Optimization of Job Shop Scheduling Problem Using Genetic Algorithm and Simulated Annealing: A Case Study of Manufacturing Industry

Optimization of Job Shop Scheduling Problem Using Genetic Algorithm and Simulated Annealing: A Case Study of Manufacturing Industry | 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 Optimization of Job Shop Scheduling Problem Using Genetic Algorithm and Simulated Annealing: A Case Study of Manufacturing Industry Shrajal Gupta, Rakesh Kumar Phanden, Biruk Wolde, Ravinder Kumar, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4762389/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 25 Jan, 2025 Read the published version in International Journal of System Assurance Engineering and Management → Version 1 posted 6 You are reading this latest preprint version Abstract Production scheduling is an important activity within the manufacturing system to improve its performance. It is a process of assigning resources to the task or vice versa, which depends upon the configuration of the shop floor and the type of products to be manufactured. In job shops, scheduling is a very complex task since it involves a variety of products to process on a limited number of machines to cut down on the amount of time it takes to do tasks. In the present work, a case study from the manufacturing industry has been taken to maximise the amount of time it takes to do tasks ( i.e., makespan) having job shop configuration. Two distinguished nature-inspired algorithms, viz Simulated Annealing (SA) and Genetic Algorithm (GA), have been pragmatic in optimising the existing schedule. The results show that GA outperform the SA by a 1.76% increment in the makespan value. Also, the GA and SA possessed better results than the company's existing production schedule by 32.23% and 31.02%, respectively. Production Scheduling Job Shop Scheduling Simulated Annealing and Genetic Algorithm Case Study Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 1. Introduction The manufacturing sectors of a country are a significant contributor to the overall economic growth of that nation [ 1 ]. It enhances the gross domestic product (GDP)/gross national product (GNP) and generates employment. GDP is directly governed by productivity, which can be improved by the effective and optimised utilisation of available resources in a manufacturing system [ 2 ]. Therefore, in a manufacturing system, it is important to create an optimised production schedule [ 3 ]. Scheduling optimises industrial system resources and improves production processes. In this process, resources are allocated to perform various production activities [ 4 ]. In other words, it is a decision-making sequencing problem in which jobs are elected for their sequence of operations on a machine. These problems are a kind of combinatorial problem that exists in the areas of production processes, sciences, and managerial activities, as well as stretching from manufacturing companies to multiprocessor scheduling [ 5 ]. In general, the scheduling problems have been categorised according to the configurations of shops such as flow-shop, open-shop, job-shop, etc. If the shop is configured with multiple types of machines and jobs, the shop is termed a job shop [ 4 – 5 ]. The job-shop scheduling problem (JSSP) falls under the category of combinatorial optimisation problem in which the best schedules are searched in a set of available alternative solutions [ 6 ]. A job shop produces low-volume items on an as-needed basis. Each machine in a job shop has its own unique processes for work's inputs and outputs, depicting that the workflow in the system is not unidirectional [ 7 ]. Among the most challenging NP-hard combinational optimisation problems is complex JSSP [ 8 ]. The job shop possessed the most typical configuration in which the scheduling problem can be stated as: there are N number of jobs, and each job has a distinct number of operations, which is to process on M number of machines [ 5 ]. An increasingly essential technique for solving optimisation issues, especially multi-objective problems, Evolutionary Algorithms (EA) have emerged in recent years. Finding the best or closest possible answer was the goal of this kind of challenge [ 9 ]. However, there are instances where this answer is difficult to acquire using a standard mathematical technique, which might only lead to a local optimum [ 10 ]. Heuristic methods like the GA, SA, and others can be used to address these types of difficult problems. GA is a search method that simulates the inheritance and evolution of life in a shared environment using strong parallels, randomisation, and the possibility of self-adaptation [ 11 ]. The theoretical foundations of the GA include the Darwinian theory of biological evolution and Mendel's notion of inheritance. GA manages the search process by using available data and assessing the fitness of chromosomes [ 12 ]. It then merges these chromosomes to provide optimal or acceptable solutions. Additionally, the GA performs other genetic operations such as selection, crossover, and mutation [ 11 – 12 ]. One objective combinatorial improvement approach that uses an analogy to the quantifiable mechanics of solid-state tempering is SA, which was introduced by Kirkpatrick et al. in 1982 [ 13 ]. In materials science, annealing refers to the process of heating a solid to a point where it allows for many atomic modifications. The next step is to chill the solid in a controlled manner until crystallisation occurs [ 14 ]. A simple way to alter SA is to utilise operators or functions that are explicitly created for the situation at hand; they are then used to construct the neighbour solution. By combining a probabilistic springing feature with shifting temporal assets and a predisposition to converge to zero in the inquiry phase, SA can avoid becoming stuck in suboptimal solutions successfully and converge towards the best possible solution [ 13 – 15 ]. GA and SA have the advantage that the coherence of optimisation problems does not limit them. Therefore, they offer a feasible alternative to conventional search algorithms for complex and nonlinear problems [ 9 – 12 ]. The present study considered a case study from the manufacturing industry. Machines in the manufacturing unit present a job shop scheduling environment. In the present study, completion time,i.e., makespan, is considered as the objective function of the study. GA and SA are two optimisation approaches used to evaluate system performance, and their results were also compared with the existing completion time. The paper is arranged as follows: Section 2 reviews Job shop scheduling literature. Section 3 describes the adaptive approach. Section 4 describes outcomes, and Section 5 draws inferences from this study. 