the mathematical model of the problem, which is an ideal and linear multi-objective optimization. The model's features, assumptions, variables, and parameters are subsequently introduced. Model assumptions . The assumptions of the problem are as follows. The type of bed is considered similar in different hospital departments. From the beginning of the modeling, the sections added to the hospital for the maintenance of corona patients have been considered in the model. Therefore, in addition to the initial period of planning (t = 0), the input information is considered from the beginning of April 2019 for one year. Only hospitalized patients who use hospital beds are considered in the model. Also, the consideration of waiting patients is omitted in the model. Model indices . Three indices are considered in the model. W = 1, 2, …, 27 Index of different departments of the hospital T = 0, 1, 2, 3, 4 Time periods index I = 1, 2, 3, 4, 5: Patient triage index Define model variables. The decision variables of the model include the following. \({G}_{it}^{+}\) Increased hospitalization duration of patient i in time period t \({G}_{it}^{-}\) Reduced hospitalization duration of patient i in time period t \({K}_{it}^{+}\) Increased waiting time of patient i in time period t \({K}_{it}^{-}\) Reduced waiting time of patient i in time period t \({X}_{wt}\) The required number of beds in section w in period t \({X}_{wt}^{+}\) The number of beds added in section w in period t compared to period t-1 \({X}_{wt}^{-}\) The number of beds decreased in section w in period t compared to period t-1 \({I}_{wt}\) The inventory of beds for department w in period t \({Y}_{wt}\) Number of beds purchased for department w in period t Model parameters. The model parameters are as follows. \({\text{N}}_{\text{w}}\) Number of beds in section w at the beginning of planning (current capacity) \({C}_{wt}\) Bed purchase cost for department w in period t \({B}_{t}\) Hospital budget for bed expansion in period t \({F}_{it}\) Average hospitalization time required for triage level i in period t \({G}_{t}\) The total duration of hospitalization in period t \({K}_{it}\) Average waiting time for triage level i in period t \({\text{M}}_{\text{t}}\) Bed maintenance cost in period t \({Q}_{\text{t}}\) Total waiting time in period t \({P}_{W}\) The initial balance of the bed in section w Objective function modeling. The utilization of goal programming is a method within the realm of multi-criteria decision-making that aims to attain a multitude of objectives in the most expeditious manner feasible (Simon 1957 ). Formulating goal programming problems is the same as linear programming issues. The goal programming concept involves expanding the linear programming model to accommodate mathematical programming encompassing multiple objectives (Charnes and Cooper 1957 ). The primary distinctions lie in deliberately acknowledging distinct objectives and preferences about each objective. The model's objective function has two objectives and consists of four parts. In function f 1 , the goal is to minimize patients' waiting time and hospitalization. Therefore, the undesirable deviations of \({Td}_{it}^{+}\) and \({Ed}_{it}^{+}\) , which respectively mean excess hospitalization time and excess patient waiting time in the hospital, should be minimized. \(Min{f}_{1}=\sum _{i\in I}\sum _{t\in T}{G}_{it}^{+}+\sum _{i\in I}\sum _{t\in T}{K}_{it}^{+}\) (1–3) Function f 2 is related to hospital costs. The first term is the cost of maintaining each bed in the hospital, and the second is buying a new bed. \(Min{f}_{2}=\sum _{w\in W}\sum _{t\in T}{M}_{t}{X}_{wt}+\sum _{w\in W}\sum _{t\in T}{C}_{wt}{Y}_{wt}\) (2–3) Limitations of model . St: \({X}_{wt}={N}_{w} \forall t\in T , t=0 , w\in W\) (3–3) \({X}_{wt-1}+{X}_{wt}^{+}-{X}_{wt}^{-}+{Y}_{wt}={X}_{wt} \forall t\in T , t>1 , w\in W\) (4 − 3) \({I}_{wt-1}+{X}_{wt}^{+}-{X}_{wt}^{-}={I}_{wt} \forall t\in T , t>1 , w\in W\) (5 − 3) \(\sum _{w\in W}{C}_{wt}{Y}_{wt}\le {B}_{t} \forall t\in T\) (6 − 3) \(\sum _{w\in W}\sum _{i\in I}{K}_{it}{X}_{wt}+{K}_{it}^{-}-{K}_{it}^{+}={Q}_{t} \forall t\in T\) (7 − 3) \(\sum _{w\in W}\sum _{i\in I}{F}_{it}{X}_{wt}+{G}_{it}^{-}-{G}_{it}^{+}={G}_{t} \forall t\in T\) (8 − 3) \({I}_{wt}={P}_{w} \forall t\in T , t=0 , w\in W\) (9 − 3) \({X}_{wt}^{+} , {X}_{wt}^{-} , {X}_{wt} , {Y}_{wt} , {I}_{wt} ,{G}_{it}^{+} , {G}_{it}^{-} , {K}_{it}^{+} , {K}_{it}^{-}\ge 0\in \text{I}\text{n}\text{t}\) (10 − 3) (3–3) The first limit shows the initial capacity of the beds in section w at the beginning of the time horizon, i.e., t = 0. (4 − 3) The following limitation is the relationship between the number of beds needed in the w sector in 2 consecutive periods. (5 − 3) The next term is the warehouse inventory variable's relationship in two consecutive periods. The number of beds in stock in department w in each period equals its corresponding variable in the previous period plus the number of beds added from the warehouse. (6 − 3) This term is called a budget constraint. In any period, the cost of purchased beds should not exceed the budget allocated for that period. (7 − 3) The waiting time of patient i in department w in period t should be less than the total waiting time. (8 − 3) The duration of hospitalization of patient i in department w in the period t should be less than the total duration of the corresponding patient. (9 − 3) This limit expresses the number of beds available in the warehouse by different departments at the beginning of planning (t = 0). (10 − 3) The last constraint expressing the nature of variables is the model, which guarantees that all variables must be integers and positive. 3.3 Verification and validation of the mathematical model The epsilon-constraint method is used to obtain Pareto efficient optimal solutions. In this method, the goal is to optimize the objective functions of the model so that one of the functions is selected and to minimize this objective. Other objectives become constraints in the model structure. The general form of the epsilon constraint model is as follows. \(max Z\left(x\right)=\left[{z}_{1}\left(x\right),{z}_{2}\left(x\right),\dots ,{z}_{k}\left(x\right)\right]\) (11 − 3) \({g}_{i}\left(x\right)\le 0,\forall i=\text{1,2},\dots ,m\) (12 − 3) St: \(max {z}_{h}\left(x\right)\) (13 − 3) \({g}_{i}\le 0,\forall i=\text{1,2},\dots ,m\) (14 − 3) \({z}_{j}\left(x\right)\ge {e}_{j},j=\text{1,2},\dots ,h-1,h+1,\dots ,k\) (15 − 3) The epsilon constraint method is used in most optimization methods, but its most common application is in solving single-objective and multi-objective models. The epsilon method algorithm includes the following steps. First step First, it is necessary to obtain the optimal values of the goals individually. In this way, the first objective function is solved with the space of constraints, and the second objective function is solved with the space of constraints until the kth objective function is solved with the space of constraints. Each time an optimal coordinate and an optimal objective pan will be obtained. Second step The values of all other goals are obtained according to step 1, resulting in the payoff Table 1 . Table 1 Payoff. \({x}^{1}\) \({z}_{1}\left({x}^{1}\right)\) \({z}_{2}\left({x}^{k}\right)\) ... \({z}_{k}\left({x}^{1}\right)\) \({x}^{2}\) \({z}_{1}\left({x}^{2}\right)\) \({z}_{2}\left({x}^{2}\right)\) ... \({z}_{k}\left({x}^{2}\right)\) ... \({x}^{k}\) ... \({z}_{1}\left({x}^{k}\right)\) ... \({z}_{2}\left({x}^{k}\right)\) ... ... \({z}_{k}\left({x}^{k}\right)\) MAX MIN Third step Each objective function's minimum and maximum values are calculated and given at the end of the Table 2 . Table 2 Optimal value for epsilon. \({e}_{j}\) \({f}_{1}\) \({f}_{2}\) 1 281800.920 281800.920 365892913646 2 281850.920 281850.920 366438520421 3 281900.920 281900.920 366440000000 4 281950.920 281950.920 366440000000 5 282000.920 282000.920 366440000000 6 282050.920 282050.920 366441952540 7 282100.920 282100.920 366446492754 8 28150.920 28150.920 366602081267 9 282200.920 282200.920 366685219523 10 282250.920 282250.920 366852200016 Fourth step The multi-objective problem becomes a single-objective problem. \(max {z}_{h} \left(x\right)\) (16 − 3) St: \({g}_{i}\le 0,\forall i=\text{1,2},\dots , m\) (17 − 3) \({z}_{j}\left(x\right)\ge {e}_{j},j=\text{1,2},\dots ,h-1,h+1,\dots , k\) (18 − 3) Fifth step Using the minimum and maximum of each problem. \({n}_{j}\le {z}_{j}\le {m}_{j}\) (19 − 3) Sixth step In the range of the objective function, different values for are considered, and the problem is solved for each value. \({e}_{j}={n}_{j}+\left[\frac{t}{r-1}\right]\left({m}_{j}-{n}_{j}\right), t=\text{0,1},2,\dots ,r-1\) (20 − 3) According to the above method, 10 points are systematically selected. R = 10 is considered, and the number of epsilons is obtained according to the mentioned formula. 3.4 Presentation of the simulation model Simulation enables decision-makers to examine, scrutinize, and assess scenarios that may not be feasible [53]. Engineers, designers, and managers consider simulation an essential tool in today's competitive world. A model must replicate the existing system's reaction to events that fluctuate over time. Discrete event simulation is a simulation technique that models the performance of a system as a discrete sequence of events occurring over time. Every occurrence occurs at a precise point in time and signifies a modification in the system's condition. A transition is defined as the process of moving from one event to another, and in a simulation, it is possible to make a direct temporal leap from one event to the following (Robinson 2005 ). The technique in question has undergone significant development since its inception, with its applications expanding to encompass a range of fields such as interactive visual modeling, simulation-based optimization, virtual reality, and simulation in various domains. Simulation-based optimization refers to integrating simulation models and optimization techniques to determine the optimal amount of input data required to enhance the performance of the simulation model (Nguyen et al. 2014 ). The method described can be understood as a systematic approach to optimizing decision variables in relation to the outputs of a simulation model. The simulation model (Fig. 2 ) of patient admission in the hospital was created with the help of Arena Rockwell Software version 14. With the help of the simulation model, it is possible to examine the bottlenecks and workstations that cause queue formation in the system. Also, patients' waiting time and hospitalization during admission to discharge and discharge from the hospital are among the most critical outputs from the simulation model. 3.5 Model simulation with AERNA software At the beginning of the course, with the help of an input analyzer and the time between patients' arrival, the distribution of their arrival is determined. Upon arrival, patients go to the emergency department, and due to the critical conditions of the spread of the coronavirus, if they need urgent treatment, they are allocated a bed without admission. The rest of the patients are directed to the reception unit and triaged; if there is an empty bed, they are admitted At the beginning of entering the hospital departments, for the three departments of orthopedics, psychiatry, and radiotherapy, patients are separated from each other by gender and transferred to their respective departments. Other patients are transferred to different hospital departments according to their conditions. After separating the patients into 27 departments, a decision is made regarding the need for hospitalized people for diagnostic measures. Diagnostic procedures include seven parts of audiometry, electrocardiogram (HeartRate), infectious diseases (Infection), X-ray, ultrasound (Sonography), Spirometry, and CT scan. After leaving the said departments, the patients who need medical care again enter the bed allocation process. Otherwise, the patients are discharged from the hospital. If there is no need for diagnostic measures, the bed is empty and cleaned by the relevant official, and the patient is removed from the admission process. 3.6 Verification and validation of the simulation model After presenting the model, it is time to verify and validate the simulation model. According to the coordination of the conceptual model and the current data and the review of the modules used in the model, the correct entry of the parameters, and the logical structure of the model, the validation of the model is confirmed. Three steps are suggested to determine the validity of the model. Design a model with significant face validity. Determine the validity of the model assumptions. Compare the changes of inputs to outputs of the model with the changes of inputs to outputs of the system. Since the time distribution between patients entering the hospital was used to enter the data, there is no need for statistical hypothesis tests to confirm the assumptions, and the model's validity is confirmed 4 Results In this section, the mathematical model and simulation results are analyzed, and optimal scenarios are searched with the help of the OptQuest tool. According to the mathematical model and the assumptions presented in the third chapter, the model is solved, and the results are obtained in this part. 4.1 Mathematical model The mathematical model is initially checked and validated using the model's indices. The 27 hospital departments (w) make up the mathematical model. The model contains patients with triage priorities 1, 2, 3, 4, and 5 (i). In addition, the model's initial periods are considered along with the four seasons of spring, summer, autumn, and winter (t) in 2019. Table 3 indicates the costs associated with procuring the hospital bed and the upkeep of the hospital bed during the five temporal intervals examined in the model. As a consequence of the monthly inflation, there has been a rise in the budget allocation to enhance hospital capacities. (Costs in millions of Rials, Convert Iranian Rials to US Dollars In April 2019 = 0.000004839) Table 3 Bed development and costs maintaining cost. ( \({B}_{t}\) ) t = 0 t = 1 t = 2 t = 3 t = 4 Cost 7800000000 15000000000 15000000000 15500000000 1590000000 ( \({\text{M}}_{\text{t}}\) ) Cost 10000000 150000000 150000000 150000000 170000000 Table 4 displays patients' hospitalization and patients' waiting times duration during the five time periods of the model. As anticipated during the initial phase of the hospital's response to the critical circumstances surrounding the proliferation of the coronavirus within the nation, there has been a notable increase in the length of patients' hospital stays. During the third period, which corresponds to the apex of the 2019 viral pandemic, there is a notable discrepancy in the length of hospital stays compared to the preceding and subsequent periods. Subsequently, the aggregate duration of waiting time resembles the overall length of hospital stay among patients, with the third period exhibiting the greatest extent. Table 4 Patient hospitalization and waiting time. ( \({G}_{t}\) ) t = 0 t = 1 t = 2 t = 3 t = 4 T 236 481 299 816.33 257 ( \({Q}_{\text{t}}\) ) T 14.62 13.17 14.75 60.83 20.67 Table 5 displays the mean duration of patient wait times and the mean duration of hospital admission for patients receiving treatment across the five triage levels (1–5) during the five time periods examined in the model. During the third period of the COVID-19 pandemic, the waiting time for medical attention notably increased, particularly in the fifth triage category, which encompasses patients with critical conditions, in comparison to previous periods. This phenomenon is observable to a certain degree in upper-level triages during the fourth period. Consistent with expectations, the mean duration of hospitalization was also comparatively lengthier during the third temporal interval compared to the remaining periods. Given that the height of the COVID-19 pandemic occurred during the autumn season of 2019, individuals presenting at hospitals with symptoms resembling those of the virus, such as colds and flu, encountered uncertain triage conditions prior to undergoing COVID-19 scans and tests. As a result, the initial triage category for these patients was often fourth, leading to prolonged hospitalization