Dynamic ergonomic workload modeling to support workforce-aware scheduling in home health care services

Dynamic ergonomic workload modeling to support workforce-aware scheduling in home health care services | 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 Dynamic ergonomic workload modeling to support workforce-aware scheduling in home health care services Zehra Durak, Elif Danisman, Ozcan Mutlu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9199727/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Background Home health care (HHC) services are expanding rapidly as health systems respond to population ageing, increasing prevalence of chronic conditions, and efforts to shift care delivery from hospitals to community settings. While these services improve accessibility and patient satisfaction, they also introduce significant workforce planning challenges. In particular, nurses providing home-based care often work in highly variable environments that can influence both physical and psychosocial workload. Despite these realities, most existing scheduling approaches in home health care focus primarily on operational efficiency indicators such as travel time, service duration, or cost. As a result, ergonomic and contextual factors that shape nurses’ workload are rarely considered in planning decisions, potentially leading to schedules that are operationally efficient but uneven in terms of staff workload and well-being. Methods This study develops a decision-support framework designed to incorporate ergonomic workload considerations into home health care scheduling. First, nurses’ perceived workload following patient visits is captured through a structured post-task assessment that evaluates multiple categories of stressors encountered during care delivery. These assessments are converted into quantitative workload scores using a fuzzy inference system that accommodates the subjective and linguistic nature of workload perceptions. To account for temporal variability in workload exposure, a multi-state Markov modeling approach is then used to estimate transitions between different workload states across consecutive visits. The resulting workload estimates are incorporated into a goal programming–based scheduling model that simultaneously considers patient demand satisfaction and equitable distribution of workload among nurses. Results Computational experiments were conducted using simulated home care scenarios of varying sizes to explore how the integration of dynamic workload information influences scheduling decisions. The results indicate that incorporating ergonomic workload estimates enables more balanced allocation of tasks across nurses while maintaining acceptable levels of service coverage. By adjusting workload limits and objective weights, decision makers can explicitly manage trade-offs between maximizing the number of completed visits and limiting excessive workload exposure for individual staff members. Conclusions Integrating dynamic ergonomic workload information into scheduling decisions provides a more comprehensive approach to workforce planning in home health care services. The proposed framework demonstrates how operational planning models can incorporate contextual and human-centered workload factors alongside traditional efficiency objectives. Such approaches may help health care organizations design more sustainable service delivery systems that protect workforce well-being while continuing to meet growing patient demand. Health Economics and Outcomes Research home health care dynamic workload modeling ergonomic nurse workload workforce sustainability multi-state Markov model decision support system Figures Figure 1 Figure 2 1. Introduction The rapid expansion of home health care (HHC) services, driven by population aging, increasing prevalence of chronic conditions, and health system cost-containment pressures, has intensified the challenge of balancing growing patient demand with the sustainability of the nursing workforce. As an alternative to traditional hospitalization, HHC improves patient satisfaction and reduces costs by delivering care within patients’ homes (Rodriguez-Verjan et al., 2018 ; Moscato et al., 2021 ). However, the decentralized and heterogeneous nature of home-based care creates operational and workforce-related complexities that differ substantially from institutional settings and therefore require adaptation of planning approaches and workforce management strategies. HHC systems involve interrelated decision problems concerning service design, allocation, and daily routing (Grieco et al., 2021 ). A substantial body of research has focused on the Home Health Care Routing and Scheduling Problem (HHCRSP), primarily aiming to minimize travel time, distance, or operational cost while satisfying patient demand (Gutiérrez and Vidal, 2013 ; Sahin and Matta, 2015 ; Fikar and Hirsch, 2017 ; Di Mascolo et al., 2021 ). Although these models have significantly improved operational efficiency, workload is predominantly conceptualized as a function of service duration and travel time. Consequently, ergonomic and psychosocial conditions that shape nurses’ perceived workload remain insufficiently integrated into scheduling decisions. Recent contributions continue to expand the scope of HHCRSP formulations by incorporating increasingly diverse operational constraints and multi-objective considerations, reflecting the growing complexity of home care planning environments (Masmoudi et al., 2024 ). Beyond these operational considerations, HHC nurses operate in diverse and unpredictable home settings that introduce additional sources of variability. Physical constraints, lack of assistive equipment, transportation demands, and challenging social interactions may increase both physical and mental strain. Moreover, these stressors vary not only across patients but also over time. Changes in patient acuity, household conditions, or nurse–patient familiarity can alter perceived task difficulty from one visit to another. Therefore, workload in HHC cannot be adequately represented through time-based metrics alone. Qualitative evidence has documented that home care professionals are exposed to a wide range of environmental and psychosocial stressors influencing their working conditions (Rydenfält et al., 2023 ). From a broader system perspective, sustaining a stable nursing workforce has been identified as a global priority in health system strengthening efforts (World Health Organization, 2020 ), particularly in the context of persistent workforce shortages and retention challenges. Empirical evidence has consistently shown that high nursing workloads are associated with burnout and job dissatisfaction (Aiken et al., 2002 ), factors that threaten workforce stability and service continuity. When ergonomic variability is not considered in planning processes, uneven workload distribution may contribute to retention risks and undermine the long-term sustainability of HHC services. While stakeholder perspectives in HHC have been widely discussed (Burgess, 2012 ), nurses’ subjective workload perceptions remain underrepresented in operational planning models. Recent health services research further emphasizes that workload regulation and supportive work conditions play a central role in nurse retention and long-term workforce sustainability (Yamamoto et al., 2024 ). Recent research has begun to acknowledge the relevance of ergonomic risk factors in HHC routing and scheduling contexts (Durak & Mutlu, 2024 ). However, existing approaches largely treat workload as a static measure and do not explicitly model how perceived strain may evolve across consecutive visits. The temporal dynamics of ergonomically induced workload—and their integration into daily scheduling decisions—remain insufficiently explored within current modeling frameworks. To address this gap, this study proposes an integrated decision-support framework that models ergonomically derived workload as a dynamic and state-dependent process within HHC scheduling. A structured post-task assessment model is introduced to capture nurses’ perceived ergonomic strain, which is translated into quantitative workload scores through a fuzzy inference approach. To represent temporal changes in workload conditions, a multi-state Markov model is employed to estimate probabilistic transitions between workload states. These predicted workload states are subsequently embedded within a goal programming–based scheduling model to generate balanced care plans that simultaneously address patient demand and anticipated workload exposure. By modeling ergonomically induced workload as a dynamic and temporally evolving variable within operational decision-making, the proposed framework advances HHC planning beyond static workload balancing. By integrating ergonomic variability and temporal workload dynamics into scheduling decisions, the proposed framework extends existing approaches to workforce-aware planning in home health care systems. 2. Methods This study develops an integrated decision-support framework to incorporate ergonomically grounded and temporally evolving workload representations into home health care (HHC) nurse scheduling decisions. Although the Home Health Care Routing and Scheduling Problem (HHCRSP) has been extensively investigated in the operations research literature (Fikar & Hirsch, 2017 ; Cissé et al., 2017 ; Di Mascolo et al., 2021 ), most existing models prioritize operational efficiency measures such as travel time, service duration, overtime, or cost minimization. Workload balancing, when considered, is generally operationalized through simplified proxies such as number of visits, total working time, or travel distance (Alves et al., 2022 ; Bahadori-Chinibelagh et al., 2019 ), and rarely reflects the multidimensional ergonomic exposure experienced by home care nurses. Empirical evidence from occupational health and ergonomics studies indicates that home healthcare professionals are exposed to heterogeneous physical, environmental, postural, and psychosocial stressors that vary across patients and over time (Bien et al., 2020 ; Suarez et al., 2017 ; Rydenfält et al., 2023 ). Unlike institutional healthcare settings, home environments are inherently uncontrolled and context-specific, leading to workload patterns that are perception-dependent and temporally dynamic. However, this temporal variability and subjectivity are largely absent from existing HHCRSP formulations. To address this gap, we conceptualize nurse workload not as a static or deterministic parameter but as a multidimensional and state-dependent process that evolves across consecutive visits. The proposed framework integrates four interrelated components: a structured post-task ergonomic assessment instrument capturing nurse-specific perceptions of predefined stressor categories, a Fuzzy Inference System (FIS) that transforms subjective and heterogeneous exposure indicators into a continuous workload score, a multi-state modeling approach to represent temporal transitions between workload states, and a goal programming–based scheduling model that embeds dynamic workload constraints into daily routing and assignment decisions. The contribution of this study lies in explicitly linking ergonomic perception, temporal workload dynamics, and operational scheduling within a unified modeling structure. By treating workload as an evolving probabilistic process rather than a static constraint, the proposed approach enables scheduling decisions to anticipate cumulative strain and support workforce sustainability alongside patient demand satisfaction. The overall structure of the proposed framework is illustrated in Fig. 1 . The methodological components of the framework are detailed in the following subsections. 