2. Literature Review In production planning, scheduling plays an important role [ 16 ]. An effective implementation of a schedule can enhance the overall productivity of the system. Over the last decade, a lot of research on successful implementations of JSSP with GA, has been conducted due to its effective real-world planning scenarios [ 17 ]. In 1985, Davis was the first one to implement GA in a JSSP [ 18 ]. In order to enhance the solution, Goncalves et al. [ 19 ] integrate GA to determine the operation's priority and the amount of delay time. They considered the local search heuristics approach and a schedule generator technique that works to construct parameterised active schedules. The modified GA optimisation approach for JSSP was considered by Wang and Zheng [ 20 ]. During the search phase, they used a representation that was based on operations and then decoded the answer into an active schedule. In this method, several state generators were used in a hybrid way, and the conventional mutation of GA was substituted with the metropolis sampling process of probabilistic jumping property SA. For JSSP on a small to medium scale, Hasan et al. [ 21 ] used GA in conjunction with heuristics task ordering to minimise makespan (C min ). In addition, Jia et al. [ 22 ] integrate GA and Gantt chart (GC) to address JSSP in a distributed manufacturing system. Their approach aims to determine optimal combinations of process plans and operating schedules for small-scale or medium-scale scheduling challenges. This was done in order to find a solution to the problem of organising a distributed manufacturing system. They identify the best combination of process plans and operation schedules. Khoudi and Berrichi [ 23 ] presented an improved GA- binary branch and bound (BBB) method that obtained more than fifty percent of answers as part of a minimum complete set for the majority of the problems. This approach was developed by combining GA with BBB. Single machine scheduling and PM planning issues were taken into consideration so as to simultaneously lessen the inclusive tardiness and amount of machines that were unavailable. Specifically, they used a hybrid GA-BBB algorithm in addition to a bi-objective branch and bound (BOBB) technique. In addition, they discovered that GA-BBB was effective in minimising the amount of time required for computing and investigated the nodes of the BOBB method. Naderi et al. [ 24 ] explored JSSP with sequence-dependent setup time (SDST) using hybridised GA (HGA) with two additional features, such as search within the immediate area and a method for diversification (restart phase), operator and parameters were fine-tuned by Taguchi method. The results indicate that the crossover operator factor has the most significant influence on the effectiveness of the algorithm, with a relative position of 32.7% on the performance of HGA. This is the case because of the crossover operator factor. Further, a comparison was also made between HGA and two additional meta-heuristic techniques that have been published in the past. The interaction graph between the quality of the algorithm and the size of the SDST suggests that the performance of the HGA was better, according to their findings. Additionally, the results indicate that the HGA was superior. Li and Chen [ 25 ] developed a structure for a two-row chromosome that was based on a working method and machine distribution to lessen C min . Defersha et al. [ 26 ] proposed a mixed-integer linear programming (MILP) model and a parallel GA for flexible JSSP by including SDST. They compared sequential GA (SGA) and parallel GA (PGA with advancement of SGA). Their results showed that MILP could be used for limited sets of difficulties, while for medium and large sets, PGA was efficient. They also found that SGA could propagate within the limit as population size increases, but it couldn’t converge. In contrast, PGA promulgates many generations easily and converges to an improved solution. They also concluded that PGA results for medium and large sets of problems were very promising and achievable within limited and allowable computational time. Wang et al. [ 29 ] considered adaptive multi-population GA in job shop scheduling problems. They used multi-populations adaptive cross-over probability and adaptive mutation probability with an elite replacement mechanism to enhance the pace of convergence. The method was evaluated for a number of traditional benchmark JSPs that have been taken from the existing body of research, and it is compared against a number of different methods. In virtually all of the benchmark examples that were evaluated, the suggested AMGA was able to yield values that were either optimum or near-optimal, as shown by the computational results. For the purpose of reducing overall tardiness, Kim et al. [ 32 ] Azzouz et al. addressed the parallel scheduling issue with divided workloads and SDST. They used simulated annealing (SA) algorithms and GA to solve the problem. They found that the suggested method saves processing time without sacrificing solution quality. Azzouz et al. [ 33 ] investigated two realistic aspects, namely SDST and learning/decline effects in flexible JSSP. They considered a bi-level algorithm for solving the problem. Their results showed that the proposed algorithm was very competitive regarding considered algorithms (i.e., VNS, TS, GA, and GTS). For future work, the planned bi-level scheme could be improved by using other meta-heuristic techniques and considering realistic, flexible manufacturing systems. Bezoui et al. [ 34 ] studied and compared a priori and a posteriori incorporation of a non-compensatory fondness model based on multi-objective optimisation and demonstrated its implication