periods during this timeframe. Table 5 Mean patient wait time & hospitalization time. \({K}_{it}\) t = 0 t = 1 t = 2 t = 3 t = 4 \({K}_{1t}\) 0.5 0.13 0.17 1.17 0,.6 \({K}_{2t}\) 0.2 0.23 0.51 2.37 0.6 \({K}_{3t}\) 0.6 0.71 0.65 2.6 0.86 \({K}_{4t}\) 1.1 1.15 0.98 3.8 2.18 \({K}_{5t}\) 1.21 1.23 2 7.36 2.5 \({F}_{it}\) \({F}_{1t}\) 10.25 32 21.17 89.33 11.17 \({F}_{2t}\) 17.36 19.28 21.08 57.71 17.95 \({F}_{3t}\) 9.49 24.62 10.25 25.3 9.75 \({F}_{4t}\) 7.13 15.25 6.25 14.25 7.85 \({F}_{5t}\) 2.2 5 4.25 8.5 2.85 Table 6 presents the bed count for departments 1 through 27 of the hospital at the outset of the model planning period. Moreover, the number of beds available in the warehouse at the beginning of the planning period for the hospital departments is as follows. Table 6 Initial bed count \({(\text{N}}_{\text{w}})\) & Number of warehouse bed d \(\left({P}_{W}\right)\) . w N P 1 0 6 2 1 11 3 1 14 4 0 4 5 2 27 6 2 30 7 2 30 8 1 16 9 3 48 10 1 18 11 3 51 12 2 35 13 1 21 14 3 47 15 2 20 16 1 16 17 2 20 18 2 30 19 2 30 20 2 39 21 0 8 22 1 12 23 2 20 24 1 18 25 2 22 26 2 21 27 0 8 Table 7 displays the costs, measured in millions of Rials, incurred by the hospital to procure beds for departments 1 through 27 from zero to four. The cost of procuring hospital beds has exhibited an upward trend from the baseline period (t = 0) to the fourth due to the concurrent rise in costs for the year. Table 7 Bed procuring cost \(\left({C}_{wt}\right)\) . w t = 0 t = 1 t = 2 t = 3 t = 4 1 120000000 140000000 140000000 145000000 150000000 2 35500000 45000000 48000000 50000000 52000000 3 6900000 70000000 70000000 70000000 80000000 4 120000000 140000000 140000000 145000000 150000000 5 120000000 140000000 140000000 145000000 150000000 6 120000000 140000000 140000000 145000000 150000000 7 120000000 140000000 140000000 145000000 150000000 8 35500000 45000000 48000000 50000000 52000000 9 35500000 45000000 48000000 50000000 52000000 10 15500000 22000000 25000000 28000000 30000000 11 120000000 140000000 140000000 145000000 150000000 12 120000000 140000000 140000000 145000000 150000000 13 120000000 140000000 140000000 145000000 150000000 14 35500000 45000000 48000000 50000000 52000000 15 40000000 45000000 48000000 50000000 52000000 16 40000000 45000000 48000000 50000000 52000000 17 15500000 22000000 25000000 28000000 30000000 18 35500000 45000000 48000000 50000000 52000000 19 35500000 45000000 48000000 50000000 52000000 20 110000000 122000000 128000000 130000000 135000000 21 120000000 140000000 140000000 145000000 150000000 22 120000000 140000000 140000000 145000000 150000000 23 40000000 45000000 48000000 50000000 52000000 24 35500000 45000000 48000000 50000000 52000000 25 35500000 45000000 48000000 50000000 52000000 26 35500000 45000000 48000000 50000000 52000000 27 6900000 70000000 70000000 70000000 80000000 4.2 Result of the model Based on the model parameters and the data of hospital departments across various periods, the model was designed and coded in optimization software. The resulting outcomes include the requisite number of beds, the number of beds added and reduced in the department, the quantity of warehouse stock, and the number of beds procured. The hospital exhibited a substantial capacity prior to the outbreak of the coronavirus and even implemented a specialized emergency ICU unit. Furthermore, the mathematical modeling failed to account for the severity of the issue. As per the hospital's model, bed shortages have not been encountered. Thus, based on the findings, purchasing a bed appears unnecessary. (Table 8 and Table 9 ) Table 8 Optimal value of the variables of the number of beds. t = 0 t = 1 t = 2 w \({X}_{wt}\) \({X}_{wt}^{+}\) \({X}_{wt}^{-}\) \({Y}_{wt}\) \({I}_{wt}\) \({X}_{wt}\) \({X}_{wt}^{+}\) \({X}_{wt}^{-}\) \({Y}_{wt}\) \({I}_{wt}\) \({X}_{wt}\) \({X}_{wt}^{+}\) \({X}_{wt}^{-}\) \({Y}_{wt}\) \({I}_{wt}\) 1 6 0 0 0 0 6 0 0 0 0 6 0 0 0 0 2 11 0 0 0 1 10 0 0 0 1 10 0 0 0 1 3 14 0 0 0 1 13 0 0 0 1 13 0 0 0 1 4 4 0 0 0 0 4 0 0 0 0 4 0 0 0 0 5 27 0 0 0 2 25 0 0 0 2 25 0 0 0 2 6 30 0 0 0 2 28 0 0 0 2 28 0 0 0 2 7 30 0 0 0 2 28 0 0 0 2 28 0 0 0 2 8 16 0 0 0 1 15 0 0 0 1 15 0 0 0 1 9 48 0 0 0 3 45 0 0 0 3 45 0 0 0 3 10 18 0 0 0 1 17 0 0 0 1 17 0 0 0 1 11 51 0 0 0 3 48 0 0 0 3 48 0 0 0 3 12 35 0 0 0 2 33 0 0 0 2 33 0 0 0 2 13 21 0 0 0 1 20 0 0 0 1 20 0 0 0 1 14 47 0 0 0 3 44 0 0 0 3 44 0 0 0 3 15 20 0 0 0 2 18 0 0 0 2 18 0 0 0 2 16 16 0 0 0 1 15 0 0 0 1 15 0 0 0 1 17 20 0 0 0 2 18 0 0 0 2 18 0 0 0 2 18 30 0 0 0 2 28 0 0 0 2 28 0 0 0 2 19 30 0 0 0 2 28 0 0 0 2 28 0 0 0 2 20 39 0 0 0 2 37 0 0 0 2 37 0 0 0 2 21 8 0 0 0 0 8 0 0 0 0 8 0 0 0 0 22 12 0 0 0 1 11 0 0 0 1 11 0 0 0 1 23 20 0 0 0 2 18 0 0 0 2 18 0 0 0 2 24 18 0 0 0 1 17 0 0 0 1 17 0 0 0 1 25 22 0 0 0 2 20 0 0 0 2 20 0 0 0 2 26 21 0 0 0 2 19 0 0 0 2 19 0 0 0 2 27 8 0 0 0 0 8 0 0 0 0 8 0 0 0 0 Table 9 Optimal value of the variables of the number of beds. t = 0 t = 1 t = 2 w \({X}_{wt}\) \({X}_{wt}^{+}\) \({X}_{wt}^{-}\) \({Y}_{wt}\) \({I}_{wt}\) \({X}_{wt}\) \({X}_{wt}^{+}\) \({X}_{wt}^{-}\) \({Y}_{wt}\) \({I}_{wt}\) \({X}_{wt}\) \({X}_{wt}^{+}\) \({X}_{wt}^{-}\) \({Y}_{wt}\) \({I}_{wt}\) 1 6 0 0 0 0 6 0 0 0 0 6 0 0 0 0 2 10 0 0 0 1 10 0 0 0 1 10 0 0 0 1 3 13 0 0 0 1 13 0 0 0 1 13 0 0 0 1 4 4 0 0 0 0 4 0 0 0 0 4 0 0 0 0 5 25 0 0 0 2 25 0 0 0 2 25 0 0 0 2 6 28 0 0 0 2 28 0 0 0 2 28 0 0 0 2 7 28 0 0 0 2 28 0 0 0 2 28 0 0 0 2 8 15 0 0 0 1 15 0 0 0 1 15 0 0 0 1 9 45 0 0 0 3 45 0 0 0 3 45 0 0 0 3 10 17 0 0 0 1 17 0 0 0 1 17 0 0 0 1 11 48 0 0 0 3 48 0 0 0 3 48 0 0 0 3 12 33 0 0 0 2 33 0 0 0 2 33 0 0 0 2 13 20 0 0 0 1 20 0 0 0 1 20 0 0 0 1 14 44 0 0 0 3 44 0 0 0 3 44 0 0 0 3 15 18 0 0 0 2 18 0 0 0 2 18 0 0 0 2 16 15 0 0 0 1 15 0 0 0 1 15 0 0 0 1 17 18 0 0 0 2 18 0 0 0 2 18 0 0 0 2 18 28 0 0 0 2 28 0 0 0 2 28 0 0 0 2 19 28 0 0 0 2 28 0 0 0 2 28 0 0 0 2 20 37 0 0 0 2 37 0 0 0 2 37 0 0 0 2 21 8 0 0 0 0 8 0 0 0 0 8 0 0 0 0 22 11 0 0 0 1 11 0 0 0 1 11 0 0 0 1 23 18 0 0 0 2 18 0 0 0 2 18 0 0 0 2 24 17 0 0 0 1 17 0 0 0 1 17 0 0 0 1 25 20 0 0 0 2 20 0 0 0 2 20 0 0 0 2 26 19 0 0 0 2 19 0 0 0 2 19 0 0 0 2 27 8 0 0 0 0 6 0 0 0 0 8 0 0 0 0 The model was constructed and operationalized utilizing GAMS optimization software based on the model's parameters and patient triage data from multiple periods. The results obtained for the increased and decreased hospitalization time and the increased and decreased waiting time of the model are as follows. (Table 10 ) Table 10 Duration of hospitalization and waiting increased and decreased. t = 0 t = 1 t = 2 t = 3 t = 4 t = 5 \({G}_{it}^{+}\) 0 28643.460 0 0 0 \({G}_{it}^{-}\) 0 0 0 0 0 \({K}_{it}^{+}\) 0 2230.800 0 0 0 \({K}_{it}^{-}\) 0 0 0 0 0 t = 0 t = 1 t = 2 t = 3 t = 4 t = 5 \({G}_{it}^{+}\) 0 0 0 0 55382.150 \({G}_{it}^{-}\) 0 0 0 0 0 \({K}_{it}^{+}\) 0 0 0 0 0 \({K}_{it}^{-}\) 0 0 0 0 0 t = 0 t = 1 t = 2 t = 3 t = 4 t = 5 \({G}_{it}^{+}\) 0 0 0 36304.0 0 \({G}_{it}^{-}\) 0 0 0 0 0 \({K}_{it}^{+}\) 0 0 0 2489.360 0 \({K}_{it}^{-}\) 0 0 0 0 0 t = 0 t = 1 t = 2 t = 3 t = 4 t = 5 \({G}_{it}^{+}\) 0 0 0 0 112530.960 \({G}_{it}^{-}\) 0 0 0 0 0 \({K}_{it}^{+}\) 0 0 0 0 0 \({K}_{it}^{-}\) 0 0 0 0 0 t = 0 t = 1 t = 2 t = 3 t = 4 t = 5 \({G}_{it}^{+}\) 0 0 0 0 28543.170 \({G}_{it}^{-}\) 0 0 0 0 0 \({K}_{it}^{+}\) 0 0 0 0 3895.270 \({K}_{it}^{-}\) 0 0 0 0 0 Typically, the hospital experiences an escalation in both hospitalization and waiting times across all temporal epochs. However, based on the model's conditions and the constraints outlined in the problem, this temporal prolongation cannot be ascribed to critical circumstances, as evidenced by the obtained outcomes. This phenomenon may be associated with the admission and hospitalization protocols for patients within the healthcare facility. 4.3 Simulation model In April 2019, a simulation of patient admission to discharge within a 30-minute timeframe was simulated at Imam Hussein Hospital in Tehran. A stable influx of corona patients characterized the study period. The hospital comprises a range of specialized units, including 27 CS ICU, Day Care, NICU, Post Cath, Post CCU/Post CSICU, ICU, Emergency ICU, Women's Orthopedics, Men's Orthopedics, Pediatrics, Surgery, Neurosurgery, Eye, Internal Women and Men (General), Women's Radiotherapy, Men's Radiotherapy, Pediatric Psychiatry (ChildrenMental), Women's Psychiatry, Men's Psychiatry, Gynecology and Obstetrics, CCU1, CCU2, Chemotherapy - Under observation, Infectious, Gastroenterology, Neurology, and Neonatal. The allocation of resources, precisely the number of beds, is standardized across all departments. The distribution of patient arrivals in all the mentioned departments has been collected and obtained according to the time information of the start and end of the activity recorded in the HIS system of the hospital. In the mentioned system, the possibility of patients withdrawing during their presence in the queue is ignored. In this structure, all patients entering the hospital have been registered under emergency and non-emergency admissions, and patients with previous appointments have been ignored in the model. Table 11 displays the mean and maximum wait times for patients across various departments within the hospital. As depicted in Table 11 , the current critical conditions indicate that the waiting time in departments dedicated to the treatment of patients suspected or confirmed to have contracted the Covid-19 virus, including the ICU, emergency ICU, CT scan examination department, and internal hospital departments, is notably more prolonged than that of other departments. Moreover, specific procedures and facilities, such as the hospital's emergency department and the management and sanitation of hospital beds post-patient discharge, commonly referred to as the length of the patient's hospital stay, have encountered prolonged mean durations. Table 11 Department queue. Department Average Maximum Value Gynecology 23.800 194.81 Pediatrics 41.6263 407.06 Spirometry 24.0269 183.82 CCU1 7.4212 114.65 CCU2 8.7702 117.60 Chemotherapy 15.0525 162.43 Audiometry 6.7550 115.31 Pediatric Psychiatry 8.6691 114.47 Cleaning 80.7331 384.78 CSICU 7.4811 123.89 CT scan 14.4681 154.00 DayCare 5.2058 67.3606 Gastroenterology 2.7715 61.7327 EmergencyCare 0.1405 2.1118 EmptyBed 1.2372 20.2894 Eye 5.5320 99.14 Internal 0.5359 20.4407 Women's Psychiatry 16.8012 166.60 HeartRate 9.2074 105.20 ICU 47.3829 253.69 Emergency ICU 3315.18 6029.36 Infection 16.2372 178.36 Infectious 14.3454 199.05 Men's Orthopedics 11.8581 127.79 Men's Psychiatry 32.8649 183.35 Neurology 4.9995 108.98 Neonatal 112.83 641.15 NICU 6.3941 66.7530 Paymenttriage 0.8243 5.2264 PostCath 0.8220 25.3473 Post CCU/Post CSICU 9403.79 17769.28 Men's Radiotherapy 159.43 679.80 Women's Radiotherapy 10.6852 98.7286 Reception 1.6214 5.6863 Sonography 4.5405 89.4667 Surgery 65.0470 393.19 Neurosurgery 174.75 856.59 Women's Orthopedics 10.1893 104.41 X-ray 28.4067 232.06 4.4 Simulation-based optimization This study discusses utilizing the OptQuest tool from the Arena software collection to minimize the model's objective function and determine the optimal number of hospital beds across various departments. The simulation model incorporates the initial objective function to minimize patients' hospitalization and waiting time. The length of hospital stay is determined by the cumulative duration of hospitalization experienced by patients across all 27 departments. The waiting time encompasses the duration of complementary treatment procedures, such as CT scan, bed vacating and re-preparation by staff, admission, triage, and emergency department procedures. The simulation was conducted with a default of 100 repetitions and an efficiency of 0.6534%. The optimal number of hospital beds was derived accordingly. (Table 12 ) Table 12 Optimal number of hospital bed. w Number 1 6 2 13 3 12 4 4 5 30 6 31 7 36 8 16 9 48 10 18 11 52 12 35 13 20 14 50 15 22 16 17 17 20 18 31 19 30 20 38 21 8 22 12 23 22 24 18 25 23 26 19 27 8 5 Conclusions and suggestions The optimal hospital bed allocation directly improves the provision of medical services and, consequently, improves physical and mental health in society (Emanuel et al. 2020 ). Waiting for the patient leads to the acute condition of the disease, increasing mental pressure on the patient and hospital staff, reducing productivity, and increasing costs (Reichert and Jacobs 2018 ). In a situation where the hospital is facing a crisis such as the spread of the coronavirus, the importance of having an efficient treatment system, especially in quickly responding to the needs of the community and controlling hospitalization and waiting time, increases even more (Soroush et al. 2022 ). In addition to reducing costs, this issue also involved reducing the patient's wait time and hospitalization duration. The hospital simulation model has 27 treatment departments and seven diagnostic departments. When the patient enters the hospital, after deciding on the emergency or non-emergency condition of the disease and the level of treatment triage, which is divided into five levels, the patient enters the relevant department separately from the treatment departments. After sorting patients by diagnostic need, a diagnosis is made. Discharged patients empty the bed capacity and clean. Other patients enter the seven sections of diagnostic measures, and after exiting this stage, a decision is made again regarding their most essential needs in terms of benefiting from the medical services or exiting the process. The simulation model used April 2019 hospital bed numbers. Before the Corona pandemic, the hospital had enough beds in different departments to accommodate patients. Although, during the simulated period, the condition of patients suspected of being infected with the coronavirus was stable, and the country had not yet experienced successive coronavirus peaks. The mathematical model is designed to minimize hospital waiting times, admissions, bed maintenance, and procurement expenses. The model's parameters include the budget for hospital bed development and purchase, the cost of buying beds by department and period, the cost of maintaining beds, and the hospital warehouse's initial bed inventory. The patient's total waiting time and hospitalization and the average waiting and hospitalization in different periods and triages are considered to shorten the admission process. The mathematical model's limitations include the following: the initial capacity of hospital beds relationship between the variable number of beds and the inventory variable in two consecutive periods budget limits number of inventories in each department at the start of the modeling time horizon two-time reduction limits The mathematical model does not consider critical conditions, so the hospital's capacity is always adequate, and There is never a shortage of beds. Furthermore, due to the hospital's emergency ICU department before the spread of the Covid-19 virus, the hospital faced less lack of bed capacity in the first year of the pandemic. The optimal value of the objective function was obtained according to the simulation model for 54310000000 billion Rials for one month. This value was obtained with a productivity rate of 65% from the present research. According to the mathematical model modeled for one year, this amount in the second objective function was 366440000000 billion Rials. The waiting time in the simulation model is 13701.22 minutes, which is the result of one month in the Corona era. This number has been calculated in the mathematical model as 2230.8 minutes in the second period, simultaneously with the simulation model. Since real-world conditions are involved in the simulated model, the increase in waiting time can be estimated. According to the evaluation and analysis of the mathematical and simulation model of the actual conditions of patient admission in the hospital, the future research suggestions are as follows. The present study only considered one aspect of the factors affecting decision-making regarding costs, waiting time, and hospitalization due to the hospital's lack of cooperation in providing the necessary information. For example, to adjust the hospital's entry process, the objective function of reducing costs related to department conversion was removed from the mathematical modeling. Adding this item to the model requires information about the space needed to develop the hospital's critical parts and physical placement. Considering the work shift and the number of personnel required by different hospital departments is another matter that can be investigated in future research and have a more comprehensive view of the issue of bed allocation. The limited warehouse space will affect the movement and placement of reduced beds in hospital departments. Considering the limitation of the hospital's inventory space (warehouse) helps to bring the mathematical model closer to the reality of the problem. The type of hospital beds can be different in the same department and different departments compared to each other. Including the treatment center beds according to the type of use will make the model more complete. Despite the difficult access to the information of patients who come to the hospital with a previous appointment, it can add more depth to the mathematical model and increase patients’ input in the simulation model Declarations Ethical Approval Not applicable Funding Not applicable.a References Abd-Alrazaq A, Hassan A, Abuelezz I, et al (2021) Overview of technologies implemented during the first wave of the covid-19 pandemic: Scoping review. J Med Internet Res 23 Aboueljinane L, Frichi Y (2022) A simulation optimization approach to investigate resource planning and coordination mechanisms in emergency systems. Simul Model Pract Theory 119:. https://doi.org/10.1016/j.simpat.2022.102586 Affleck A, Parks P, Drummond A, et al (2013) Emergency department overcrowding and access block. 