2.1. Ergonomic Workload Conceptualization in Home Health Care Workload balancing has increasingly been recognized as an important objective within the Home Health Care Routing and Scheduling Problem (HHCRSP). According to the comprehensive classification proposed by Di Mascolo et al. ( 2021 ), objectives in HHCRSP can broadly be grouped into cost-related criteria and preference-related criteria, where balanced workload is considered a staff-oriented preference. However, despite its acknowledged importance, workload balancing remains relatively underrepresented in the literature and is frequently operationalized through simplified quantitative proxies such as total working time, number of visits, travel duration, or overtime (Alves et al., 2022 ; Bahadori-Chinibelagh et al., 2019 ). Some studies attempt to combine multiple operational components when balancing workload. For instance, Hertz and Lahrichi ( 2009 ) simultaneously consider visit load, transaction load, and travel load. Nevertheless, these approaches remain primarily operational in nature and do not explicitly incorporate ergonomic exposure or perception-based strain factors into the workload construct. Empirical research in occupational health indicates that home healthcare nurses are exposed to a diverse set of physical, environmental, postural, and psychosocial stressors (Bien et al., 2020 ; Suarez et al., 2017 ). Unlike hospital environments, home care settings are highly heterogeneous and largely uncontrollable. Nurses may encounter variations in space constraints, temperature, ventilation, lighting conditions, aggressive pets, unsafe hygiene environments, and challenging interactions with patients or relatives. Furthermore, workload perception may vary not only across different patients but also across repeated visits to the same patient due to changes in environmental conditions, patient acuity, or relational dynamics (Rydenfält et al., 2023 ). Despite this multidimensional and perception-dependent structure, existing HHCRSP models largely treat workload as static, deterministic, and nurse-independent. Such simplifications limit the ability of scheduling models to reflect the true ergonomic burden experienced in practice. In this study, workload is conceptualized as a multidimensional construct arising from four categories of stressors: (i) physical job demand, (ii) environmental stressors, (iii) body motion and postural strain, and (iv) mental job demand. These categories are derived from ergonomic literature and adapted to the home care context. The specific ergonomic stressors considered under each category are presented in Table 1 . Table 1 The ergonomic stressors Physical job demand stressors (S1) P1: activities such as lifting or turning the patient P2: carrying service-specific equipment/materials Environmental stressors (S2) E1: humidity and temperature E2: noise E3: lighting conditions E4: pet behavior E5: chemical risks E6: poor air quality (insufficient ventilation, bad smells, cigarette smoke, etc.) E7: unhygienic conditions Body motion and postural stressors (S3) B1: activities such as walking for a long time, using stairs, etc. B2: activities such as bending, squatting, standing, etc. Mental job demand stressors (S4) M1: making critical decisions M2: activities such as thinking, remembering, and searching M3: informing the patient and/or the patient's relatives M4: difficult patient behaviors M5: negative behaviors of the patient's relatives M6: adverse traffic conditions Rather than relying on physiological measurements—which are impractical in mobile care settings—we adopt a structured post-task subjective assessment approach to capture nurse-specific workload perception following each visit. This conceptualization forms the foundation for the quantitative modeling components described in the subsequent sections. Durak and Mutlu ( 2024 ) proposed an ergonomic workload quantification framework in which post-task assessments were transformed into analytical workload scores and directly incorporated into a mathematical scheduling model. In that study, the most recently observed workload value was assumed to represent the expected workload in subsequent planning periods. While this approach enabled workload-aware scheduling, it did not explicitly model stochastic transitions between workload states over time. The present study advances this framework by introducing a multi-state modeling approach to capture temporal workload evolution and by embedding predicted workload states within a goal programming–based scheduling structure. 2.2. Fuzzy-Based Workload Quantification The multidimensional and perception-dependent structure of ergonomic workload in home healthcare requires a modeling approach capable of handling linguistic evaluations and subjective judgments. Since nurses evaluate stressors in qualitative terms such as “low,” “moderate,” or “high,” deterministic aggregation methods are insufficient to capture the inherent ambiguity of perception-based assessments. Fuzzy set theory, introduced by Zadeh ( 1965 ), provides a suitable mathematical framework for modeling imprecise and linguistically expressed information in complex human-centered systems. Fuzzy-based workload assessment has been applied in various ergonomic contexts. (Chen et al., 1994 ; Liou and Wang, 1994 ; Jung, 1998 ; Jung, 2000 ) developed fuzzy approaches to integrate multiple stress factors into composite workload indices. Jung and Jung ( 2001 ) further proposed an overall workload assessment technique incorporating multiple ergonomic dimensions. While fuzzy logic has also been used in HHCRSP studies to model uncertainties related to demand, travel time, or service duration (Shi et al., 2017 ; Tohidifard et al., 2018 ; Fathollahi-Fard et al., 2020 ), its application for modeling ergonomic workload perception within scheduling decisions remains limited. In this study, a Fuzzy Inference System (FIS) is developed to transform post-task questionnaire responses into a continuous workload score ranging between 0 and 100. Following each patient visit, nurses evaluate predefined ergonomic stressors using a structured questionnaire. Each stressor is rated using linguistic levels, which are converted into numerical scores and aggregated within four stressor categories defined in Section 2.1. During the fuzzification stage, aggregated stressor scores are mapped onto linguistic terms using triangular membership functions. The inference mechanism is based on the Mamdani approach (Mamdani and Assilian, 1975 ), where a set of expert-defined IF–THEN rules capture the combined effects of physical, environmental, postural, and mental stressors on overall workload. The complete rule base, developed in consultation with domain experts in home health care operations, is provided in Appendix A. In the final stage, the defuzzification process employs the center-of-gravity method to generate a crisp workload score. The overall structure of the developed FIS is presented in Fig. 2 . The resulting output represents the observed workload level associated with a specific nurse–patient visit. These observed workload scores serve as the quantitative basis for modeling temporal workload transitions in the subsequent subsection. 2.3. Multi-State Modeling of Temporal Workload Dynamics While the FIS provides a quantified workload score for each completed nurse–patient visit, operational scheduling decisions require an estimation of workload levels expected in future visits. In home healthcare settings, workload perception is inherently dynamic. Environmental conditions, patient acuity, relational factors, and contextual stressors may evolve over time, leading to variability in perceived strain across consecutive visits to the same patient. To represent this temporal variability, a multi-state modeling approach based on the Markov assumption is adopted. Multi-state models describe systems that evolve through a finite number of discrete states, where the probability of transitioning to a future state depends on the current state (Jackson, 2011 ). Such models have been widely applied in healthcare research to represent progressive or fluctuating processes under uncertainty (Sato and Zouain, 2010 ; Uhry et al., 2010 ; Xiong et al., 2021 ). In contrast to deterministic forecasting methods, multi-state models provide a probabilistic structure for capturing transitions between levels of a variable over time. In the proposed framework, continuous workload scores obtained from the FIS are categorized into five discrete workload states: very low (0–19), low (20–39), normal (40–59), high (60–79), and very high (80–100). For each nurse–patient pair, historical workload observations are used to estimate transition probabilities between these states. The resulting transition probability matrix defines the likelihood of moving from one workload state to another in the subsequent visit. Based on the estimated transition probabilities, the most probable next workload state is identified, and the midpoint of the corresponding workload interval is used as the expected workload value for the next planning period. In this manner, future workload is treated as a probabilistic state-dependent variable rather than a fixed continuation of the most recent observation. Durak and Mutlu ( 2024 ) incorporated observed workload values directly into a scheduling model by assuming that the most recently observed workload level represents the expected workload in subsequent planning periods. While this assumption enabled workload-aware scheduling, it did not explicitly model probabilistic transitions between workload states. The present study extends this approach by explicitly incorporating state-transition dynamics, thereby allowing the scheduling model to account for potential workload escalation or reduction across consecutive visits. By modeling workload evolution as a probabilistic state-transition process, the proposed framework captures temporal uncertainty and cumulative strain patterns that are otherwise neglected in static formulations. The estimated workload values derived from the multi-state model are subsequently embedded within the goal programming scheduling structure described in the next subsection. 