within flexible JSSP. The results showed that their proposed model and optimisation strategy provide more high-quality solutions in less time. They suggested that future studies should focus on improving GA's performance by integrating and testing more operators, restricting the usage of mathematical programs using heuristics or incorporating them into a metaheuristic method. Sharma and Jain [ 27 ] studied nine dispatching rules for considered stochastic dynamic JSSP with SDST using simulation. They considered two different levels of preparation times, which were found to be less than or one. The system performance was measured using eight shop performance measures. They concluded that the system's performance is impacted by shop utilisation and setup time. Further, Sharma and Jain [ 28 ] studied thirteen dispatching rules (nine from the literature and four new setups oriented) using simulation in job shop scheduling problems. They conducted a study with 90% shop utilisation and setup time to processing time ratio to be less than one. The authors found that the proposed setup-oriented dispatching rule performed better than the existing dispatching rule. As suggested, work can be extended, including limited buffer, machine failure, order cancellation, and transportation time in JSSP with setup time in future studies. In order to limit the overall cost of the system, Fakher et al. [ 30 ] presented an inspection procedure that was carried out on a single machine with defective maintenance. The approach took into account the machine's age, as well as other factors, including lot size and the quality decision. This inspected machine was used to study the hidden state of the system. According to their findings, the nonconformity rate and quality cost were shown to have an impact on the effective age of machines. In addition to this, they discovered that the best gap between non-integrated and joint models was reached to be between 0.2% and 17.1%. They recommended including the non-linear equation in the model for implementation in the future. Holi and Kumar [ 31 ] address the effect of routing flexibility on JSSP with SDST using GA. The system’s performance was measured in terms of C min . They considered two case studies in their work, i.e., five machines with five-part types and ten machines with ten-part types. Their results indicated that routing flexibility level one for the first study and level two for the second case study provided the best results. They came to the conclusion that increasing the system's routing flexibility, after a certain degree, results in a decline in the system's performance. According to Chen et al. [ 8 ], the reliability threshold for flexible JSSP utilising SdSt was 0.82. Corrective maintenance was shown to have the best success rate. It turned out that the strategy also made machines more reliable and available. They found that both the availability and dependability of the machines were enhanced by their approach. Gupta and Jain [ 35 ] studied two reliability-oriented maintenance strategies in JSSP. They found that for the considered system. Their result showed that for considered system performance measures, 0.74%, 0.78%, and 0.82% reliability threshold limits provided the optimal result except for NOTJ and MT. Further, Gupta and Jain [ 36 ] examined the impact of routing flexibility (RF) in conjunction with reliability-based preventive maintenance. They discovered that, up to a certain point, routing flexibility improved system performance. Further, Flexible JSSP with reliability-based preventative maintenance and machine failure was also investigated by Gupta and Jain [ 37 ] in their multi-objective optimisation investigation. Rani et al. [ 38 ] investigated the impact of RF in Flexible JSSP on order release policies with setup time and varied dispatching rules. The present study considered a case study from the Hibret Manufacturing and Machine Building Industry. The company's scenario depicts the shop as a job shop with scheduling problems, with 15 jobs and 10 machines. Further, the problem can be defined in the following mannerː “There is a job shop consisting of “m” machines which can process “n” job types simultaneously. Job types arrive continuously over a period of time in the shop. Each job type requires several operations for completion, and each operation can be performed on more than one machine. The processing times of jobs on machines are stochastic in nature and known. The objective is to analyse and optimise the system performance measures, i.e., completion time (makespan) of the system using two different optimisation approaches, GA and SA, and performance measures, which are also compared with company exiting completion time. 3. Adopted Methodology This section presents the details of the adopted methodology. SA-based GA approaches have been adopted to optimise the case study. For constructing the model, various assumptions, such as pre-emption, are not permitted. The job can not process more than one machine concurrently, and the machine will not undergo any maintenance activity in line with the literature. [ 27 , 28 ] are taken in the present work. Further, the details of SA and GA are given below. 3.1. Simulated Annealing (SA) The SA algorithm is an optimisation tool that uses the concept of cooling metal behaviours to find solutions to difficult or impossible combinatorial optimisation problems. The SA technique is introduced as a model-free optimisation approach for solving NP-hard problems. Kirkpatrick et al. [ 13 ] were the first to provide simulated annealing as a solution to optimisation difficulties. It has been effectively used to solve several combinatorial optimisation issues in various fields, including neural networks, code design, scheduling, image processing, and computer-aided design of integrated circuits. The concept of physical annealing of solids serves as an inspiration for SA [ 14 ]. Annealing is a heat treatment process in which a crystal structure is achieved with the least energy consumption and minimum defects by heating metal to high temperatures and cooling slowly [ 9 ]. A local search method known as simulated annealing is used to replicate the melting and cooling processes that occur during the processing of metals. It exhibits a changing starting temperature that is first set at a very high level and then progressively decreases over time. The temperature is slowly reduced so that the search space becomes smaller for the metropolis simulation. The system will be settled into the most favourable state when the temperature is low enough. The SA optimization algorithm utilizes a closely resembling "controlled cooling" handle for nonphysical optimization issues. The fitness function of the optimisation problem is the adjustment of the low vitality bonds at the warming stages of the improvement issue. SA will seek out its neighbours in order to obtain an optimal solution, since it only has one option for a solution. "The temperature" determines how long SA will spend looking for the optimal answer. In the present scheduling problem makespan is considered as shop performance measure [ 9 – 14 ]. 