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Manage Sci 66:. https://doi.org/10.1287/mnsc.2019.3395 Soroush F, Nabilou B, Faramarzi A, Yusefzadeh H (2022) A study of the evacuation and allocation of hospital beds during the Covid-19 epidemic: a case study in Iran. BMC Health Serv Res 22:1–7. https://doi.org/10.1186/S12913-022-08286-7/TABLES/4 Tengilimoğlu D, Zekioğlu A, Tosun N, et al (2021) Impacts of COVID-19 pandemic period on depression, anxiety and stress levels of the healthcare employees in Turkey. Leg Med 48:. https://doi.org/10.1016/j.legalmed.2020.101811 Wu W, Xie S, Tan J, Ouyang T (2022) An integrated design of LNG cold energy recovery for supply demand balance using energy storage devices. Renew Energy 183:. https://doi.org/10.1016/j.renene.2021.11.066 Zangrillo A, Beretta L, Silvani P, et al (2020) Fast reshaping of intensive care unit facilities in a large metropolitan hospital in Milan, Italy: Facing the COVID-19 pandemic emergency. Critical Care and Resuscitation 22: Zeinalnezhad M, Chofreh AG, Goni FA, et al (2020) Simulation and improvement of patients’ workflow in heart clinics during covid-19 pandemic using timed coloured petri nets. Int J Environ Res Public Health 17:. https://doi.org/10.3390/ijerph17228577 Zhou W, Wang A, Wang X, et al (2020) Impact of hospital bed shortages on the containment of covid-19 in wuhan. Int J Environ Res Public Health 17:. https://doi.org/10.3390/ijerph17228560 Zong K, Luo C (2022) Reinforcement learning based framework for COVID-19 resource allocation. Comput Ind Eng 167:107960. https://doi.org/10.1016/J.CIE.2022.107960 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 14 Nov, 2024 Read the published version in Operations Research Forum → Version 1 posted Editorial decision: Revision requested 15 Jul, 2024 Reviews received at journal 14 Jul, 2024 Reviews received at journal 08 Jul, 2024 Reviews received at journal 03 Jul, 2024 Reviewers agreed at journal 27 Jun, 2024 Reviewers agreed at journal 16 Jun, 2024 Reviewers agreed at journal 13 Jun, 2024 Reviewers invited by journal 13 Jun, 2024 Editor assigned by journal 04 Jun, 2024 Submission checks completed at journal 04 Jun, 2024 First submitted to journal 02 Jun, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4515650","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":314936355,"identity":"03dddd72-39ab-4116-8fb5-566095964286","order_by":0,"name":"Reza Maleki","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8klEQVRIiWNgGAWjYBADGQYexsbHPyqg3AQitPAAtTQbM5xhkCBFCwObNGMbVAs+YN7e/vADY44dDz/P4TbpwnmH6xjYDz9geLgHtxaZMweSJRi3JfNI9jY2W8/cdliCgSfNgCHhGW4tEhIJB4BamHkMzjM23uAFaWHIAfrlAB4t8g+bfzBuq+exP8/YIME7B6iF/w0BLRLMbEBbDvMY8DY2SfM2ALVIELKFJ43NInHbcR6JMwebDWccS5dsk3hmcACvFvbjj2983FYtx9+T/vDBhxprfn7+5IcPf+DRAgYJyBw2ICakYRSMglEwCkYBAQAAq31KbpnQDUsAAAAASUVORK5CYII=","orcid":"","institution":"University of Tehran","correspondingAuthor":true,"prefix":"","firstName":"Reza","middleName":"","lastName":"Maleki","suffix":""},{"id":314936356,"identity":"cccb1206-187a-421f-844b-cf683492e400","order_by":1,"name":"Mohammadreza Taghizadeh-Yazdi","email":"","orcid":"","institution":"University of Tehran","correspondingAuthor":false,"prefix":"","firstName":"Mohammadreza","middleName":"","lastName":"Taghizadeh-Yazdi","suffix":""},{"id":314936357,"identity":"b579037c-444f-4c62-8a6a-7310f35a2ca6","order_by":2,"name":"Rohollah Ghasemi","email":"","orcid":"","institution":"University of Tehran","correspondingAuthor":false,"prefix":"","firstName":"Rohollah","middleName":"","lastName":"Ghasemi","suffix":""},{"id":314936358,"identity":"7a21c404-b525-4a83-a985-e072505241ab","order_by":3,"name":"Samar Rivandi","email":"","orcid":"","institution":"University of Tehran","correspondingAuthor":false,"prefix":"","firstName":"Samar","middleName":"","lastName":"Rivandi","suffix":""}],"badges":[],"createdAt":"2024-06-02 05:08:27","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4515650/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4515650/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s43069-024-00389-7","type":"published","date":"2024-11-14T15:57:22+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":58760849,"identity":"61a9d64a-3889-4447-ab1c-a510788ad015","added_by":"auto","created_at":"2024-06-20 18:51:43","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":151165,"visible":true,"origin":"","legend":"\u003cp\u003eResearch executive process\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-4515650/v1/2f3d0a86a47a7cf47e6478c6.png"},{"id":58760827,"identity":"f2b56aa8-03b5-4298-9a7d-9dbe7df73cc9","added_by":"auto","created_at":"2024-06-20 18:51:35","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":59840,"visible":true,"origin":"","legend":"\u003cp\u003eSimulation model\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-4515650/v1/93b15884d38fc3c515c59ead.png"},{"id":69285492,"identity":"07d28a48-b778-408a-bcc6-314def801940","added_by":"auto","created_at":"2024-11-18 19:26:07","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1814892,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4515650/v1/d2085823-0a0c-43a3-8e99-4a43d1bd5c5f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":" A Hybrid Mathematical-Simulation Approach to Hospital Beds Capacity Optimization for COVID-19 Pandemic Conditions","fulltext":[{"header":"Highlights","content":"\u003cp\u003eHospital bed optimization improves patient care, wait times, and costs\u003c/p\u003e\n\u003cp\u003e\u0026bull;\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;Hospital bed allocation is crucial, especially during pandemics like COVID-19\u003c/p\u003e\n\u003cp\u003e\u0026bull;\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;Financial constraints and bed capacity limit the mathematical framework\u003c/p\u003e\n\u003cp\u003e\u0026bull;\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;Simulation-based optimization serves as a supplement to mathematical modeling\u003c/p\u003e\n\u003cp\u003e\u0026bull; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;Real-world conditions aid mathematical modeling for healthcare resource allocation\u003c/p\u003e"},{"header":"1 Introduction","content":"\u003cp\u003eCapacity design is one of the operational managers' most significant strategic decisions (Sazvar et al. \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). There are two concerns in capacity design; the first concern is the cost of shortages when demand exceeds supply, and the second concern is the cost of lost opportunities for available capacity that occur in situations where demand is less than supply (Kalvig and Machacek \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Shurrab et al. \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Wu et al. \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). The Coronavirus pandemic is one of the main challenges of the healthcare industry in the current century, which has involved the entire human population in a short period (Abd-Alrazaq et al. \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Menhat et al. \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). This unanticipated disaster left many industries with supply and demand uncertainty (Grida et al. \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Even industries such as hotels, airlines, and others experienced a decline in demand (Denizci Guillet and Chu \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Dey Tirtha et al. \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2022\u003c/span\u003e); However, this situation showed its other side in the health sector, and the demand for using hospital services (Rees et al. \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Izadi et al. \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) was met with such a growth that the lack of hospital beds followed (Delgado et al. \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAccording to the evidence, global healthcare systems were under tremendous pressure even before the pandemic due to a lack of proper planning to use 100% of hospital bed capacity (Andersen et al. \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; German et al. \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eA high level of bed occupancy can adversely affect patient care because it becomes more challenging to direct the most appropriate bed for patient care. Additionally, the lack of beds can increase the infection rate (Zhou et al. \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), improper patient placement in the clinic (Song et al. \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), and pressure on the staff (Tengilimoğlu et al. \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). In addition, many countries consider hospital overcrowding a global and national crisis (Quarto et al. \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). One of the main factors of over-occupancy is the poor planning of required bed capacity (Makarem et al. \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). On average, hospitals with bed occupancy rates above 85% are subject to bed shortages, frequent capacity crises, contagion, and infection (Bosque-Mercader and Siciliani \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). The number of available beds falls whenever the demand for urgent care rises. Thus, the hospital's ability to treat patients is weakened, and the delay in treatment is increased due to a lack of resources and medical staff.\u003c/p\u003e \u003cp\u003eOvercrowding in hospitals is the result of four key factors; equipment (including lack of beds, lack of restrooms, and lack of used tools), lack of human resources (lack of doctors, nurses, treatment staff, and administrative personnel), inappropriate procedures (caused by unfavorable planning and lack of appropriate executive instructions), and the hospital's physical environment (Makarem et al. \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eInefficient hospital bed management causes countless problems for patients, managers, doctors, and nurses. Increased patient waiting time, delays in the discharge process, the need for unplanned changes in the number of employees, lack of resources, and misallocation of patients all result from inefficient bed management planning (Makarem et al. \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). In addition to the lengthy wait time for patients, which causes inappropriate planning by doctors and nurses, one should also add the lack of proper treatment by treating doctors (Nowak et al. \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). However, when the patient is finally allocated a bed, the hospital faces a blocked transfer situation (Affleck et al. \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). For instance, the patient's condition is determined by moving from one bed to another, and each hospital department is classified with different treatment methods. A patient suffering from a stroke should be transferred to the appropriate ward and bed. Due to a lack of prior planning, this bottleneck occurs, preventing the patient from being placed in a suitable bed (Kim et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe spread of Corona has caused concern that the hospitalization of critically ill patients may face problems due to the lack of beds in the ICU department. In such circumstances, in all countries affected by the disease, beds in other departments may also be transferred to the intensive care unit (Zangrillo et al. \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Making facility changes on this scale can take significant time and cause severe disruption when these resources are most needed. Compared to most big countries affected by this disease, Iran faced a significant shortage of hospital beds in proportion to its population (Halpern and Tan \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Therefore, a novel approach to health care is presented in this article to maximize the use of resources and reduce costs in a dynamic and unpredictable environment, such as a hospital facing a bed shortage due to the critical situation of the spread of Coronavirus. The methods of discrete event simulation and ideal multi-objective optimization based on simulation have been combined to solve the problem.\u003c/p\u003e \u003cp\u003eAccording to Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the research implementation process consists of 10 steps.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"2 Theorical Background","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Hospital capacity planning\u003c/h2\u003e \u003cp\u003eThe COVID-19 pandemic has made hospital capacity planning a crucial aspect of healthcare management, as it plays a significant role in controlling healthcare expenses and maintaining high standards of patient care (Sen-Crowe et al. \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Recent studies highlight the importance of hospital bed capacity in the face of increased demand for medical services during the pandemic (Sen-Crowe et al. \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). It is founded that hospital bed capacity significantly impacts the spread of COVID-19, emphasizing the need for efficient bed planning and capacity analysis (Kokudo and Sugiyama \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe COVID-19 pandemic has considerably influenced hospital bed capacity, staffing, and (Moghadas et al. \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Effective planning is essential to manage the demand for medical services during the pandemic, and dynamic modeling and optimization of hospital bed allocation have been suggested as a solution (Kokudo and Sugiyama \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAmidst the COVID-19 outbreak, an intelligent decision support system (DSS) has been developed to aid in planning physician shifts (G\u0026uuml;ler and Ge\u0026ccedil;ici \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). This system aims to facilitate efficient and effective capacity planning. Contemporary research consistently emphasizes the importance of effective hospital bed management and capacity evaluation in pandemics, offering various methodologies. Recent research has focused on the modeling, analysis, and optimization framework for allocating hospital beds during the spread of the coronavirus (Sarkar et al. \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The utilization of reinforcement learning has facilitated the implementation of a technique for the dynamic allocation of hospital beds (Zong and Luo \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) and introduced a deep reinforcement learning approach for dynamic hospital bed allocation. Using a methodology grounded in a fuzzy rule-based approach (Jena et al. \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) and a dynamic programming model for the allocation of beds (Ma et al. \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) has facilitated the healthcare sector in delivering optimal patient care.