2.4. Goal Programming Scheduling Model Home Health Care Routing and Scheduling Problems involve multiple and often competing objectives, including service efficiency and equitable workload distribution. In addition to standard operational constraints such as time windows, skill compatibility, and working time limits, the proposed model incorporates dynamically estimated ergonomic workload into daily assignment and routing decisions. To balance these objectives, a weighted goal programming (GP) formulation is employed. This approach enables the simultaneous regulation of daily workload exposure and fulfillment of patient demand through adjustable priority weights. The scheduling problem is defined for a set of nurses with heterogeneous skill levels who depart from the HHC center, perform their assigned visits within an eight-hour shift, and return to the center without overtime. Each nurse is required to take a one-hour lunch break within a predefined time interval, and this break may include travel time. Time windows are treated as strict constraints: early arrivals result in waiting, whereas late arrivals are not permitted. Each patient can be visited at most once, and nurse–patient skill compatibility must be satisfied. Service times are deterministic and known in advance, and travel times are assumed to be proportional to distances. The number of nurses is fixed, and no explicit patient or nurse preference structures are considered. Workload values may vary across nurse–patient pairs, reflecting the ergonomic variability captured through the proposed assessment and dynamic workload modeling framework. Let \(\:{x}_{i,j,s}\:\) denote the routing decision variable indicating whether nurse s travels from node i to node j . Arrival time and waiting time variables are defined to ensure time feasibility. The workload parameter \(\:{wl}_{i,s}\:\) represents the dynamically estimated workload associated with nurse s serving patient i , as derived from the multi-state modeling framework described in Section 2.3. The weighted goal programming objective function minimizes the normalized deviations associated with workload regulation and patient coverage: $$\:{Min}{w}_{1}\left(\frac{\sum\:_{s=1}^{m}{dwl}_{s}^{+}}{{f}_{1}}\right)+{w}_{2}\left(\frac{{drv}^{-}}{{f}_{2}}\right)$$ Workload regulation is enforced through a goal constraint linking the total assigned workload of each nurse with the predetermined maximum daily workload threshold Max_load. Additional constraints ensure routing flow conservation, departure and return to the HHC center, lunch break allocation within the specified interval, time window compliance through Big-M propagation logic, maximum daily working time (540 minutes), and appropriate binary and non-negativity conditions. The complete mathematical formulation, including all sets, indices, parameters, decision variables, and constraints, is presented in Appendix B. The routing structure remains consistent with standard HHCRSP formulations; the contribution of the proposed model lies in embedding dynamically estimated workload parameters within the goal programming framework to enable workload-aware scheduling decisions without altering the fundamental routing architecture. 3. Computational results and discussion This section evaluates the operational implications of integrating dynamically estimated ergonomic workload into home health care scheduling. The computational experiments are designed to analyze how the proposed framework manages trade-offs between workload regulation and patient demand satisfaction under varying workload limits and policy weight configurations. The results illustrate how dynamic workload modeling influences assignment decisions compared to purely time-based planning approaches. 3.1. Experimental Design Due to the absence of standardized benchmark datasets in the HHCRSP literature, stemming from variations in modeling assumptions and objectives, problem-specific test instances were generated following established practices in the field (Di Mascolo et al., 2021 ). Three problem sizes were considered: 20 patients with 3 nurses (20×3), 25 patients with 4 nurses (25×4), and 30 patients with 5 nurses (30×5). The smallest instance is presented in Table 2 to illustrate the structure of the data. Patient coordinates were randomly generated within the range [0,100], and the HHC center was positioned at (50,50). Distances were computed using Euclidean metrics, assuming proportionality between travel distance and travel time. Service times were generated between 1 and 30 minutes. The planning horizon spans 540 minutes (8:00 AM–5:00 PM), and patient time windows were defined within this interval. A mandatory one-hour lunch break was scheduled within [180,360] minutes. Skill compatibility between nurses and patients was represented using binary parameters. Estimated workload values for the next visit were obtained by processing simulated post-task questionnaire data through the FIS and subsequently applying the developed multi-state modeling framework. All instances were solved using CPLEX 12.2.0.0 within the GAMS 23.5.1 environment. 3.2. Results and Policy Trade-Off Analysis Table 3 presents computational results under different maximum workload thresholds (100, 150, and 200 units) and varying objective weight combinations. For each problem size, multiple configurations of workload weight \(\:{w}_{1}\) and demand weight \(\:{w}_{2}\) were examined to analyze trade-offs between ergonomic workload regulation and service coverage. The final two columns of Table 3 report deviations from the workload and demand targets. These deviations quantify the compromise between limiting nurse workload exposure and maximizing the number of completed visits. For example, in the 20×3 instance with a maximum workload limit of 100 units and weights \(\:{w}_{1}\:\) = 0.3 and \(\:{w}_{2}\) = 0.7, the model results in a positive workload deviation of 20 units and 6 unmet patient visits. As the allowable workload threshold increases (e.g., to 150 or 200 units), workload deviations decrease and demand satisfaction improves. Across all tested scenarios, larger instances (e.g., 30×5) exhibit greater flexibility in balancing objectives. Increased staffing capacity allows the system to better absorb workload variability while maintaining higher service coverage levels. These results highlight the sensitivity of scheduling outcomes to both workload thresholds and objective weight configurations. 3.3. Managerial Implications for Workforce Sustainability The computational findings demonstrate that incorporating dynamic ergonomic workload into scheduling decisions provides a structured mechanism for managing workforce-related trade-offs. Rather than implicitly prioritizing full demand coverage at the expense of nurse exposure, the proposed framework allows decision makers to explicitly regulate acceptable workload levels. By adjusting the workload threshold (Max_load) and objective weights, managers can determine whether short-term service maximization or long-term workforce protection should be prioritized. Under stricter workload limits, some reduction in service coverage may occur; however, this reduction prevents systematic overexposure of specific nurses to excessive strain. From a sustainability perspective, this flexibility is critical. Integrating dynamically estimated workload values enables more balanced task allocation over time and may support staff retention while mitigating burnout risks in home health care systems. The proposed framework thus functions not only as a routing optimization tool but also as a workforce-aware decision-support mechanism that aligns operational efficiency with long-term workforce stability. Table 2 The details of the instance with 3 nurses and 20 patients Patient No Coordinates of patient homes Service time (min.) Time window (min.) Possession of the necessary skills Estimated workload value for the next visit X coordinate Y coordinate Earliest Latest Nurse 1 Nurse 2 Nurse 3 Nurse 1 Nurse 2 Nurse 3 1 21 19 20 0 540 1 1 1 10 10 30 2 83 30 21 0 540 1 1 1 70 50 70 3 19 45 23 0 360 1 1 1 30 50 50 4 43 20 22 120 540 1 1 1 50 90 50 5 27 71 30 0 540 1 0 1 30 - 30 6 21 82 28 0 540 1 1 1 70 90 50 7 53 39 23 0 540 1 1 1 10 50 30 8 89 71 28 0 540 1 1 1 90 90 50 9 77 32 24 0 540 1 1 1 90 50 90 10 94 30 29 0 540 1 1 1 90 10 50 11 84 19 23 0 540 1 1 1 50 30 30 12 89 21 15 0 540 1 1 1 70 70 50 13 9 83 24 0 540 1 1 1 30 70 10 14 98 37 26 0 540 1 1 0 50 50 - 15 21 20 24 0 540 1 1 1 90 10 50 16 19 11 16 0 540 1 1 1 90 50 70 17 37 89 30 0 540 0 1 1 - 90 30 18 23 41 25 0 540 1 1 1 30 70 50 19 24 86 19 0 540 1 1 1 90 50 10 20 88 38 20 0 540 1 1 1 90 10 10 Table 3 Computational results Problem size Max_load w 1 w 2 Z f 1 f 2 \(\:\sum\:_{s=1}^{m}{dwl}_{s}^{+}\) \(\:{drv}^{-}:\) 20x3 100 0.3 0.7 0.23 300 20 20 6 0.4 0.6 0.207 300 20 20 6 0.5 0.5 0.175 300 20 0 7 0.6 0.4 0.14 300 20 0 7 0.7 0.3 0.105 300 20 0 7 150 0.3 0.7 0.113 450 20 170 0 0.4 0.6 0.108 450 20 20 3 0.5 0.5 0.097 450 20 20 3 0.6 0.4 0.08 450 20 0 4 0.7 0.3 0.06 450 20 0 4 200 0.3 0.7 0.01 600 20 20 0 0.4 0.6 0.013 600 20 20 0 0.5 0.5 0.017 600 20 20 0 0.6 0.4 0.02 600 20 20 0 0.7 0.3 0.015 600 20 0 1 25x4 100 0.3 0.7 0.091 400 25 10 3 0.4 0.6 0.082 400 25 10 3 0.5 0.5 0.072 400 25 10 3 0.6 0.4 0.063 400 25 10 3 0.7 0.3 0.048 400 25 0 4 150 0.3 0.7 0.005 600 25 10 0 0.4 0.6 0.007 600 25 10 0 0.5 0.5 0.008 600 25 10 0 0.6 0.4 0.01 600 25 10 0 0.7 0.3 0.012 600 25 10 0 200 0.3 0.7 0.004 800 25 10 0 0.4 0.6 0 800 25 0 0 0.5 0.5 0 800 25 0 0 0.6 0.4 0 800 25 0 0 0.7 0.3 0 800 25 0 0 30x5 100 0.3 0.7 0.071 500 30 40 2 0.4 0.6 0.068 500 30 10 3 0.5 0.5 0.060 500 30 10 3 0.6 0.4 0.052 500 30 10 3 0.7 0.3 0.040 500 30 0 4 150 0.3 0.7 0.004 750 30 10 0 0.4 0.6 0.01 750 30 20 0 0.5 0.5 0.013 750 30 20 0 0.6 0.4 0.013 750 30 0 1 0.7 0.3 0.01 750 30 0 1 200 0.3 0.7 0 1000 30 0 0 0.4 0.6 0.02 1000 30 0 1 0.5 0.5 0 1000 30 0 0 0.6 0.4 0 1000 30 0 0 0.7 0.3 0.01 1000 30 0 1 4. Conclusion Home health care (HHC) has emerged as a rapidly expanding alternative to conventional hospitalization, increasing the operational complexity of workforce planning in decentralized care environments. Given the physically and psychosocially demanding conditions faced by HHC nurses, incorporating ergonomic considerations into scheduling decisions is essential for sustaining workforce stability and service quality. This study proposed an integrated decision-support framework that models and embeds dynamic ergonomic workload into home health care routing and scheduling. Unlike conventional HHCRSP formulations that approximate workload using time-based proxies, the proposed approach quantifies perceived ergonomic strain through a structured post-task assessment and a fuzzy inference system. Temporal variability in workload is subsequently modeled through a multi-state framework, enabling the estimation of future workload exposure for each nurse–patient pair. These dynamically estimated workload values are then incorporated into a goal programming–based scheduling model to generate balanced and policy-sensitive work plans. The computational results demonstrate that integrating dynamic workload estimates alters scheduling trade-offs between service coverage and workload regulation. By adjusting workload thresholds and objective weights, decision makers can explicitly manage the balance between short-term demand satisfaction and long-term workforce protection. This structured flexibility supports more sustainable allocation policies and reduces the risk of systematic nurse overexposure. From a managerial perspective, the proposed framework extends traditional efficiency-driven routing models toward workforce-aware planning. Overall, the study illustrates how ergonomic workload dynamics can be incorporated into home health care scheduling to support more workforce-aware planning approaches. 