3.2. Genetic Algorithm (GA) GA-based strategy was also used in this current study. The initial stage in the GA process is encoding. In the work that is being presented here, an operation-oriented representation is considered. Here, the design of a chromosomal bit (gene) is accomplished by a number process plan (i.e. numeric) [ 12 ]. The fixed sequence/order of the chromosomal bits represents a part type's associated process plan. Table 1 shows the example sets of chromosomes. As an example, let's say that there are three distinct part types x, y, and z. Each has multiple process plans (MPP). Any MPPs assigned to a certain component type may process that type. Here is an example of how this data might be encoded: {3, 6, 5}. Where 3 denotes processing part-type x according to its subsequent process plan, 6 denotes processing part-type y according to its initial process plan, and 5 denotes processing part-type z according to its process plan [ 6 ]. The study uses a randomly generated initial population. The linear ranking approach is used for selection, with stochastic universal sampling. To implement this strategy, individuals within the population are ranked according to their level of fitness, and the anticipated value of each individual is determined not by their level of fitness but rather by their particular rank [ 39 ]. After assigning the anticipated value, use the stochastic universal sampling technique to choose parents. Therefore, a mating pool that is comprised of people who have been chosen is created. Further, in the next step, the two-point crossover method is applied to individuals in the mating pool. In the two-point crossover method, randomly, two strings are selected to make a pair from the mating pool. The crossover probability (pc = 0.8) is used to estimate the essentiality of carrying out the crossover for each pair [ 11 ]. Table 2 depicts the crossover step. After that, in the subsequent stage, which is known as a mutation, a mutation operator of the reciprocal exchange type is applied to the offspring that were formed as a result of the crossover operation, with the amount of mutation probability being equal to 0.2 (i.e., pm = 0.2) [ 7 ]. The mutation point, from the beginning to the end, is chosen at random twice, and the process plans at these locations are switched while the rest of the bits remain the same. Table 3 demonstrates the mutation of the procedure. Following the mutation process, all of the individuals that are subjected to the mutation operation are examined via the application of a mutation strategy. This is done to guarantee that no part type surpasses the set of process plans that have been provided. In addition, a repair method randomly selects a process plan from the provided range to replace anyone that surpasses the set number of concerned process plans of the component type at any particular location or site of the string. The elitist method is ingrained in linear ranking selection for reproduction. Elitism is responsible for the transmission of just a few numbers of the most admirable people from the previous population to the subsequent generation. In the present work, in order to transfer the best individual form from the previous population to the next generation, a 0.9 elitism rate is considered. The termination criteria in this study are considered as a maximum number of generations, i.e., corresponding to the number of jobs (n) multiplied by the number of machines (m) [ 6 – 12 ]. In order to prevent the population from converging too quickly, a restart method is used, drawing inspiration from a similar technique utilised by Ruiz and Maroto [ 40 ]. Consequently, every generation saves the highest possible fitness value. The restart phase begins to renew the population if the best fitness value remains unchanged for longer than the pre-specified number of generations, i.e., best_generation. In the present investigation, the value of best_generation is set as 15, i.e. if the maximum fitness value in the population remains unchanged for more than 15 generations, the restart phase will be activated. The flow chart that illustrates how GA operates may be seen in Fig. 1 [ 12 ]. The procedure is as described below: Step 1: Reduce the population by sorting its fitness values from highest to lowest. Step 2: Eliminate the first 20% of individuals from the shorted list. Step 3: To regenerate the remaining 80% of persons on the reduced list, we will use the following strategy: We will create 50% of the new chromosomes by exchanging mutations with the top 20% of individuals who were sent. We will also make an additional 50% of the chromosomes at random. To replace the 80% worst person in the prior population, freshly produced genetic material must outperform the fitness value of the 80% worst person in the population. Duplicating chromosomes is also forbidden in the freshly produced 80% of the population. The present work considers minimising makespan as a system performance measure. 