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Capacity design methods and models in hospital\u003c/h2\u003e \u003cp\u003e \u003cb\u003eApplication of mathematical modeling for hospital capacity design\u003c/b\u003e. In recent years, hospital capacity management has relied heavily on optimal planning. Utilizing the multi-objective optimization method to allocate hospital beds in real-world conditions by factoring in bed utilization rate, patient waiting time, and hospital revenue are prevalent in the healthcare literature (Behnamian and Gharabaghli \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). In addition, a decision-support tool with a stochastic demand model for bed allocation has been developed (Fernandez et al. \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). This tool has demonstrated its ability to increase bed utilization and decrease patient wait times. The mixed integer linear programming (MILP) model contributes significantly to optimizing hospital resources (Chouba et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). This model can evaluate and demonstrate various restrictions, such as admission criteria and personnel requirements, to increase bed utilization and decrease patient waiting time. Moreover, the optimal allocation of human resources in therapeutic environments is a rapidly growing field of research in optimal planning (Hafezalkotob et al. \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe application of Data Envelopment Analysis (DEA) has assisted healthcare organizations with strategic planning and bed allocation (Soroush et al. \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) Additionally, reducing resource consumption in the health industry by establishing goals using the goal programming methodology is possible. In order to minimize network cost, maximize network coverage, and maximize network reliability in a health network and the overall framework, the deviation between the three objectives was optimized (Hasani and Sheikh \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cb\u003eApplication of simulation in hospital capacity design\u003c/b\u003e. Several contemporary research works have demonstrated that simulation in hospital capacity design can enhance patient flow, diminish wait times, and elevate healthcare efficiency and satisfaction (Barros et al. \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). These studies continue to explore the application of simulation in healthcare, focusing on optimizing patient flow, reducing wait times, and augmenting overall efficiency and contentment (Kovalchuk et al. \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Numerous academics have simulated patient flow in the emergency room using simulation approaches, and they have then suggested viable solutions to eliminate bottlenecks and boost operational effectiveness (Peng et al. \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). In order to determine how triage methods affect patient wait times, simulation has also been used (Kobayashi et al. \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). This technique has helped to define specific protocols that will drastically cut down on wait times. Researchers are now looking into how simulation might be combined with other tools and processes to improve healthcare quality. Machine learning, artificial intelligence (AI), and simulation algorithms have been combined in recent studies to maximize the use of hospital resources, particularly in the emergency department (Olave-Rojas and Nickel \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Ortiz-Barrios et al. \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Investigations into the impact of telemedicine on patient flow and wait times also use simulation approaches (Nikolaeva et al. \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Research shows that telemedicine can significantly decrease waiting times and boost patient satisfaction.\u003c/p\u003e \u003cp\u003eThe COVID-19 pandemic has highly strained healthcare systems globally, leading to overwhelming hospital capacities. Simulation techniques have been increasingly utilized in the design of hospital capacity during the COVID-19 pandemic, incorporating intricate systems and processes (Currie et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). The Covid-19 pandemic has brought to light particular bottlenecks and inefficiencies in hospital simulation procedures (Zeinalnezhad et al. \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Researchers have employed discrete event simulation to determine the most effective staffing and resource allocation strategies for mitigating the impact of COVID-19 patient care in emergency departments (Melman et al. \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Simulation has been instrumental in enhancing the safety of human resources in the healthcare sector amidst the ongoing pandemic. The researchers have used simulation techniques to investigate the potential for COVID-19 transmission among medical center employees utilizing personal protective equipment (PPE) (Mosher et al. \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). The simulation of hospital capacity design is subject to variation as the epidemic progresses and presents novel challenges.\u003c/p\u003e \u003cp\u003e \u003cb\u003eApplication of Simulation-based optimization in hospital capacity design\u003c/b\u003e. Simulation-based optimization is an effective method for decision-making in hospital capacity design, as it blends the advantages of simulation and optimization (Aboueljinane and Frichi \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). This powerful tool helps to understand complex systems, evaluate their performance under uncertainty, and find the best solutions from a broader range of options. The medical field and resource allocation have seen numerous recent studies that have utilized simulation-based optimization, including hospital bed allocation (Daldoul et al. \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Fattahi et al. \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Overcrowding, particularly in emergency departments, can result from insufficient resource allocation and increase the risk of death (Nahhas et al. \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2017\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe significance of simulation-based optimization in hospital capacity design has been made clear by the COVID-19 pandemic. Hospital selection in emergency medical service systems has been researched, with proximity, hospital treatment capabilities, and the shortest line or most available beds as the primary selection factors (Rol\u0026oacute;n and Cadavid \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Queuing models, discrete event simulation, and mixed linear integer programming are examples of solution methods (Rol\u0026oacute;n and Cadavid \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Hospital capacity command centers, which feature multidisciplinary teams managing patient flow operations using real-time data, have also been investigated (Franklin et al. \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). However, peer-reviewed research on their layout and efficacy is still in infancy. During the COVID-19 pandemic, these methods can be modified to optimize hospital capacity design, resulting in effective resource allocation and enhanced patient care.\u003c/p\u003e \u003c/div\u003e"},{"header":"3 Research methodology","content":"\u003cp\u003eIn this study, the presentation of the simulation model and comparison of its outcomes using the Arena software's OptQuest optimization tool will aid in drawing conclusions and offering suggestions for the future.\u003c/p\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Research limitations\u003c/h2\u003e \u003cp\u003eThe current model is subject to data limitations, which limit its capacity to accommodate more than one inter-departmental transfer per patient. Additionally, the model lacks information in incorporating data about multiple transfers among various departments within the hospital. In reality, individuals necessitating intensive care or encountering frequent fluctuations in their medical condition may undergo numerous hospital transfers throughout their hospitalization period. The model is restricted to emergency patients as it lacks access to patients' information with appointments, precluding individuals treated with a prior appointment from being included.\u003c/p\u003e \u003cp\u003eThe proposed model operates under the assumption of resource homogeneity, whereby resources are considered to be uniform and devoid of any variation. Including crucial resources, such as healthcare professionals and hospital beds, within a simulation model can provide a more accurate and all-encompassing depiction. This study is based on the premise that all patients adhere to their scheduled appointments on time. In the context of clinical settings, it is a frequent occurrence for patients to arrive late for their scheduled appointments, despite having a predetermined time slot.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Presentation of optimization/mathematical model\u003c/h2\u003e \u003cp\u003eThis section is presented the mathematical model of the problem, which is an ideal and linear multi-objective optimization. The model's features, assumptions, variables, and parameters are subsequently introduced.\u003c/p\u003e \u003cp\u003e \u003cb\u003eModel assumptions\u003c/b\u003e. The assumptions of the problem are as follows.\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eThe type of bed is considered similar in different hospital departments.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eFrom the beginning of the modeling, the sections added to the hospital for the maintenance of corona patients have been considered in the model. Therefore, in addition to the initial period of planning (t\u0026thinsp;=\u0026thinsp;0), the input information is considered from the beginning of April 2019 for one year.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eOnly hospitalized patients who use hospital beds are considered in the model. Also, the consideration of waiting patients is omitted in the model.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eModel indices\u003c/b\u003e. Three indices are considered in the model.\u003c/p\u003e \u003cp\u003eW\u0026thinsp;=\u0026thinsp;1, 2, \u0026hellip;, 27 Index of different departments of the hospital\u003c/p\u003e \u003cp\u003eT\u0026thinsp;=\u0026thinsp;0, 1, 2, 3, 4 Time periods index\u003c/p\u003e \u003cp\u003eI\u0026thinsp;=\u0026thinsp;1, 2, 3, 4, 5: Patient triage index\u003c/p\u003e \u003cp\u003e \u003cb\u003eDefine model variables.\u003c/b\u003e The decision variables of the model include the following.\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({G}_{it}^{+}\\)\u003c/span\u003e \u003c/span\u003e Increased hospitalization duration of patient i in time period t\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({G}_{it}^{-}\\)\u003c/span\u003e \u003c/span\u003e Reduced hospitalization duration of patient i in time period t\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({K}_{it}^{+}\\)\u003c/span\u003e \u003c/span\u003e Increased waiting time of patient i in time period t\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({K}_{it}^{-}\\)\u003c/span\u003e \u003c/span\u003e Reduced waiting time of patient i in time period t\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({X}_{wt}\\)\u003c/span\u003e \u003c/span\u003e The required number of beds in section w in period t\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({X}_{wt}^{+}\\)\u003c/span\u003e \u003c/span\u003e The number of beds added in section w in period t compared to period t-1\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({X}_{wt}^{-}\\)\u003c/span\u003e \u003c/span\u003e The number of beds decreased in section w in period t compared to period t-1\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({I}_{wt}\\)\u003c/span\u003e \u003c/span\u003e The inventory of beds for department w in period t\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({Y}_{wt}\\)\u003c/span\u003e \u003c/span\u003e Number of beds purchased for department w in period t\u003c/p\u003e \u003cp\u003e \u003cb\u003eModel parameters.\u003c/b\u003e The model parameters are as follows.\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({\\text{N}}_{\\text{w}}\\)\u003c/span\u003e \u003c/span\u003e Number of beds in section w at the beginning of planning (current capacity)\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({C}_{wt}\\)\u003c/span\u003e \u003c/span\u003e Bed purchase cost for department w in period t\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({B}_{t}\\)\u003c/span\u003e \u003c/span\u003e Hospital budget for bed expansion in period t\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({F}_{it}\\)\u003c/span\u003e \u003c/span\u003e Average hospitalization time required for triage level i in period t\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({G}_{t}\\)\u003c/span\u003e \u003c/span\u003e The total duration of hospitalization in period t\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({K}_{it}\\)\u003c/span\u003e \u003c/span\u003e Average waiting time for triage level i in period t\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({\\text{M}}_{\\text{t}}\\)\u003c/span\u003e \u003c/span\u003e Bed maintenance cost in period t\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({Q}_{\\text{t}}\\)\u003c/span\u003e \u003c/span\u003e Total waiting time in period t\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({P}_{W}\\)\u003c/span\u003e \u003c/span\u003e The initial balance of the bed in section w\u003c/p\u003e \u003cp\u003e \u003cb\u003eObjective function modeling.\u003c/b\u003e The utilization of goal programming is a method within the realm of multi-criteria decision-making that aims to attain a multitude of objectives in the most expeditious manner feasible (Simon \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e1957\u003c/span\u003e). Formulating goal programming problems is the same as linear programming issues. The goal programming concept involves expanding the linear programming model to accommodate mathematical programming encompassing multiple objectives (Charnes and Cooper \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e1957\u003c/span\u003e). The primary distinctions lie in deliberately acknowledging distinct objectives and preferences about each objective.\u003c/p\u003e \u003cp\u003eThe model's objective function has two objectives and consists of four parts. In function f\u003csub\u003e1\u003c/sub\u003e, the goal is to minimize patients' waiting time and hospitalization. Therefore, the undesirable deviations of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Td}_{it}^{+}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Ed}_{it}^{+}\\)\u003c/span\u003e\u003c/span\u003e, which respectively mean excess hospitalization time and excess patient waiting time in the hospital, should be minimized.\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(Min{f}_{1}=\\sum _{i\\in I}\\sum _{t\\in T}{G}_{it}^{+}+\\sum _{i\\in I}\\sum _{t\\in T}{K}_{it}^{+}\\)\u003c/span\u003e \u003c/span\u003e (1\u0026ndash;3)\u003c/p\u003e \u003cp\u003eFunction f\u003csub\u003e2\u003c/sub\u003e is related to hospital costs. The first term is the cost of maintaining each bed in the hospital, and the second is buying a new bed.