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Einstein (São Paulo) 8:376–379 Shi Y, Boudouh T, Grunder O (2017) A hybrid genetic algorithm for a home health care routing problem with time window and fuzzy demand. Expert Syst Appl 72:160–176 Suarez R, Agbonifo N, Hittle B, Davis K, Freeman A (2017) Frequency and risk of occupational health and safety hazards for home healthcare workers. Home Health Care Manage Pract 29(4):207–215 Tohidifard M, Tavakkoli-Moghaddam R, Navazi F, Partovi M (2018) A multi-depot home care routing problem with time windows and fuzzy demands solving by particle swarm optimization and genetic algorithm. IFAC-PapersOnLine 51(11):358–363 Uhry Z, Hédelin G, Colonna M, Asselain B, Arveux P, Rogel A, Duffy SW (2010) Multi-state Markov models in cancer screening evaluation: a brief review and case study. Stat Methods Med Res 19(5):463–486 World Health Organization (2020) State of the world's nursing 2020: Investing in education, jobs and leadership. World Health Organization Xiong J, Fang Q, Chen J, Li Y, Li H, Li W, Zheng X (2021) States transitions inference of postpartum depression based on multi-state Markov model. Int J Environ Res Public Health 18(14):7449 Yamamoto K, Nasu K, Nakayoshi Y, Takase M (2024) Sustaining the nursing workforce-exploring enabling and motivating factors for the retention of returning nurses: a qualitative descriptive design. BMC Nurs 23(1):248 Zadeh LA (1965) Fuzzy sets Inform control 8(3):338–353 Additional Declarations The authors declare no competing interests. Supplementary Files supplementary.docx Cite Share Download PDF Status: Posted Version 1 posted 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-9199727","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":610632579,"identity":"b096024e-cc41-4d86-aa26-a55432c4742a","order_by":0,"name":"Zehra Durak","email":"","orcid":"","institution":"pamukkale university","correspondingAuthor":false,"prefix":"","firstName":"Zehra","middleName":"","lastName":"Durak","suffix":""},{"id":610632580,"identity":"ccf1871c-c71d-4217-b0dd-491abaf9f4b2","order_by":1,"name":"Elif Danisman","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABCElEQVRIiWNgGAWjYDACdsaGDwxsDCAEBBUSjA1ASgKvFmbGxhkILWfgWgzwaGFgnAFVz8DA2MZAWAs/M3NjA0OZXR4f/+nEz4XzLGQ3HGA+eJuH4U8+Li2SzYxALeeSi9kkcjdLz9wmYbzhAFuyNQ+DgWUDDi0GhxnbHzC2MSe2SfBukObdJpG44QCPmTRQC06X2R8G2sLYVp/Yxn9282/eOSAt/N/wajFgBms5nNjGkLtNmrcBbAsbXi0SIFsSzh0HOix3mzXPMQnjmYfZjC3nGBjj1MLf3v6w4UNZdeL8/rObb/PU1Mn2HW9+eONNhRyeiAGCBBQeM9jBeDWMglEwCkbBKCAAAF27TxpT1rAIAAAAAElFTkSuQmCC","orcid":"","institution":"Izmir Democracy University","correspondingAuthor":true,"prefix":"","firstName":"Elif","middleName":"","lastName":"Danisman","suffix":""},{"id":610632581,"identity":"efcd0c7f-05f5-4247-aabd-efcd19730b18","order_by":2,"name":"Ozcan Mutlu","email":"","orcid":"","institution":"pamukkale university","correspondingAuthor":false,"prefix":"","firstName":"Ozcan","middleName":"","lastName":"Mutlu","suffix":""}],"badges":[],"createdAt":"2026-03-23 11:17:18","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9199727/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9199727/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105310912,"identity":"4d57ec3a-df99-4e03-87e9-f40a053d0888","added_by":"auto","created_at":"2026-03-24 15:13:01","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":119311,"visible":true,"origin":"","legend":"\u003cp\u003eConceptual architecture of the proposed workload-aware scheduling framework\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-9199727/v1/baa17c93ceca77de0dfff334.png"},{"id":105310825,"identity":"cbf94d4b-f359-41f0-9b61-b32ebd1bd0d2","added_by":"auto","created_at":"2026-03-24 15:12:37","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":41712,"visible":true,"origin":"","legend":"\u003cp\u003eStructure of the proposed fuzzy inference system\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-9199727/v1/c0469f5d5d404dfc192b2263.png"},{"id":105310948,"identity":"f9b17d81-5d19-4925-aac9-fd344076ef02","added_by":"auto","created_at":"2026-03-24 15:13:10","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1207426,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9199727/v1/2df5cd20-6384-470f-9ab1-3dfc316df2b3.pdf"},{"id":105310816,"identity":"96d2c86c-7241-49f5-82a8-2c0989250eb8","added_by":"auto","created_at":"2026-03-24 15:12:32","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":19972,"visible":true,"origin":"","legend":"","description":"","filename":"supplementary.docx","url":"https://assets-eu.researchsquare.com/files/rs-9199727/v1/c8ad73e0c0d6a4a5c6b08749.docx"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eDynamic ergonomic workload modeling to support workforce-aware scheduling in home health care services\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe rapid expansion of home health care (HHC) services, driven by population aging, increasing prevalence of chronic conditions, and health system cost-containment pressures, has intensified the challenge of balancing growing patient demand with the sustainability of the nursing workforce. As an alternative to traditional hospitalization, HHC improves patient satisfaction and reduces costs by delivering care within patients\u0026rsquo; homes (Rodriguez-Verjan et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Moscato et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). However, the decentralized and heterogeneous nature of home-based care creates operational and workforce-related complexities that differ substantially from institutional settings and therefore require adaptation of planning approaches and workforce management strategies.\u003c/p\u003e \u003cp\u003eHHC systems involve interrelated decision problems concerning service design, allocation, and daily routing (Grieco et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). A substantial body of research has focused on the Home Health Care Routing and Scheduling Problem (HHCRSP), primarily aiming to minimize travel time, distance, or operational cost while satisfying patient demand (Guti\u0026eacute;rrez and Vidal, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Sahin and Matta, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Fikar and Hirsch, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Di Mascolo et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Although these models have significantly improved operational efficiency, workload is predominantly conceptualized as a function of service duration and travel time. Consequently, ergonomic and psychosocial conditions that shape nurses\u0026rsquo; perceived workload remain insufficiently integrated into scheduling decisions. Recent contributions continue to expand the scope of HHCRSP formulations by incorporating increasingly diverse operational constraints and multi-objective considerations, reflecting the growing complexity of home care planning environments (Masmoudi et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eBeyond these operational considerations, HHC nurses operate in diverse and unpredictable home settings that introduce additional sources of variability. Physical constraints, lack of assistive equipment, transportation demands, and challenging social interactions may increase both physical and mental strain. Moreover, these stressors vary not only across patients but also over time. Changes in patient acuity, household conditions, or nurse\u0026ndash;patient familiarity can alter perceived task difficulty from one visit to another. Therefore, workload in HHC cannot be adequately represented through time-based metrics alone. Qualitative evidence has documented that home care professionals are exposed to a wide range of environmental and psychosocial stressors influencing their working conditions (Rydenf\u0026auml;lt et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eFrom a broader system perspective, sustaining a stable nursing workforce has been identified as a global priority in health system strengthening efforts (World Health Organization, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), particularly in the context of persistent workforce shortages and retention challenges. Empirical evidence has consistently shown that high nursing workloads are associated with burnout and job dissatisfaction (Aiken et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2002\u003c/span\u003e), factors that threaten workforce stability and service continuity. When ergonomic variability is not considered in planning processes, uneven workload distribution may contribute to retention risks and undermine the long-term sustainability of HHC services. While stakeholder perspectives in HHC have been widely discussed (Burgess, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2012\u003c/span\u003e), nurses\u0026rsquo; subjective workload perceptions remain underrepresented in operational planning models. Recent health services research further emphasizes that workload regulation and supportive work conditions play a central role in nurse retention and long-term workforce sustainability (Yamamoto et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eRecent research has begun to acknowledge the relevance of ergonomic risk factors in HHC routing and scheduling contexts (Durak \u0026amp; Mutlu, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). However, existing approaches largely treat workload as a static measure and do not explicitly model how perceived strain may evolve across consecutive visits. The temporal dynamics of ergonomically induced workload\u0026mdash;and their integration into daily scheduling decisions\u0026mdash;remain insufficiently explored within current modeling frameworks.