4. Results and Discussion The findings obtained after adopting the methods outlined before are presented in this section. Table 4 depicts the details of the case study,i.e., a job shop consisting of 10 machines and 15 jobs. Using makespan performance metrics for GA and SA optimisation strategies, we compare the shop's performance to the current situation. The result of each approach is described below: 4.1 Simulated Annealing Result: This sub-section presents the optimisation result of the considered case study for makespan performance measures using simulated annealing. The optimisation test was conducted using MATLAB® 2020a. Figure 2 depicts the convergence curve opted using the SA optimisation approach. Table 5 shows the optimisation results using SA with the best chromosome setting for optimal performance value. The optimisation results show that the optimum makespan value using the simulated annealing optimisation approach is 1247 at the best chromosome set, as shown in Table 5 . 4.2 Genetic Algorithm Results This sub-section presents the optimisation result of the considered case study for makespan performance measures using the GA approach. The optimisation test was conducted in MATLAB® 2020a. Figure 3 depicts the convergence curve opted using the GA optimisation approach. In the present study, the maximum number of iterations is set at 250. Table 5 shows the optimisation results using GA with the best chromosome setting for optimal performance value. The optimisation results show that the optimum makespan value using the genetic algorithm optimisation approach is 1225 at the best chromosome set, as demonstrated in Table 5 . 4.3 Comparison Results: This section presents the comparison results of considered optimisation techniques, i.e., SA and GA and the companies' current scenario. Table 6 shows comparative results between SA, GA, and company schedules with the chromosome setting and makespan value. It depicts that using SA and GA approaches, makespan values are 1247 and 1225, respectively. Further, the company's current makespan value is 1808. This shows that using an SA optimisation technique, the makespan value can be reduced by up to 31.02%. However, using the GA optimisation approach, the makespan value can be reduced by up to 32.25%. Further, GA reduced makespan by 1.76% as compared to the SA approach. Figure 3 shows a comparative result between GA and SA. Table 6 and Fig. 4 show that the genetic algorithm outperforms SA and the company's current scenario. Thus, it can be safely concluded that to improve makespan, a genetic algorithm showed setting should be used. Figure 5 represents a Gant chart of the optimal schedule using the GA approach. The present study will provide an optimal schedule to optimise the system performance measure, i.e., makespan, which will help the considered company to improve its overall production performance. 5. Conclusions The present investigation presents a case study from a manufacturing industry to optimise the maximum completion time of jobs ( i.e. , makespan) having job shop configuration. Two distinguished nature-inspired algorithms, viz Simulated Annealing (SA) and Genetic Algorithm (GA), have been applied to optimise the existing schedule. The results show that GA outperform the SA by a 1.76% increment in the makespan value. Also, GA and SA possessed better results than the company's existing production schedule by 32.25% and 31.02%, respectively. The present study can be extended by incorporating various real-time scenarios such as maintenance time, random machine failure, transportation time, and sudden cancellation of customer orders. The problem can also be optimised by considering various optimisation approaches with various system performance measures. Declarations Funding: This research received no external funding. Conflicts of interests/Competing interests: Authors do not have any conflict of interest with this manuscript’s content. The authors have followed all ethical responsibilities mentioned by the journal. Data availability statement: All enquiries about data and its availability should be directed to the authors. References H. Zhang, G. Xu, R. Pan, and H. 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Jain, “Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach,” CIRP J. Manuf. Sci. Technol. , vol. 10, pp. 110–119, 2015, doi: 10.1016/j.cirpj.2015.03.003. L. Xu, Q. Wang, and S. Huang, “Dynamic order acceptance and scheduling problem with sequence-dependent setup time,” Int. J. Prod. Res. , vol. 53, no. 19, pp. 5797–5808, 2015, doi: 10.1080/00207543.2015.1005768. H. Beneshti-Fakher, M. Nourelfath, and M. Gendreau, “Joint planning of production and maintenance in a single machine deteriorating system,” IFAC-PapersOnLine , vol. 49, no. 12, pp. 745–750, 2016, doi: 10.1016/j.ifacol.2016.07.863. S. Holi and B. P. Shivakumar, “Routing Flexibility in Job Shop Scheduling Problem-A Genetic Algorithm Approach,” Int. J. Res. Sci. Innov. | , vol. V, no. Xi, pp. 60–64, 2018, [Online]. Available: www.rsisinternational.org J. G. Kim, S. Song, and B. J. Jeong, “Minimising total tardiness for the identical parallel machine scheduling problem with splitting jobs and sequence-dependent setup times,” Int. J. Prod. Res. , vol. 58, no. 6, pp. 1628–1643, 2020, doi: 10.1080/00207543.2019.1672900. A. Azzouz, M. Ennigrou, and L. Ben Said, “A self-adaptive hybrid algorithm for solving flexible job-shop problem with sequence dependent setup time,” Procedia Comput. Sci. , vol. 112, pp. 457–466, 2017, doi: 10.1016/j.procs.2017.08.023. M. Bezoui, A. L. Olteanu, and M. Sevaux, “Integrating preferences within multiobjective flexible job shop scheduling,” Eur. J. Oper. Res. , no. xxxx, 2022, doi: 10.1016/j.ejor.2022.07.002. S. Gupta and A. Jain, “Assessing the Effect of Reliability-Based Maintenance Approach in Job Shop Scheduling with Setup Time and Energy Consideration Using Simulation; A Simulation Study,” Smart Sci. , vol. 9, no. 4, pp. 283–304, 2021, doi: 10.1080/23080477.2021.1938502. R. Gupta, Shrajal, Jain, Ajai, Chan, Felix TS, Phanden Kumar, “A study on simulation-based optimization of a stochastic flexible job shop scheduling undergoing preventive maintenance with sequence-dependent setup time,” Int. J. Interact. Des. Manuf. , pp. 1–18, 2023. S. Gupta and A. Jain, “Analysis of Integrated Preventive Maintenance and Machine Failure in Stochastic Flexible Job Shop Scheduling with Sequence-dependent Setup Time,” Smart Sci. , vol. 10, no. 3, pp. 175–197, 2022, doi: 10.1080/23080477.2021.1992823. S. Rani, A. Jain, and S. Angra, “Effect of Routing Flexibility on the Performance of Order Release Policies in a Flexible Job Shop with Sequence-Dependent