\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(Min{f}_{2}=\\sum _{w\\in W}\\sum _{t\\in T}{M}_{t}{X}_{wt}+\\sum _{w\\in W}\\sum _{t\\in T}{C}_{wt}{Y}_{wt}\\)\u003c/span\u003e \u003c/span\u003e (2\u0026ndash;3)\u003c/p\u003e \u003cp\u003e \u003cb\u003eLimitations of model\u003c/b\u003e. St:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({X}_{wt}={N}_{w} \\forall t\\in T , t=0 , w\\in W\\)\u003c/span\u003e \u003c/span\u003e (3\u0026ndash;3)\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({X}_{wt-1}+{X}_{wt}^{+}-{X}_{wt}^{-}+{Y}_{wt}={X}_{wt} \\forall t\\in T , t\u0026gt;1 , w\\in W\\)\u003c/span\u003e \u003c/span\u003e (4\u0026thinsp;\u0026minus;\u0026thinsp;3)\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({I}_{wt-1}+{X}_{wt}^{+}-{X}_{wt}^{-}={I}_{wt} \\forall t\\in T , t\u0026gt;1 , w\\in W\\)\u003c/span\u003e \u003c/span\u003e (5\u0026thinsp;\u0026minus;\u0026thinsp;3)\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\sum _{w\\in W}{C}_{wt}{Y}_{wt}\\le {B}_{t} \\forall t\\in T\\)\u003c/span\u003e \u003c/span\u003e (6\u0026thinsp;\u0026minus;\u0026thinsp;3)\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\sum _{w\\in W}\\sum _{i\\in I}{K}_{it}{X}_{wt}+{K}_{it}^{-}-{K}_{it}^{+}={Q}_{t} \\forall t\\in T\\)\u003c/span\u003e \u003c/span\u003e (7\u0026thinsp;\u0026minus;\u0026thinsp;3)\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\sum _{w\\in W}\\sum _{i\\in I}{F}_{it}{X}_{wt}+{G}_{it}^{-}-{G}_{it}^{+}={G}_{t} \\forall t\\in T\\)\u003c/span\u003e \u003c/span\u003e (8\u0026thinsp;\u0026minus;\u0026thinsp;3)\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({I}_{wt}={P}_{w} \\forall t\\in T , t=0 , w\\in W\\)\u003c/span\u003e \u003c/span\u003e (9\u0026thinsp;\u0026minus;\u0026thinsp;3)\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({X}_{wt}^{+} , {X}_{wt}^{-} , {X}_{wt} , {Y}_{wt} , {I}_{wt} ,{G}_{it}^{+} , {G}_{it}^{-} , {K}_{it}^{+} , {K}_{it}^{-}\\ge 0\\in \\text{I}\\text{n}\\text{t}\\)\u003c/span\u003e \u003c/span\u003e (10\u0026thinsp;\u0026minus;\u0026thinsp;3)\u003c/p\u003e \u003cp\u003e(3\u0026ndash;3) The first limit shows the initial capacity of the beds in section w at the beginning of the time horizon, i.e., t\u0026thinsp;=\u0026thinsp;0.\u003c/p\u003e \u003cp\u003e(4\u0026thinsp;\u0026minus;\u0026thinsp;3) The following limitation is the relationship between the number of beds needed in the w sector in 2 consecutive periods.\u003c/p\u003e \u003cp\u003e(5\u0026thinsp;\u0026minus;\u0026thinsp;3) The next term is the warehouse inventory variable's relationship in two consecutive periods. The number of beds in stock in department w in each period equals its corresponding variable in the previous period plus the number of beds added from the warehouse.\u003c/p\u003e \u003cp\u003e(6\u0026thinsp;\u0026minus;\u0026thinsp;3) This term is called a budget constraint. In any period, the cost of purchased beds should not exceed the budget allocated for that period.\u003c/p\u003e \u003cp\u003e(7\u0026thinsp;\u0026minus;\u0026thinsp;3) The waiting time of patient i in department w in period t should be less than the total waiting time.\u003c/p\u003e \u003cp\u003e(8\u0026thinsp;\u0026minus;\u0026thinsp;3) The duration of hospitalization of patient i in department w in the period t should be less than the total duration of the corresponding patient.\u003c/p\u003e \u003cp\u003e(9\u0026thinsp;\u0026minus;\u0026thinsp;3) This limit expresses the number of beds available in the warehouse by different departments at the beginning of planning (t\u0026thinsp;=\u0026thinsp;0).\u003c/p\u003e \u003cp\u003e(10\u0026thinsp;\u0026minus;\u0026thinsp;3) The last constraint expressing the nature of variables is the model, which guarantees that all variables must be integers and positive.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Verification and validation of the mathematical model\u003c/h2\u003e \u003cp\u003eThe epsilon-constraint method is used to obtain Pareto efficient optimal solutions. In this method, the goal is to optimize the objective functions of the model so that one of the functions is selected and to minimize this objective. Other objectives become constraints in the model structure. The general form of the epsilon constraint model is as follows.\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(max Z\\left(x\\right)=\\left[{z}_{1}\\left(x\\right),{z}_{2}\\left(x\\right),\\dots ,{z}_{k}\\left(x\\right)\\right]\\)\u003c/span\u003e \u003c/span\u003e (11\u0026thinsp;\u0026minus;\u0026thinsp;3)\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({g}_{i}\\left(x\\right)\\le 0,\\forall i=\\text{1,2},\\dots ,m\\)\u003c/span\u003e \u003c/span\u003e (12\u0026thinsp;\u0026minus;\u0026thinsp;3)\u003c/p\u003e \u003cp\u003eSt:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(max {z}_{h}\\left(x\\right)\\)\u003c/span\u003e \u003c/span\u003e (13\u0026thinsp;\u0026minus;\u0026thinsp;3)\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({g}_{i}\\le 0,\\forall i=\\text{1,2},\\dots ,m\\)\u003c/span\u003e \u003c/span\u003e (14\u0026thinsp;\u0026minus;\u0026thinsp;3)\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({z}_{j}\\left(x\\right)\\ge {e}_{j},j=\\text{1,2},\\dots ,h-1,h+1,\\dots ,k\\)\u003c/span\u003e \u003c/span\u003e (15\u0026thinsp;\u0026minus;\u0026thinsp;3)\u003c/p\u003e \u003cp\u003eThe epsilon constraint method is used in most optimization methods, but its most common application is in solving single-objective and multi-objective models.\u003c/p\u003e \u003cp\u003eThe epsilon method algorithm includes the following steps.\u003c/p\u003e \u003cp\u003e \u003cstrong\u003eFirst step\u003c/strong\u003e \u003cp\u003eFirst, it is necessary to obtain the optimal values of the goals individually. In this way, the first objective function is solved with the space of constraints, and the second objective function is solved with the space of constraints until the kth objective function is solved with the space of constraints. Each time an optimal coordinate and an optimal objective pan will be obtained.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eSecond step\u003c/strong\u003e \u003cp\u003eThe values of all other goals are obtained according to step 1, resulting in the payoff Table \u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePayoff.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}^{1}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({z}_{1}\\left({x}^{1}\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({z}_{2}\\left({x}^{k}\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e...\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({z}_{k}\\left({x}^{1}\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}^{2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({z}_{1}\\left({x}^{2}\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({z}_{2}\\left({x}^{2}\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e...\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({z}_{k}\\left({x}^{2}\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e...\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}^{k}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e...\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({z}_{1}\\left({x}^{k}\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e...\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({z}_{2}\\left({x}^{k}\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e...\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e...\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({z}_{k}\\left({x}^{k}\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMAX\u003c/p\u003e \u003cp\u003eMIN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eThird step\u003c/strong\u003e \u003cp\u003eEach objective function's minimum and maximum values are calculated and given at the end of the Table \u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eOptimal value for epsilon.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({e}_{j}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{1}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e281800.920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e281800.920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e365892913646\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e281850.920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e281850.920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e366438520421\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e281900.920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e281900.920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e366440000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e281950.920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e281950.920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e366440000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e282000.920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e282000.920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e366440000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e282050.920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e282050.920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e366441952540\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e282100.920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e282100.920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e366446492754\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e28150.920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e28150.920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e366602081267\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e282200.920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e282200.920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e366685219523\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e282250.920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e282250.920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e366852200016\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eFourth step\u003c/strong\u003e \u003cp\u003eThe multi-objective problem becomes a single-objective problem.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(max {z}_{h} \\left(x\\right)\\)\u003c/span\u003e \u003c/span\u003e (16\u0026thinsp;\u0026minus;\u0026thinsp;3)\u003c/p\u003e \u003cp\u003eSt:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({g}_{i}\\le 0,\\forall i=\\text{1,2},\\dots , m\\)\u003c/span\u003e \u003c/span\u003e (17\u0026thinsp;\u0026minus;\u0026thinsp;3)\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({z}_{j}\\left(x\\right)\\ge {e}_{j},j=\\text{1,2},\\dots ,h-1,h+1,\\dots , k\\)\u003c/span\u003e \u003c/span\u003e (18\u0026thinsp;\u0026minus;\u0026thinsp;3)\u003c/p\u003e \u003cp\u003e \u003cstrong\u003eFifth step\u003c/strong\u003e \u003cp\u003eUsing the minimum and maximum of each problem.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({n}_{j}\\le {z}_{j}\\le {m}_{j}\\)\u003c/span\u003e \u003c/span\u003e (19\u0026thinsp;\u0026minus;\u0026thinsp;3)\u003c/p\u003e \u003cp\u003e \u003cstrong\u003eSixth step\u003c/strong\u003e \u003cp\u003eIn the range of the objective function, different values for are considered, and the problem is solved for each value.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({e}_{j}={n}_{j}+\\left[\\frac{t}{r-1}\\right]\\left({m}_{j}-{n}_{j}\\right), t=\\text{0,1},2,\\dots ,r-1\\)\u003c/span\u003e \u003c/span\u003e (20\u0026thinsp;\u0026minus;\u0026thinsp;3)\u003c/p\u003e \u003cp\u003eAccording to the above method, 10 points are systematically selected. R\u0026thinsp;=\u0026thinsp;10 is considered, and the number of epsilons is obtained according to the mentioned formula.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Presentation of the simulation model\u003c/h2\u003e \u003cp\u003eSimulation enables decision-makers to examine, scrutinize, and assess scenarios that may not be feasible [53]. Engineers, designers, and managers consider simulation an essential tool in today's competitive world. A model must replicate the existing system's reaction to events that fluctuate over time.\u003c/p\u003e \u003cp\u003eDiscrete event simulation is a simulation technique that models the performance of a system as a discrete sequence of events occurring over time. Every occurrence occurs at a precise point in time and signifies a modification in the system's condition. A transition is defined as the process of moving from one event to another, and in a simulation, it is possible to make a direct temporal leap from one event to the following (Robinson \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). The technique in question has undergone significant development since its inception, with its applications expanding to encompass a range of fields such as interactive visual modeling, simulation-based optimization, virtual reality, and simulation in various domains.\u003c/p\u003e \u003cp\u003eSimulation-based optimization refers to integrating simulation models and optimization techniques to determine the optimal amount of input data required to enhance the performance of the simulation model (Nguyen et al. \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). The method described can be understood as a systematic approach to optimizing decision variables in relation to the outputs of a simulation model.\u003c/p\u003e \u003cp\u003eThe simulation model (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) of patient admission in the hospital was created with the help of Arena Rockwell Software version 14. With the help of the simulation model, it is possible to examine the bottlenecks and workstations that cause queue formation in the system. Also, patients' waiting time and hospitalization during admission to discharge and discharge from the hospital are among the most critical outputs from the simulation model.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.5 Model simulation with AERNA software\u003c/h2\u003e \u003cp\u003eAt the beginning of the course, with the help of an input analyzer and the time between patients' arrival, the distribution of their arrival is determined. Upon arrival, patients go to the emergency department, and due to the critical conditions of the spread of the coronavirus, if they need urgent treatment, they are allocated a bed without admission. The rest of the patients are directed to the reception unit and triaged; if there is an empty bed, they are admitted\u003c/p\u003e \u003cp\u003eAt the beginning of entering the hospital departments, for the three departments of orthopedics, psychiatry, and radiotherapy, patients are separated from each other by gender and transferred to their respective departments. Other patients are transferred to different hospital departments according to their conditions.\u003c/p\u003e \u003cp\u003eAfter separating the patients into 27 departments, a decision is made regarding the need for hospitalized people for diagnostic measures. Diagnostic procedures include seven parts of audiometry, electrocardiogram (HeartRate), infectious diseases (Infection), X-ray, ultrasound (Sonography), Spirometry, and CT scan. After leaving the said departments, the patients who need medical care again enter the bed allocation process. Otherwise, the patients are discharged from the hospital.\u003c/p\u003e \u003cp\u003eIf there is no need for diagnostic measures, the bed is empty and cleaned by the relevant official, and the patient is removed from the admission process.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.6 Verification and validation of the simulation model\u003c/h2\u003e \u003cp\u003eAfter presenting the model, it is time to verify and validate the simulation model. According to the coordination of the conceptual model and the current data and the review of the modules used in the model, the correct entry of the parameters, and the logical structure of the model, the validation of the model is confirmed. Three steps are suggested to determine the validity of the model.\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eDesign a model with significant face validity.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eDetermine the validity of the model assumptions.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eCompare the changes of inputs to outputs of the model with the changes of inputs to outputs of the system.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eSince the time distribution between patients entering the hospital was used to enter the data, there is no need for statistical hypothesis tests to confirm the assumptions, and the model's validity is confirmed\u003c/p\u003e \u003c/div\u003e"},{"header":"4 Results","content":"\u003cp\u003eIn this section, the mathematical model and simulation results are analyzed, and optimal scenarios are searched with the help of the OptQuest tool. According to the mathematical model and the assumptions presented in the third chapter, the model is solved, and the results are obtained in this part.