\u003c/p\u003e \u003cp\u003eTo address this gap, this study proposes an integrated decision-support framework that models ergonomically derived workload as a dynamic and state-dependent process within HHC scheduling. A structured post-task assessment model is introduced to capture nurses\u0026rsquo; perceived ergonomic strain, which is translated into quantitative workload scores through a fuzzy inference approach. To represent temporal changes in workload conditions, a multi-state Markov model is employed to estimate probabilistic transitions between workload states. These predicted workload states are subsequently embedded within a goal programming\u0026ndash;based scheduling model to generate balanced care plans that simultaneously address patient demand and anticipated workload exposure.\u003c/p\u003e \u003cp\u003eBy modeling ergonomically induced workload as a dynamic and temporally evolving variable within operational decision-making, the proposed framework advances HHC planning beyond static workload balancing. By integrating ergonomic variability and temporal workload dynamics into scheduling decisions, the proposed framework extends existing approaches to workforce-aware planning in home health care systems.\u003c/p\u003e"},{"header":"2. Methods","content":"\u003cp\u003eThis study develops an integrated decision-support framework to incorporate ergonomically grounded and temporally evolving workload representations into home health care (HHC) nurse scheduling decisions. Although the Home Health Care Routing and Scheduling Problem (HHCRSP) has been extensively investigated in the operations research literature (Fikar \u0026amp; Hirsch, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Ciss\u0026eacute; et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Di Mascolo et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), most existing models prioritize operational efficiency measures such as travel time, service duration, overtime, or cost minimization. Workload balancing, when considered, is generally operationalized through simplified proxies such as number of visits, total working time, or travel distance (Alves et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Bahadori-Chinibelagh et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), and rarely reflects the multidimensional ergonomic exposure experienced by home care nurses.\u003c/p\u003e \u003cp\u003eEmpirical evidence from occupational health and ergonomics studies indicates that home healthcare professionals are exposed to heterogeneous physical, environmental, postural, and psychosocial stressors that vary across patients and over time (Bien et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Suarez et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Rydenf\u0026auml;lt et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Unlike institutional healthcare settings, home environments are inherently uncontrolled and context-specific, leading to workload patterns that are perception-dependent and temporally dynamic. However, this temporal variability and subjectivity are largely absent from existing HHCRSP formulations.\u003c/p\u003e \u003cp\u003eTo address this gap, we conceptualize nurse workload not as a static or deterministic parameter but as a multidimensional and state-dependent process that evolves across consecutive visits. The proposed framework integrates four interrelated components:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003ea structured post-task ergonomic assessment instrument capturing nurse-specific perceptions of predefined stressor categories,\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003ea Fuzzy Inference System (FIS) that transforms subjective and heterogeneous exposure indicators into a continuous workload score,\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003ea multi-state modeling approach to represent temporal transitions between workload states, and\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003ea goal programming\u0026ndash;based scheduling model that embeds dynamic workload constraints into daily routing and assignment decisions.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eThe contribution of this study lies in explicitly linking ergonomic perception, temporal workload dynamics, and operational scheduling within a unified modeling structure. By treating workload as an evolving probabilistic process rather than a static constraint, the proposed approach enables scheduling decisions to anticipate cumulative strain and support workforce sustainability alongside patient demand satisfaction. The overall structure of the proposed framework is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe methodological components of the framework are detailed in the following subsections.\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Ergonomic Workload Conceptualization in Home Health Care\u003c/h2\u003e \u003cp\u003eWorkload balancing has increasingly been recognized as an important objective within the Home Health Care Routing and Scheduling Problem (HHCRSP). According to the comprehensive classification proposed by Di Mascolo et al. (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), objectives in HHCRSP can broadly be grouped into cost-related criteria and preference-related criteria, where balanced workload is considered a staff-oriented preference. However, despite its acknowledged importance, workload balancing remains relatively underrepresented in the literature and is frequently operationalized through simplified quantitative proxies such as total working time, number of visits, travel duration, or overtime (Alves et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Bahadori-Chinibelagh et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eSome studies attempt to combine multiple operational components when balancing workload. For instance, Hertz and Lahrichi (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2009\u003c/span\u003e) simultaneously consider visit load, transaction load, and travel load. Nevertheless, these approaches remain primarily operational in nature and do not explicitly incorporate ergonomic exposure or perception-based strain factors into the workload construct.\u003c/p\u003e \u003cp\u003eEmpirical research in occupational health indicates that home healthcare nurses are exposed to a diverse set of physical, environmental, postural, and psychosocial stressors (Bien et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Suarez et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Unlike hospital environments, home care settings are highly heterogeneous and largely uncontrollable. Nurses may encounter variations in space constraints, temperature, ventilation, lighting conditions, aggressive pets, unsafe hygiene environments, and challenging interactions with patients or relatives. Furthermore, workload perception may vary not only across different patients but also across repeated visits to the same patient due to changes in environmental conditions, patient acuity, or relational dynamics (Rydenf\u0026auml;lt et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eDespite this multidimensional and perception-dependent structure, existing HHCRSP models largely treat workload as static, deterministic, and nurse-independent. Such simplifications limit the ability of scheduling models to reflect the true ergonomic burden experienced in practice.\u003c/p\u003e \u003cp\u003eIn this study, workload is conceptualized as a multidimensional construct arising from four categories of stressors: (i) physical job demand, (ii) environmental stressors, (iii) body motion and postural strain, and (iv) mental job demand. These categories are derived from ergonomic literature and adapted to the home care context. The specific ergonomic stressors considered under each category are presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\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\u003eThe ergonomic stressors\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=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePhysical job demand stressors (S1)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eP1: activities such as lifting or turning the patient\u003c/p\u003e \u003cp\u003eP2: carrying service-specific equipment/materials\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEnvironmental stressors (S2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eE1: humidity and temperature\u003c/p\u003e \u003cp\u003eE2: noise\u003c/p\u003e \u003cp\u003eE3: lighting conditions\u003c/p\u003e \u003cp\u003eE4: pet behavior\u003c/p\u003e \u003cp\u003eE5: chemical risks\u003c/p\u003e \u003cp\u003eE6: poor air quality (insufficient ventilation, bad smells, cigarette smoke, etc.)\u003c/p\u003e \u003cp\u003eE7: unhygienic conditions\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBody motion and postural stressors (S3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eB1: activities such as walking for a long time, using stairs, etc.\u003c/p\u003e \u003cp\u003eB2: activities such as bending, squatting, standing, etc.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMental job demand stressors (S4)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eM1: making critical decisions\u003c/p\u003e \u003cp\u003eM2: activities such as thinking, remembering, and searching\u003c/p\u003e \u003cp\u003eM3: informing the patient and/or the patient's relatives\u003c/p\u003e \u003cp\u003eM4: difficult patient behaviors\u003c/p\u003e \u003cp\u003eM5: negative behaviors of the patient's relatives\u003c/p\u003e \u003cp\u003eM6: adverse traffic conditions\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\u003eRather than relying on physiological measurements\u0026mdash;which are impractical in mobile care settings\u0026mdash;we adopt a structured post-task subjective assessment approach to capture nurse-specific workload perception following each visit. This conceptualization forms the foundation for the quantitative modeling components described in the subsequent sections.\u003c/p\u003e \u003cp\u003eDurak and Mutlu (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) proposed an ergonomic workload quantification framework in which post-task assessments were transformed into analytical workload scores and directly incorporated into a mathematical scheduling model. In that study, the most recently observed workload value was assumed to represent the expected workload in subsequent planning periods. While this approach enabled workload-aware scheduling, it did not explicitly model stochastic transitions between workload states over time. The present study advances this framework by introducing a multi-state modeling approach to capture temporal workload evolution and by embedding predicted workload states within a goal programming\u0026ndash;based scheduling structure.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Fuzzy-Based Workload Quantification\u003c/h2\u003e \u003cp\u003eThe multidimensional and perception-dependent structure of ergonomic workload in home healthcare requires a modeling approach capable of handling linguistic evaluations and subjective judgments. Since nurses evaluate stressors in qualitative terms such as \u0026ldquo;low,\u0026rdquo; \u0026ldquo;moderate,\u0026rdquo; or \u0026ldquo;high,\u0026rdquo; deterministic aggregation methods are insufficient to capture the inherent ambiguity of perception-based assessments. Fuzzy set theory, introduced by Zadeh (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e1965\u003c/span\u003e), provides a suitable mathematical framework for modeling imprecise and linguistically expressed information in complex human-centered systems.