Setup Time: A Simulation Study,” Smart Sci. , vol. 00, no. 00, pp. 1–16, 2022, doi: 10.1080/23080477.2022.2040205. C. T. Baker and B. P. Dzielinski, “Simulation of a Simplified Job Shop,” Manage. Sci. , vol. 6, no. 3, pp. 311–323, 1960, doi: 10.1287/mnsc.6.3.311. R. Ruiz, J. Carlos García-Díaz, and C. Maroto, “Considering scheduling and preventive maintenance in the flowshop sequencing problem,” Comput. Oper. Res. , vol. 34, no. 11, pp. 3314–3330, 2007, doi: 10.1016/j.cor.2005.12.007. Tables Tables 1 to 6 are available in the Supplementary Files section Supplementary Files TablemRakesh.docx Cite Share Download PDF Status: Published Journal Publication published 25 Jan, 2025 Read the published version in International Journal of System Assurance Engineering and Management → Version 1 posted Editorial decision: Accept 15 Jan, 2025 Editor assigned by journal 02 Jan, 2025 Reviewers agreed at journal 19 Dec, 2024 Reviewers invited by journal 19 Dec, 2024 Editor invited by journal 19 Dec, 2024 First submitted to journal 18 Dec, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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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-4762389","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":392478546,"identity":"9d6bbfcf-0aea-4b5d-b4ff-79ccf5d93cc6","order_by":0,"name":"Shrajal Gupta","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABCUlEQVRIie2RsUrEQBCGJyyktJ5U9woLwpIibB7EZo+FtRJ8gBS5Riu1FXwG4SrryMLZiGkjSZHgC2wlKUSczV0lJGdpsR/sMAv78c8yAIHAfwSnk+4vimdUo031B8VXBtBfGq+UxxU4KFHv7HRdVFYPN4NLC5Tb9u7ZKV7Lx2tLKUV2Nqfw7uUUcYd621mGirf66XVNys5clHMKGkCMUfNGw6SIipSotLPK6t6wEb8nhY2Kv2lRD8sKNCbG5AolKTGlVFI0R1I4KWlyiyrprEgV10o0lKIW/uIHa/Ezy0/azcf7+CVzUZ8PvSuy+cEIRltZl/sFUeOrWnjuiRxAftgpNYFAIBD4xQ+y/2OLSWnsJQAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0001-6309-8656","institution":"Jagan Institute of Management Studies","correspondingAuthor":true,"prefix":"","firstName":"Shrajal","middleName":"","lastName":"Gupta","suffix":""},{"id":392478547,"identity":"cb372457-c3a2-4ed1-90c1-f49302830668","order_by":1,"name":"Rakesh Kumar Phanden","email":"","orcid":"","institution":"Amity University 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Algorithm\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-4762389/v1/af4ad8892de6a378413a2c8e.png"},{"id":72206160,"identity":"4c1e167c-534d-46e0-99b1-4ad27a15cfd6","added_by":"auto","created_at":"2024-12-23 16:41:52","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":15033,"visible":true,"origin":"","legend":"\u003cp\u003eSimulated annealing convergence curve\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-4762389/v1/ab21b02d249abcb6bfb18992.png"},{"id":72206161,"identity":"e7bd3aa1-841c-4e7b-8b60-f5d28c5508b7","added_by":"auto","created_at":"2024-12-23 16:41:52","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":19116,"visible":true,"origin":"","legend":"\u003cp\u003eGenetic algorithm convergence curve\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4762389/v1/f36a079fb37bbb76b9f603eb.png"},{"id":72206166,"identity":"770b6847-d4e5-43ca-86b4-8398fae2c443","added_by":"auto","created_at":"2024-12-23 16:41:52","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":19907,"visible":true,"origin":"","legend":"\u003cp\u003eGenetic Algorithm and Simulated Anneling Comparison Chart\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4762389/v1/e59930892206cefc89b566e4.png"},{"id":72206159,"identity":"d8a6f9fb-a73d-4ec7-9f7d-dc78248a8966","added_by":"auto","created_at":"2024-12-23 16:41:52","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":55615,"visible":true,"origin":"","legend":"\u003cp\u003eResults in Gantt chart\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4762389/v1/13bb8b68a14d9b94861046f2.png"},{"id":74858560,"identity":"38902ace-a740-444e-b49d-1311434055a3","added_by":"auto","created_at":"2025-01-27 16:11:33","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":585480,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4762389/v1/054bb789-7182-4056-a4b3-7c071d56068d.pdf"},{"id":72207802,"identity":"ea79bf51-0620-4013-a9ca-31194ede06f1","added_by":"auto","created_at":"2024-12-23 16:57:52","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":51645,"visible":true,"origin":"","legend":"","description":"","filename":"TablemRakesh.docx","url":"https://assets-eu.researchsquare.com/files/rs-4762389/v1/a8840a627d007a08e545b0ef.docx"}],"financialInterests":"","formattedTitle":"Optimization of Job Shop Scheduling Problem Using Genetic Algorithm and Simulated Annealing: A Case Study of Manufacturing Industry","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe manufacturing sectors of a country are a significant contributor to the overall economic growth of that nation [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. It enhances the gross domestic product (GDP)/gross national product (GNP) and generates employment. GDP is directly governed by productivity, which can be improved by the effective and optimised utilisation of available resources in a manufacturing system [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Therefore, in a manufacturing system, it is important to create an optimised production schedule [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Scheduling optimises industrial system resources and improves production processes. In this process, resources are allocated to perform various production activities [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. In other words, it is a decision-making sequencing problem in which jobs are elected for their sequence of operations on a machine. These problems are a kind of combinatorial problem that exists in the areas of production processes, sciences, and managerial activities, as well as stretching from manufacturing companies to multiprocessor scheduling [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. In general, the scheduling problems have been categorised according to the configurations of shops such as flow-shop, open-shop, job-shop, etc. If the shop is configured with multiple types of machines and jobs, the shop is termed a job shop [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. The job-shop scheduling problem (JSSP) falls under the category of combinatorial