\u003c/p\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Mathematical model\u003c/h2\u003e \u003cp\u003eThe mathematical model is initially checked and validated using the model's indices. The 27 hospital departments (w) make up the mathematical model. The model contains patients with triage priorities 1, 2, 3, 4, and 5 (i). In addition, the model's initial periods are considered along with the four seasons of spring, summer, autumn, and winter (t) in 2019.\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e indicates the costs associated with procuring the hospital bed and the upkeep of the hospital bed during the five temporal intervals examined in the model. As a consequence of the monthly inflation, there has been a rise in the budget allocation to enhance hospital capacities. (Costs in millions of Rials, Convert Iranian Rials to US Dollars In April 2019\u0026thinsp;=\u0026thinsp;0.000004839)\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eBed development and costs maintaining cost.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e(\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({B}_{t}\\)\u003c/span\u003e\u003c/span\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;4\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCost\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e7800000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e15000000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e15000000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e15500000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1590000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e(\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{M}}_{\\text{t}}\\)\u003c/span\u003e\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCost\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e150000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e150000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e150000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e170000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e displays patients' hospitalization and patients' waiting times duration during the five time periods of the model. As anticipated during the initial phase of the hospital's response to the critical circumstances surrounding the proliferation of the coronavirus within the nation, there has been a notable increase in the length of patients' hospital stays. During the third period, which corresponds to the apex of the 2019 viral pandemic, there is a notable discrepancy in the length of hospital stays compared to the preceding and subsequent periods. Subsequently, the aggregate duration of waiting time resembles the overall length of hospital stay among patients, with the third period exhibiting the greatest extent.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePatient hospitalization and waiting time.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e(\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({G}_{t}\\)\u003c/span\u003e\u003c/span\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;4\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e236\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e481\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e299\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e816.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e257\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e(\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Q}_{\\text{t}}\\)\u003c/span\u003e\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e14.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e13.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e14.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e60.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e20.67\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e displays the mean duration of patient wait times and the mean duration of hospital admission for patients receiving treatment across the five triage levels (1\u0026ndash;5) during the five time periods examined in the model. During the third period of the COVID-19 pandemic, the waiting time for medical attention notably increased, particularly in the fifth triage category, which encompasses patients with critical conditions, in comparison to previous periods. This phenomenon is observable to a certain degree in upper-level triages during the fourth period. Consistent with expectations, the mean duration of hospitalization was also comparatively lengthier during the third temporal interval compared to the remaining periods. Given that the height of the COVID-19 pandemic occurred during the autumn season of 2019, individuals presenting at hospitals with symptoms resembling those of the virus, such as colds and flu, encountered uncertain triage conditions prior to undergoing COVID-19 scans and tests. As a result, the initial triage category for these patients was often fourth, leading to prolonged hospitalization periods during this timeframe.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMean patient wait time \u0026amp; hospitalization time.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({K}_{it}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;4\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({K}_{1t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0,.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({K}_{2t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({K}_{3t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.86\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({K}_{4t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({K}_{5t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e7.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({F}_{it}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({F}_{1t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e21.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e89.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e11.17\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({F}_{2t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e17.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e19.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e21.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e57.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e17.95\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({F}_{3t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e9.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e24.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e10.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e25.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e9.75\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({F}_{4t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e7.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e15.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e14.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e7.85\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({F}_{5t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.85\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e presents the bed count for departments 1 through 27 of the hospital at the outset of the model planning period. Moreover, the number of beds available in the warehouse at the beginning of the planning period for the hospital departments is as follows.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eInitial bed count \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({(\\text{N}}_{\\text{w}})\\)\u003c/span\u003e\u003c/span\u003e \u0026amp; Number of warehouse bed d\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left({P}_{W}\\right)\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ew\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eN\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eP\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e27\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e48\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e51\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e47\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e39\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e displays the costs, measured in millions of Rials, incurred by the hospital to procure beds for departments 1 through 27 from zero to four. The cost of procuring hospital beds has exhibited an upward trend from the baseline period (t\u0026thinsp;=\u0026thinsp;0) to the fourth due to the concurrent rise in costs for the year.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eBed procuring cost \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left({C}_{wt}\\right)\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ew\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;4\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e120000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e140000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e140000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e145000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e150000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e35500000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e45000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e48000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e50000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e52000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6900000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e70000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e70000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e70000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e80000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e120000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e140000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e140000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e145000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e150000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e120000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e140000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e140000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e145000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e150000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e120000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e140000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e140000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e145000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e150000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e120000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e140000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e140000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e145000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e150000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e35500000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e45000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e48000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e50000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e52000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e35500000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e45000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e48000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e50000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e52000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e15500000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e22000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e25000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e28000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e30000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e120000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e140000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e140000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e145000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e150000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e120000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e140000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e140000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e145000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e150000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e120000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e140000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e140000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e145000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e150000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e35500000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e45000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e48000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e50000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e52000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e40000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e45000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e48000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e50000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e52000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e40000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e45000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e48000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e50000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e52000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e15500000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e22000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e25000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e28000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e30000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e35500000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e45000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e48000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e50000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e52000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e35500000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e45000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e48000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e50000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e52000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e110000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e122000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e128000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e130000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e135000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e120000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e140000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e140000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e145000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e150000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e120000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e140000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e140000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e145000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e150000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e40000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e45000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e48000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e50000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e52000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e35500000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e45000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e48000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e50000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e52000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e35500000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e45000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e48000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e50000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e52000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e35500000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e45000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e48000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e50000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e52000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6900000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e70000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e70000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e70000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e80000000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Result of the model\u003c/h2\u003e \u003cp\u003eBased on the model parameters and the data of hospital departments across various periods, the model was designed and coded in optimization software. The resulting outcomes include the requisite number of beds, the number of beds added and reduced in the department, the quantity of warehouse stock, and the number of beds procured.