\u003c/p\u003e \u003cp\u003eFuzzy-based workload assessment has been applied in various ergonomic contexts. (Chen et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e1994\u003c/span\u003e; Liou and Wang, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e1994\u003c/span\u003e; Jung, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Jung, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2000\u003c/span\u003e) developed fuzzy approaches to integrate multiple stress factors into composite workload indices. Jung and Jung (\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2001\u003c/span\u003e) further proposed an overall workload assessment technique incorporating multiple ergonomic dimensions. While fuzzy logic has also been used in HHCRSP studies to model uncertainties related to demand, travel time, or service duration (Shi et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Tohidifard et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Fathollahi-Fard et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), its application for modeling ergonomic workload perception within scheduling decisions remains limited.\u003c/p\u003e \u003cp\u003eIn this study, a Fuzzy Inference System (FIS) is developed to transform post-task questionnaire responses into a continuous workload score ranging between 0 and 100. Following each patient visit, nurses evaluate predefined ergonomic stressors using a structured questionnaire. Each stressor is rated using linguistic levels, which are converted into numerical scores and aggregated within four stressor categories defined in Section 2.1.\u003c/p\u003e \u003cp\u003eDuring the fuzzification stage, aggregated stressor scores are mapped onto linguistic terms using triangular membership functions. The inference mechanism is based on the Mamdani approach (Mamdani and Assilian, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e1975\u003c/span\u003e), where a set of expert-defined IF\u0026ndash;THEN rules capture the combined effects of physical, environmental, postural, and mental stressors on overall workload. The complete rule base, developed in consultation with domain experts in home health care operations, is provided in Appendix A. In the final stage, the defuzzification process employs the center-of-gravity method to generate a crisp workload score.\u003c/p\u003e \u003cp\u003eThe overall structure of the developed FIS is presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe resulting output represents the observed workload level associated with a specific nurse\u0026ndash;patient visit. These observed workload scores serve as the quantitative basis for modeling temporal workload transitions in the subsequent subsection.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3. Multi-State Modeling of Temporal Workload Dynamics\u003c/h2\u003e \u003cp\u003eWhile the FIS provides a quantified workload score for each completed nurse\u0026ndash;patient visit, operational scheduling decisions require an estimation of workload levels expected in future visits. In home healthcare settings, workload perception is inherently dynamic. Environmental conditions, patient acuity, relational factors, and contextual stressors may evolve over time, leading to variability in perceived strain across consecutive visits to the same patient.\u003c/p\u003e \u003cp\u003eTo represent this temporal variability, a multi-state modeling approach based on the Markov assumption is adopted. Multi-state models describe systems that evolve through a finite number of discrete states, where the probability of transitioning to a future state depends on the current state (Jackson, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). Such models have been widely applied in healthcare research to represent progressive or fluctuating processes under uncertainty (Sato and Zouain, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Uhry et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Xiong et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). In contrast to deterministic forecasting methods, multi-state models provide a probabilistic structure for capturing transitions between levels of a variable over time.\u003c/p\u003e \u003cp\u003eIn the proposed framework, continuous workload scores obtained from the FIS are categorized into five discrete workload states: very low (0\u0026ndash;19), low (20\u0026ndash;39), normal (40\u0026ndash;59), high (60\u0026ndash;79), and very high (80\u0026ndash;100). For each nurse\u0026ndash;patient pair, historical workload observations are used to estimate transition probabilities between these states. The resulting transition probability matrix defines the likelihood of moving from one workload state to another in the subsequent visit.\u003c/p\u003e \u003cp\u003eBased on the estimated transition probabilities, the most probable next workload state is identified, and the midpoint of the corresponding workload interval is used as the expected workload value for the next planning period. In this manner, future workload is treated as a probabilistic state-dependent variable rather than a fixed continuation of the most recent observation.\u003c/p\u003e \u003cp\u003eDurak and Mutlu (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) incorporated observed workload values directly into a scheduling model by assuming that the most recently observed workload level represents the expected workload in subsequent planning periods. While this assumption enabled workload-aware scheduling, it did not explicitly model probabilistic transitions between workload states. The present study extends this approach by explicitly incorporating state-transition dynamics, thereby allowing the scheduling model to account for potential workload escalation or reduction across consecutive visits.\u003c/p\u003e \u003cp\u003eBy modeling workload evolution as a probabilistic state-transition process, the proposed framework captures temporal uncertainty and cumulative strain patterns that are otherwise neglected in static formulations. The estimated workload values derived from the multi-state model are subsequently embedded within the goal programming scheduling structure described in the next subsection.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4. Goal Programming Scheduling Model\u003c/h2\u003e \u003cp\u003eHome Health Care Routing and Scheduling Problems involve multiple and often competing objectives, including service efficiency and equitable workload distribution. In addition to standard operational constraints such as time windows, skill compatibility, and working time limits, the proposed model incorporates dynamically estimated ergonomic workload into daily assignment and routing decisions.\u003c/p\u003e \u003cp\u003eTo balance these objectives, a weighted goal programming (GP) formulation is employed. This approach enables the simultaneous regulation of daily workload exposure and fulfillment of patient demand through adjustable priority weights.\u003c/p\u003e \u003cp\u003eThe scheduling problem is defined for a set of nurses with heterogeneous skill levels who depart from the HHC center, perform their assigned visits within an eight-hour shift, and return to the center without overtime. Each nurse is required to take a one-hour lunch break within a predefined time interval, and this break may include travel time.\u003c/p\u003e \u003cp\u003eTime windows are treated as strict constraints: early arrivals result in waiting, whereas late arrivals are not permitted. Each patient can be visited at most once, and nurse\u0026ndash;patient skill compatibility must be satisfied. Service times are deterministic and known in advance, and travel times are assumed to be proportional to distances. The number of nurses is fixed, and no explicit patient or nurse preference structures are considered. Workload values may vary across nurse\u0026ndash;patient pairs, reflecting the ergonomic variability captured through the proposed assessment and dynamic workload modeling framework.\u003c/p\u003e \u003cp\u003eLet \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{i,j,s}\\:\\)\u003c/span\u003e\u003c/span\u003edenote the routing decision variable indicating whether nurse \u003cem\u003es\u003c/em\u003e travels from node \u003cem\u003ei\u003c/em\u003e to node \u003cem\u003ej\u003c/em\u003e. Arrival time and waiting time variables are defined to ensure time feasibility. The workload parameter \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{wl}_{i,s}\\:\\)\u003c/span\u003e\u003c/span\u003erepresents the dynamically estimated workload associated with nurse\u003c/p\u003e \u003cp\u003e \u003cem\u003es\u003c/em\u003e serving patient \u003cem\u003ei\u003c/em\u003e, as derived from the multi-state modeling framework described in Section 2.3.\u003c/p\u003e \u003cp\u003eThe weighted goal programming objective function minimizes the normalized deviations associated with workload regulation and patient coverage:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:{Min}{w}_{1}\\left(\\frac{\\sum\\:_{s=1}^{m}{dwl}_{s}^{+}}{{f}_{1}}\\right)+{w}_{2}\\left(\\frac{{drv}^{-}}{{f}_{2}}\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWorkload regulation is enforced through a goal constraint linking the total assigned workload of each nurse with the predetermined maximum daily workload threshold \u003cem\u003eMax_load.\u003c/em\u003e Additional constraints ensure routing flow conservation, departure and return to the HHC center, lunch break allocation within the specified interval, time window compliance through Big-M propagation logic, maximum daily working time (540 minutes), and appropriate binary and non-negativity conditions.\u003c/p\u003e \u003cp\u003eThe complete mathematical formulation, including all sets, indices, parameters, decision variables, and constraints, is presented in Appendix B. The routing structure remains consistent with standard HHCRSP formulations; the contribution of the proposed model lies in embedding dynamically estimated workload parameters within the goal programming framework to enable workload-aware scheduling decisions without altering the fundamental routing architecture.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Computational results and discussion","content":"\u003cp\u003eThis section evaluates the operational implications of integrating dynamically estimated ergonomic workload into home health care scheduling. The computational experiments are designed to analyze how the proposed framework manages trade-offs between workload regulation and patient demand satisfaction under varying workload limits and policy weight configurations. The results illustrate how dynamic workload modeling influences assignment decisions compared to purely time-based planning approaches.