optimisation problem in which the best schedules are searched in a set of available alternative solutions [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. A job shop produces low-volume items on an as-needed basis. Each machine in a job shop has its own unique processes for work's inputs and outputs, depicting that the workflow in the system is not unidirectional [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Among the most challenging NP-hard combinational optimisation problems is complex JSSP [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. The job shop possessed the most typical configuration in which the scheduling problem can be stated as: there are N number of jobs, and each job has a distinct number of operations, which is to process on \u003cem\u003eM\u003c/em\u003e number of machines [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAn increasingly essential technique for solving optimisation issues, especially multi-objective problems, Evolutionary Algorithms (EA) have emerged in recent years. Finding the best or closest possible answer was the goal of this kind of challenge [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. However, there are instances where this answer is difficult to acquire using a standard mathematical technique, which might only lead to a local optimum [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Heuristic methods like the GA, SA, and others can be used to address these types of difficult problems. GA is a search method that simulates the inheritance and evolution of life in a shared environment using strong parallels, randomisation, and the possibility of self-adaptation [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. The theoretical foundations of the GA include the Darwinian theory of biological evolution and Mendel's notion of inheritance. GA manages the search process by using available data and assessing the fitness of chromosomes [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. It then merges these chromosomes to provide optimal or acceptable solutions. Additionally, the GA performs other genetic operations such as selection, crossover, and mutation [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. One objective combinatorial improvement approach that uses an analogy to the quantifiable mechanics of solid-state tempering is SA, which was introduced by Kirkpatrick et al. in 1982 [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. In materials science, annealing refers to the process of heating a solid to a point where it allows for many atomic modifications. The next step is to chill the solid in a controlled manner until crystallisation occurs [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. A simple way to alter SA is to utilise operators or functions that are explicitly created for the situation at hand; they are then used to construct the neighbour solution. By combining a probabilistic springing feature with shifting temporal assets and a predisposition to converge to zero in the inquiry phase, SA can avoid becoming stuck in suboptimal solutions successfully and converge towards the best possible solution [\u003cspan additionalcitationids=\"CR14\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. GA and SA have the advantage that the coherence of optimisation problems does not limit them. Therefore, they offer a feasible alternative to conventional search algorithms for complex and nonlinear problems [\u003cspan additionalcitationids=\"CR10 CR11\" citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe present study considered a case study from the manufacturing industry. Machines in the manufacturing unit present a job shop scheduling environment. In the present study, completion time,i.e., makespan, is considered as the objective function of the study. GA and SA are two optimisation approaches used to evaluate system performance, and their results were also compared with the existing completion time.\u003c/p\u003e \u003cp\u003eThe paper is arranged as follows: Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e reviews Job shop scheduling literature. Section \u003cspan refid=\"Sec3\" class=\"InternalRef\"\u003e3\u003c/span\u003e describes the adaptive approach. Section \u003cspan refid=\"Sec6\" class=\"InternalRef\"\u003e4\u003c/span\u003e describes outcomes, and Section \u003cspan refid=\"Sec10\" class=\"InternalRef\"\u003e5\u003c/span\u003e draws inferences from this study.\u003c/p\u003e"},{"header":"2. Literature Review","content":"\u003cp\u003eIn production planning, scheduling plays an important role [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. An effective implementation of a schedule can enhance the overall productivity of the system. Over the last decade, a lot of research on successful implementations of JSSP with GA, has been conducted due to its effective real-world planning scenarios [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. In 1985, Davis was the first one to implement GA in a JSSP [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. In order to enhance the solution, Goncalves et al. [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] integrate GA to determine the operation's priority and the amount of delay time. They considered the local search heuristics approach and a schedule generator technique that works to construct parameterised active schedules. The modified GA optimisation approach for JSSP was considered by Wang and Zheng [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. During the search phase, they used a representation that was based on operations and then decoded the answer into an active schedule. In this method, several state generators were used in a hybrid way, and the conventional mutation of GA was substituted with the metropolis sampling process of probabilistic jumping property SA. For JSSP on a small to medium scale, Hasan et al. [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] used GA in conjunction with heuristics task ordering to minimise makespan (C\u003csub\u003emin\u003c/sub\u003e). In addition, Jia et al. [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] integrate GA and Gantt chart (GC) to address JSSP in a distributed manufacturing system. Their approach aims to determine