\u003c/p\u003e \u003cp\u003eThe hospital exhibited a substantial capacity prior to the outbreak of the coronavirus and even implemented a specialized emergency ICU unit. Furthermore, the mathematical modeling failed to account for the severity of the issue. As per the hospital's model, bed shortages have not been encountered. Thus, based on the findings, purchasing a bed appears unnecessary. (Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab9\" class=\"InternalRef\"\u003e9\u003c/span\u003e)\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eOptimal value of the variables of the number of beds.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"16\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c14\" colnum=\"14\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c15\" colnum=\"15\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c16\" colnum=\"16\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c13\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c14\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c15\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c16\"\u003e\u0026nbsp;\u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ew\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X}_{wt}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X}_{wt}^{+}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X}_{wt}^{-}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Y}_{wt}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I}_{wt}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X}_{wt}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X}_{wt}^{+}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X}_{wt}^{-}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Y}_{wt}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I}_{wt}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X}_{wt}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X}_{wt}^{+}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X}_{wt}^{-}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Y}_{wt}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I}_{wt}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab9\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 9\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eOptimal value of the variables of the number of beds.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"16\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c14\" colnum=\"14\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c15\" colnum=\"15\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c16\" colnum=\"16\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c13\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c14\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c15\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c16\"\u003e\u0026nbsp;\u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ew\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X}_{wt}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X}_{wt}^{+}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X}_{wt}^{-}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Y}_{wt}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I}_{wt}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X}_{wt}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X}_{wt}^{+}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X}_{wt}^{-}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Y}_{wt}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I}_{wt}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X}_{wt}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X}_{wt}^{+}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X}_{wt}^{-}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Y}_{wt}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I}_{wt}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e 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align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e 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align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e 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align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e 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\u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e 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align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e 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align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e 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align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e 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align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe model was constructed and operationalized utilizing GAMS optimization software based on the model's parameters and patient triage data from multiple periods. The results obtained for the increased and decreased hospitalization time and the increased and decreased waiting time of the model are as follows. (Table\u0026nbsp;\u003cspan refid=\"Tab10\" class=\"InternalRef\"\u003e10\u003c/span\u003e)\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab10\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 10\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDuration of hospitalization and waiting increased and decreased.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;5\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({G}_{it}^{+}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e28643.460\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({G}_{it}^{-}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({K}_{it}^{+}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2230.800\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({K}_{it}^{-}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({G}_{it}^{+}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e55382.150\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({G}_{it}^{-}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({K}_{it}^{+}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({K}_{it}^{-}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({G}_{it}^{+}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e36304.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({G}_{it}^{-}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({K}_{it}^{+}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2489.360\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({K}_{it}^{-}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({G}_{it}^{+}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e112530.960\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({G}_{it}^{-}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({K}_{it}^{+}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({K}_{it}^{-}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003et\u0026thinsp;=\u0026thinsp;5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({G}_{it}^{+}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e28543.170\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({G}_{it}^{-}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({K}_{it}^{+}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3895.270\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({K}_{it}^{-}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTypically, the hospital experiences an escalation in both hospitalization and waiting times across all temporal epochs. However, based on the model's conditions and the constraints outlined in the problem, this temporal prolongation cannot be ascribed to critical circumstances, as evidenced by the obtained outcomes. This phenomenon may be associated with the admission and hospitalization protocols for patients within the healthcare facility.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Simulation model\u003c/h2\u003e \u003cp\u003eIn April 2019, a simulation of patient admission to discharge within a 30-minute timeframe was simulated at Imam Hussein Hospital in Tehran. A stable influx of corona patients characterized the study period. The hospital comprises a range of specialized units, including 27 CS ICU, Day Care, NICU, Post Cath, Post CCU/Post CSICU, ICU, Emergency ICU, Women's Orthopedics, Men's Orthopedics, Pediatrics, Surgery, Neurosurgery, Eye, Internal Women and Men (General), Women's Radiotherapy, Men's Radiotherapy, Pediatric Psychiatry (ChildrenMental), Women's Psychiatry, Men's Psychiatry, Gynecology and Obstetrics, CCU1, CCU2, Chemotherapy - Under observation, Infectious, Gastroenterology, Neurology, and Neonatal. The allocation of resources, precisely the number of beds, is standardized across all departments.\u003c/p\u003e \u003cp\u003eThe distribution of patient arrivals in all the mentioned departments has been collected and obtained according to the time information of the start and end of the activity recorded in the HIS system of the hospital. In the mentioned system, the possibility of patients withdrawing during their presence in the queue is ignored. In this structure, all patients entering the hospital have been registered under emergency and non-emergency admissions, and patients with previous appointments have been ignored in the model.\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab11\" class=\"InternalRef\"\u003e11\u003c/span\u003e displays the mean and maximum wait times for patients across various departments within the hospital.\u003c/p\u003e \u003cp\u003eAs depicted in Table\u0026nbsp;\u003cspan refid=\"Tab11\" class=\"InternalRef\"\u003e11\u003c/span\u003e, the current critical conditions indicate that the waiting time in departments dedicated to the treatment of patients suspected or confirmed to have contracted the Covid-19 virus, including the ICU, emergency ICU, CT scan examination department, and internal hospital departments, is notably more prolonged than that of other departments. Moreover, specific procedures and facilities, such as the hospital's emergency department and the management and sanitation of hospital beds post-patient discharge, commonly referred to as the length of the patient's hospital stay, have encountered prolonged mean durations.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab11\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 11\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDepartment queue.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDepartment\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAverage\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMaximum Value\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGynecology\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e23.800\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e194.81\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePediatrics\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e41.6263\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e407.06\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpirometry\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24.0269\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e183.82\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCCU1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e7.4212\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e114.65\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCCU2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8.7702\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e117.60\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eChemotherapy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e15.0525\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e162.43\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAudiometry\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6.7550\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e115.31\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePediatric Psychiatry\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8.6691\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e114.47\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCleaning\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e80.7331\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e384.78\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCSICU\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e7.4811\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e123.89\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCT scan\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e14.4681\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e154.00\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDayCare\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5.2058\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e67.3606\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGastroenterology\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.7715\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e61.7327\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEmergencyCare\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.1405\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.1118\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEmptyBed\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.2372\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20.2894\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEye\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5.5320\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e99.14\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInternal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.5359\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20.4407\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWomen's Psychiatry\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e16.8012\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e166.60\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHeartRate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e9.2074\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e105.20\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eICU\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e47.3829\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e253.69\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEmergency ICU\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3315.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6029.36\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInfection\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e16.2372\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e178.36\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInfectious\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e14.3454\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e199.05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMen's Orthopedics\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e11.8581\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e127.79\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMen's Psychiatry\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e32.8649\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e183.35\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNeurology\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.9995\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e108.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNeonatal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e112.