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Experimental Design\u003c/h2\u003e \u003cp\u003eDue to the absence of standardized benchmark datasets in the HHCRSP literature, stemming from variations in modeling assumptions and objectives, problem-specific test instances were generated following established practices in the field (Di Mascolo et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThree problem sizes were considered: 20 patients with 3 nurses (20\u0026times;3), 25 patients with 4 nurses (25\u0026times;4), and 30 patients with 5 nurses (30\u0026times;5). The smallest instance is presented in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e to illustrate the structure of the data.\u003c/p\u003e \u003cp\u003ePatient coordinates were randomly generated within the range [0,100], and the HHC center was positioned at (50,50). Distances were computed using Euclidean metrics, assuming proportionality between travel distance and travel time. Service times were generated between 1 and 30 minutes. The planning horizon spans 540 minutes (8:00 AM\u0026ndash;5:00 PM), and patient time windows were defined within this interval. A mandatory one-hour lunch break was scheduled within [180,360] minutes.\u003c/p\u003e \u003cp\u003eSkill compatibility between nurses and patients was represented using binary parameters. Estimated workload values for the next visit were obtained by processing simulated post-task questionnaire data through the FIS and subsequently applying the developed multi-state modeling framework.\u003c/p\u003e \u003cp\u003eAll instances were solved using CPLEX 12.2.0.0 within the GAMS 23.5.1 environment.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Results and Policy Trade-Off Analysis\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e presents computational results under different maximum workload thresholds (100, 150, and 200 units) and varying objective weight combinations. For each problem size, multiple configurations of workload weight \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{w}_{1}\\)\u003c/span\u003e\u003c/span\u003e and demand weight \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{w}_{2}\\)\u003c/span\u003e\u003c/span\u003e were examined to analyze trade-offs between ergonomic workload regulation and service coverage.\u003c/p\u003e \u003cp\u003eThe final two columns of Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e report deviations from the workload and demand targets. These deviations quantify the compromise between limiting nurse workload exposure and maximizing the number of completed visits.\u003c/p\u003e \u003cp\u003eFor example, in the 20\u0026times;3 instance with a maximum workload limit of 100 units and weights \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{w}_{1}\\:\\)\u003c/span\u003e\u003c/span\u003e= 0.3 and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{w}_{2}\\)\u003c/span\u003e\u003c/span\u003e = 0.7, the model results in a positive workload deviation of 20 units and 6 unmet patient visits. As the allowable workload threshold increases (e.g., to 150 or 200 units), workload deviations decrease and demand satisfaction improves.\u003c/p\u003e \u003cp\u003eAcross all tested scenarios, larger instances (e.g., 30\u0026times;5) exhibit greater flexibility in balancing objectives. Increased staffing capacity allows the system to better absorb workload variability while maintaining higher service coverage levels. These results highlight the sensitivity of scheduling outcomes to both workload thresholds and objective weight configurations.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.3. Managerial Implications for Workforce Sustainability\u003c/h2\u003e \u003cp\u003eThe computational findings demonstrate that incorporating dynamic ergonomic workload into scheduling decisions provides a structured mechanism for managing workforce-related trade-offs. Rather than implicitly prioritizing full demand coverage at the expense of nurse exposure, the proposed framework allows decision makers to explicitly regulate acceptable workload levels.\u003c/p\u003e \u003cp\u003eBy adjusting the workload threshold (Max_load) and objective weights, managers can determine whether short-term service maximization or long-term workforce protection should be prioritized. Under stricter workload limits, some reduction in service coverage may occur; however, this reduction prevents systematic overexposure of specific nurses to excessive strain.\u003c/p\u003e \u003cp\u003eFrom a sustainability perspective, this flexibility is critical. Integrating dynamically estimated workload values enables more balanced task allocation over time and may support staff retention while mitigating burnout risks in home health care systems. The proposed framework thus functions not only as a routing optimization tool but also as a workforce-aware decision-support mechanism that aligns operational efficiency with long-term workforce stability.\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\u003eThe details of the instance with 3 nurses and 20 patients\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"14\"\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 \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" 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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003ePatient\u003c/p\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eCoordinates of patient homes\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eService time\u003c/p\u003e \u003cp\u003e(min.)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003eTime window (min.)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003ePossession of the necessary skills\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c14\" namest=\"c12\"\u003e \u003cp\u003eEstimated workload value for the next visit\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eX coordinate\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eY coordinate\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eEarliest\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eLatest\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eNurse 1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eNurse 2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eNurse 3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e \u003cp\u003eNurse 1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c13\"\u003e \u003cp\u003eNurse 2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c14\"\u003e \u003cp\u003eNurse 3\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\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e540\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e30\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\u003e83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e540\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e70\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\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e360\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e50\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\u003e43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e540\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e50\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\u003e27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e540\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\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\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e540\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e50\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\u003e53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e540\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\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\u003e89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e540\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e50\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\u003e77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e540\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e90\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\u003e94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e540\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e50\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\u003e84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e540\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e30\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\u003e89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e540\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e50\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\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e540\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e10\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\u003e98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e540\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e-\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\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e540\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e50\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\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e540\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e70\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\u003e37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e540\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e30\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\u003e23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e540\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e50\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\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e540\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e10\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\u003e88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e540\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e10\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=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComputational results\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\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=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProblem size\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eMax_load\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eZ\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003ef\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003ef\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sum\\:_{s=1}^{m}{dwl}_{s}^{+}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{drv}^{-}:\\)\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\" morerows=\"14\" rowspan=\"15\"\u003e \u003cp\u003e20x3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.207\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.175\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.105\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003e150\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.113\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e450\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e170\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.108\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e450\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.097\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e450\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e450\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e450\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.017\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.015\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"14\" rowspan=\"15\"\u003e \u003cp\u003e25x4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.091\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.082\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.072\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.063\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.048\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003e150\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.007\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.008\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.012\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e800\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e800\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e800\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e800\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e800\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"14\" rowspan=\"15\"\u003e \u003cp\u003e30x5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.071\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.068\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.060\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.052\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.040\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003e150\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e750\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e750\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e750\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e750\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e750\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\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":"4. Conclusion","content":"\u003cp\u003eHome health care (HHC) has emerged as a rapidly expanding alternative to conventional hospitalization, increasing the operational complexity of workforce planning in decentralized care environments. Given the physically and psychosocially demanding conditions faced by HHC nurses, incorporating ergonomic considerations into scheduling decisions is essential for sustaining workforce stability and service quality.\u003c/p\u003e \u003cp\u003eThis study proposed an integrated decision-support framework that models and embeds dynamic ergonomic workload into home health care routing and scheduling. Unlike conventional HHCRSP formulations that approximate workload using time-based proxies, the proposed approach quantifies perceived ergonomic strain through a structured post-task assessment and a fuzzy inference system. Temporal variability in workload is subsequently modeled through a multi-state framework, enabling the estimation of future workload exposure for each nurse\u0026ndash;patient pair. These dynamically estimated workload values are then incorporated into a goal programming\u0026ndash;based scheduling model to generate balanced and policy-sensitive work plans.\u003c/p\u003e \u003cp\u003eThe computational results demonstrate that integrating dynamic workload estimates alters scheduling trade-offs between service coverage and workload regulation. By adjusting workload thresholds and objective weights, decision makers can explicitly manage the balance between short-term demand satisfaction and long-term workforce protection. This structured flexibility supports more sustainable allocation policies and reduces the risk of systematic nurse overexposure.\u003c/p\u003e \u003cp\u003eFrom a managerial perspective, the proposed framework extends traditional efficiency-driven routing models toward workforce-aware planning. Overall, the study illustrates how ergonomic workload dynamics can be incorporated into home health care scheduling to support more workforce-aware planning approaches.\u003c/p\u003e \u003cp\u003eFuture research may explore validation using real-world datasets, integration of travel time uncertainty, and longitudinal assessment of cumulative workload exposure.\u003c/p\u003e "},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eEthics Statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study is based on simulated data and does not involve human participants or real patient information. Therefore, ethical approval was not required.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research received no external funding.\u003c/p\u003e\n\u003cp\u003eConflict of Interest\u003c/p\u003e\n\u003cp\u003eThe authors declare no conflict of interest.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAiken LH, Clarke SP, Sloane DM, Sochalski J, Silber JH (2002) Hospital nurse staffing and patient mortality, nurse burnout, and job dissatisfaction. JAMA 288(16):1987\u0026ndash;1993\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAlves F, Costa LA, Rocha AMA, Pereira AI, Leit\u0026atilde;o P (2022) The Sustainable Home Health Care Process Based on Multi-Criteria Decision-Support. 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Int J Man Mach Stud 7(1):1\u0026ndash;13\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMasmoudi M, Euchi J, Siarry P (2024) Home healthcare routing and scheduling: operations research approaches and contemporary challenges. Ann Oper Res 343(2):701\u0026ndash;751\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMoscato S, Sichi V, Giannelli A, Palumbo P, Ostan R, Varani S, Pannuti R, Chiari L (2021) Virtual reality in home palliative care: brief report on the effect on cancer-related symptomatology. Front Psychol 12:709154\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRodriguez-Verjan C, Augusto V, Xie X (2018) Home health-care network design: Location and configuration of home health-care centers. 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BMC Nurs 23(1):248\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZadeh LA (1965) Fuzzy sets Inform control 8(3):338\u0026ndash;353\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"home health care, dynamic workload modeling, ergonomic nurse workload, workforce sustainability, multi-state Markov model, decision support system","lastPublishedDoi":"10.21203/rs.3.rs-9199727/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9199727/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eBackground\u003c/h2\u003e \u003cp\u003eHome health care (HHC) services are expanding rapidly as health systems respond to population ageing, increasing prevalence of chronic conditions, and efforts to shift care delivery from hospitals to community settings. While these services improve accessibility and patient satisfaction, they also introduce significant workforce planning challenges. In particular, nurses providing home-based care often work in highly variable environments that can influence both physical and psychosocial workload. Despite these realities, most existing scheduling approaches in home health care focus primarily on operational efficiency indicators such as travel time, service duration, or cost. As a result, ergonomic and contextual factors that shape nurses\u0026rsquo; workload are rarely considered in planning decisions, potentially leading to schedules that are operationally efficient but uneven in terms of staff workload and well-being.\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e \u003cp\u003eThis study develops a decision-support framework designed to incorporate ergonomic workload considerations into home health care scheduling. First, nurses\u0026rsquo; perceived workload following patient visits is captured through a structured post-task assessment that evaluates multiple categories of stressors encountered during care delivery. These assessments are converted into quantitative workload scores using a fuzzy inference system that accommodates the subjective and linguistic nature of workload perceptions. To account for temporal variability in workload exposure, a multi-state Markov modeling approach is then used to estimate transitions between different workload states across consecutive visits. The resulting workload estimates are incorporated into a goal programming\u0026ndash;based scheduling model that simultaneously considers patient demand satisfaction and equitable distribution of workload among nurses.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e \u003cp\u003eComputational experiments were conducted using simulated home care scenarios of varying sizes to explore how the integration of dynamic workload information influences scheduling decisions. The results indicate that incorporating ergonomic workload estimates enables more balanced allocation of tasks across nurses while maintaining acceptable levels of service coverage. By adjusting workload limits and objective weights, decision makers can explicitly manage trade-offs between maximizing the number of completed visits and limiting excessive workload exposure for individual staff members.\u003c/p\u003e\u003ch2\u003eConclusions\u003c/h2\u003e \u003cp\u003eIntegrating dynamic ergonomic workload information into scheduling decisions provides a more comprehensive approach to workforce planning in home health care services. The proposed framework demonstrates how operational planning models can incorporate contextual and human-centered workload factors alongside traditional efficiency objectives. Such approaches may help health care organizations design more sustainable service delivery systems that protect workforce well-being while continuing to meet growing patient demand.\u003c/p\u003e","manuscriptTitle":"Dynamic ergonomic workload modeling to support workforce-aware scheduling in home health care services","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-24 15:09:46","doi":"10.21203/rs.3.rs-9199727/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"c0a637ea-04e7-429a-9bea-ec6c658be6a0","owner":[],"postedDate":"March 24th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":64968856,"name":"Health Economics and Outcomes Research"}],"tags":[],"updatedAt":"2026-03-24T15:09:46+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-24 15:09:46","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9199727","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9199727","identity":"rs-9199727","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}