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e641.15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNICU\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6.3941\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e66.7530\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePaymenttriage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.8243\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.2264\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePostCath\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.8220\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e25.3473\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePost CCU/Post CSICU\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e9403.79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e17769.28\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMen's Radiotherapy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e159.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e679.80\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWomen's Radiotherapy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10.6852\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e98.7286\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eReception\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.6214\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.6863\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSonography\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.5405\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e89.4667\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSurgery\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e65.0470\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e393.19\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNeurosurgery\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e174.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e856.59\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWomen's Orthopedics\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10.1893\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e104.41\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eX-ray\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e28.4067\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e232.06\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e4.4 Simulation-based optimization\u003c/h2\u003e \u003cp\u003eThis study discusses utilizing the OptQuest tool from the Arena software collection to minimize the model's objective function and determine the optimal number of hospital beds across various departments. The simulation model incorporates the initial objective function to minimize patients' hospitalization and waiting time. The length of hospital stay is determined by the cumulative duration of hospitalization experienced by patients across all 27 departments. The waiting time encompasses the duration of complementary treatment procedures, such as CT scan, bed vacating and re-preparation by staff, admission, triage, and emergency department procedures. The simulation was conducted with a default of 100 repetitions and an efficiency of 0.6534%. The optimal number of hospital beds was derived accordingly. (Table\u0026nbsp;\u003cspan refid=\"Tab12\" class=\"InternalRef\"\u003e12\u003c/span\u003e)\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab12\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 12\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eOptimal number of hospital bed.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ew\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNumber\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e31\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e36\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e48\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e52\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e31\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e38\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e23\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"5 Conclusions and suggestions","content":"\u003cp\u003eThe optimal hospital bed allocation directly improves the provision of medical services and, consequently, improves physical and mental health in society (Emanuel et al. \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Waiting for the patient leads to the acute condition of the disease, increasing mental pressure on the patient and hospital staff, reducing productivity, and increasing costs (Reichert and Jacobs \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). In a situation where the hospital is facing a crisis such as the spread of the coronavirus, the importance of having an efficient treatment system, especially in quickly responding to the needs of the community and controlling hospitalization and waiting time, increases even more (Soroush et al. \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). In addition to reducing costs, this issue also involved reducing the patient's wait time and hospitalization duration. The hospital simulation model has 27 treatment departments and seven diagnostic departments. When the patient enters the hospital, after deciding on the emergency or non-emergency condition of the disease and the level of treatment triage, which is divided into five levels, the patient enters the relevant department separately from the treatment departments. After sorting patients by diagnostic need, a diagnosis is made. Discharged patients empty the bed capacity and clean. Other patients enter the seven sections of diagnostic measures, and after exiting this stage, a decision is made again regarding their most essential needs in terms of benefiting from the medical services or exiting the process. The simulation model used April 2019 hospital bed numbers. Before the Corona pandemic, the hospital had enough beds in different departments to accommodate patients. Although, during the simulated period, the condition of patients suspected of being infected with the coronavirus was stable, and the country had not yet experienced successive coronavirus peaks.\u003c/p\u003e \u003cp\u003eThe mathematical model is designed to minimize hospital waiting times, admissions, bed maintenance, and procurement expenses. The model's parameters include the budget for hospital bed development and purchase, the cost of buying beds by department and period, the cost of maintaining beds, and the hospital warehouse's initial bed inventory. The patient's total waiting time and hospitalization and the average waiting and hospitalization in different periods and triages are considered to shorten the admission process. The mathematical model's limitations include the following:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003ethe initial capacity of hospital beds\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003erelationship between the variable number of beds and the inventory variable in two consecutive periods\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003ebudget limits\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003enumber of inventories in each department at the start of the modeling time horizon\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003etwo-time reduction limits\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThe mathematical model does not consider critical conditions, so the hospital's capacity is always adequate, and There is never a shortage of beds. Furthermore, due to the hospital's emergency ICU department before the spread of the Covid-19 virus, the hospital faced less lack of bed capacity in the first year of the pandemic.\u003c/p\u003e \u003cp\u003eThe optimal value of the objective function was obtained according to the simulation model for 54310000000\u0026nbsp;billion Rials for one month. This value was obtained with a productivity rate of 65% from the present research. According to the mathematical model modeled for one year, this amount in the second objective function was 366440000000\u0026nbsp;billion Rials. The waiting time in the simulation model is 13701.22 minutes, which is the result of one month in the Corona era. This number has been calculated in the mathematical model as 2230.8 minutes in the second period, simultaneously with the simulation model. Since real-world conditions are involved in the simulated model, the increase in waiting time can be estimated.\u003c/p\u003e \u003cp\u003eAccording to the evaluation and analysis of the mathematical and simulation model of the actual conditions of patient admission in the hospital, the future research suggestions are as follows.\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eThe present study only considered one aspect of the factors affecting decision-making regarding costs, waiting time, and hospitalization due to the hospital's lack of cooperation in providing the necessary information. For example, to adjust the hospital's entry process, the objective function of reducing costs related to department conversion was removed from the mathematical modeling. Adding this item to the model requires information about the space needed to develop the hospital's critical parts and physical placement.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eConsidering the work shift and the number of personnel required by different hospital departments is another matter that can be investigated in future research and have a more comprehensive view of the issue of bed allocation.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe limited warehouse space will affect the movement and placement of reduced beds in hospital departments. Considering the limitation of the hospital's inventory space (warehouse) helps to bring the mathematical model closer to the reality of the problem.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe type of hospital beds can be different in the same department and different departments compared to each other. Including the treatment center beds according to the type of use will make the model more complete.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eDespite the difficult access to the information of patients who come to the hospital with a previous appointment, it can add more depth to the mathematical model and increase patients\u0026rsquo; input in the simulation model\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eEthical Approval\u003c/p\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e\n\u003cp\u003eFunding\u003c/p\u003e\n\u003cp\u003eNot applicable.a\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAbd-Alrazaq A, Hassan A, Abuelezz I, et al (2021) Overview of technologies implemented during the first wave of the covid-19 pandemic: Scoping review. 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Critical Care and Resuscitation 22:\u003c/li\u003e\n\u003cli\u003eZeinalnezhad M, Chofreh AG, Goni FA, et al (2020) Simulation and improvement of patients\u0026rsquo; workflow in heart clinics during covid-19 pandemic using timed coloured petri nets. Int J Environ Res Public Health 17:. https://doi.org/10.3390/ijerph17228577\u003c/li\u003e\n\u003cli\u003eZhou W, Wang A, Wang X, et al (2020) Impact of hospital bed shortages on the containment of covid-19 in wuhan. Int J Environ Res Public Health 17:. https://doi.org/10.3390/ijerph17228560\u003c/li\u003e\n\u003cli\u003eZong K, Luo C (2022) Reinforcement learning based framework for COVID-19 resource allocation. Comput Ind Eng 167:107960. https://doi.org/10.1016/J.CIE.2022.107960\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"operations-research-forum","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Operations Research Forum](https://link.springer.com/journal/43069)","snPcode":"43069","submissionUrl":"https://submission.nature.com/new-submission/43069/3","title":"Operations Research Forum","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Hospital beds capacity, COVID-19 pandemic, Simulation-based optimization, Discrete event simulation, Mathematical modeling","lastPublishedDoi":"10.21203/rs.3.rs-4515650/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4515650/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe Covid-19 pandemic was an unforeseen threat to human survival, and the efficiency of the health sector faced a severe challenge. The lack of hospital beds was one of the most critical concerns, and optimizing the capacity of hospital beds was considered one of the key issues.\u003c/p\u003e \u003cp\u003eDue to the ageing of the population and the occasional occurrence of environmental and health crises, the demand for health services and the need for improved planning and administration are increasing daily. Therefore, the optimal allocation of hospital resources, particularly the number of beds, the essential criterion for a medical center\u0026rsquo;s capacity, can substantially reduce patient waiting time and treatment costs and improve services.\u003c/p\u003e \u003cp\u003eAn ideal multi-objective integer programming problem is presented in this study for optimizing the number of hospital beds and reducing costs of the length of stay and length of hospital stay. The problem also considers constraints relating to critical circumstances, given the Corona's prevalence. Moreover, the optimal answer is obtained using a simulation model, mathematical optimization, and a simulation-based optimization approach.\u003c/p\u003e \u003cp\u003eFor this purpose, mathematical modelling was used to minimize patients' waiting time, hospitalizations, and maintenance costs of existing beds and purchasing a new bed. Following that, real-world conditions were introduced into the problem using the simulation model and information acquired from one month of hospitalization of patients during the Coronavirus outbreak at Imam Hussein Hospital in Tehran. After comparing mathematical and simulated models, the OptQuest simulation-based optimization technique revealed the ideal number of hospital beds.\u003c/p\u003e","manuscriptTitle":" A Hybrid Mathematical-Simulation Approach to Hospital Beds Capacity Optimization for COVID-19 Pandemic Conditions","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-06-20 18:50:51","doi":"10.21203/rs.3.rs-4515650/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-07-15T13:49:49+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-07-14T16:12:15+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-07-08T18:36:43+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-07-03T07:12:56+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"49320634396932135365538034347804051197","date":"2024-06-27T08:12:41+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"240046295190543745299986098447895672810","date":"2024-06-16T05:17:25+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"19575758379242243948482241938313971101","date":"2024-06-13T22:21:24+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-06-13T12:45:24+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-06-04T22:24:39+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-06-04T22:24:13+00:00","index":"","fulltext":""},{"type":"submitted","content":"Operations Research Forum","date":"2024-06-02T04:57:25+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"operations-research-forum","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Operations Research Forum](https://link.springer.com/journal/43069)","snPcode":"43069","submissionUrl":"https://submission.nature.com/new-submission/43069/3","title":"Operations Research Forum","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"24822bed-757d-48bf-bb0a-ba56ad2b8704","owner":[],"postedDate":"June 20th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-11-18T19:20:20+00:00","versionOfRecord":{"articleIdentity":"rs-4515650","link":"https://doi.org/10.1007/s43069-024-00389-7","journal":{"identity":"operations-research-forum","isVorOnly":false,"title":"Operations Research Forum"},"publishedOn":"2024-11-14 15:57:22","publishedOnDateReadable":"November 14th, 2024"},"versionCreatedAt":"2024-06-20 18:50:51","video":"","vorDoi":"10.1007/s43069-024-00389-7","vorDoiUrl":"https://doi.org/10.1007/s43069-024-00389-7","workflowStages":[]},"version":"v1","identity":"rs-4515650","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4515650","identity":"rs-4515650","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}