optimal combinations of process plans and operating schedules for small-scale or medium-scale scheduling challenges. This was done in order to find a solution to the problem of organising a distributed manufacturing system. They identify the best combination of process plans and operation schedules. Khoudi and Berrichi [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] presented an improved GA- binary branch and bound (BBB) method that obtained more than fifty percent of answers as part of a minimum complete set for the majority of the problems. This approach was developed by combining GA with BBB. Single machine scheduling and PM planning issues were taken into consideration so as to simultaneously lessen the inclusive tardiness and amount of machines that were unavailable. Specifically, they used a hybrid GA-BBB algorithm in addition to a bi-objective branch and bound (BOBB) technique. In addition, they discovered that GA-BBB was effective in minimising the amount of time required for computing and investigated the nodes of the BOBB method.\u003c/p\u003e \u003cp\u003eNaderi et al. [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] explored JSSP with sequence-dependent setup time (SDST) using hybridised GA (HGA) with two additional features, such as search within the immediate area and a method for diversification (restart phase), operator and parameters were fine-tuned by Taguchi method. The results indicate that the crossover operator factor has the most significant influence on the effectiveness of the algorithm, with a relative position of 32.7% on the performance of HGA. This is the case because of the crossover operator factor. Further, a comparison was also made between HGA and two additional meta-heuristic techniques that have been published in the past. The interaction graph between the quality of the algorithm and the size of the SDST suggests that the performance of the HGA was better, according to their findings. Additionally, the results indicate that the HGA was superior. Li and Chen [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e] developed a structure for a two-row chromosome that was based on a working method and machine distribution to lessen C\u003csub\u003emin\u003c/sub\u003e. Defersha et al. [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] proposed a mixed-integer linear programming (MILP) model and a parallel GA for flexible JSSP by including SDST. They compared sequential GA (SGA) and parallel GA (PGA with advancement of SGA). Their results showed that MILP could be used for limited sets of difficulties, while for medium and large sets, PGA was efficient. They also found that SGA could propagate within the limit as population size increases, but it couldn\u0026rsquo;t converge. In contrast, PGA promulgates many generations easily and converges to an improved solution. They also concluded that PGA results for medium and large sets of problems were very promising and achievable within limited and allowable computational time. Wang et al. [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] considered adaptive multi-population GA in job shop scheduling problems. They used multi-populations adaptive cross-over probability and adaptive mutation probability with an elite replacement mechanism to enhance the pace of convergence. The method was evaluated for a number of traditional benchmark JSPs that have been taken from the existing body of research, and it is compared against a number of different methods. In virtually all of the benchmark examples that were evaluated, the suggested AMGA was able to yield values that were either optimum or near-optimal, as shown by the computational results.\u003c/p\u003e \u003cp\u003eFor the purpose of reducing overall tardiness, Kim et al. [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e] Azzouz et al. addressed the parallel scheduling issue with divided workloads and SDST. They used simulated annealing (SA) algorithms and GA to solve the problem. They found that the suggested method saves processing time without sacrificing solution quality. Azzouz et al. [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e] investigated two realistic aspects, namely SDST and learning/decline effects in flexible JSSP. They considered a bi-level algorithm for solving the problem. Their results showed that the proposed algorithm was very competitive regarding considered algorithms (i.e., VNS, TS, GA, and GTS). For future work, the planned bi-level scheme could be improved by using other meta-heuristic techniques and considering realistic, flexible manufacturing systems. Bezoui et al. [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e] studied and compared a priori and a posteriori incorporation of a non-compensatory fondness model based on multi-objective optimisation and demonstrated its implication within flexible JSSP. The results showed that their proposed model and optimisation strategy provide more high-quality solutions in less time. They suggested that future studies should focus on improving GA's performance by integrating and testing more operators, restricting the usage of mathematical programs using heuristics or incorporating them into a metaheuristic method.\u003c/p\u003e \u003cp\u003eSharma and Jain [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] studied nine dispatching rules for considered stochastic dynamic JSSP with SDST using simulation. They considered two different levels of preparation times, which were found to be less than or one. The system performance was measured using eight shop performance measures. They concluded that the system's performance is impacted by shop utilisation and setup time. Further, Sharma and Jain [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e] studied thirteen dispatching rules (nine from the literature and four new setups oriented) using simulation in job shop scheduling problems. They conducted a study with 90% shop utilisation and setup time to processing time ratio to be less than one. The authors found that the proposed setup-oriented dispatching rule performed better than the existing dispatching rule. As suggested, work can be extended, including limited buffer, machine failure, order cancellation, and transportation time in JSSP with setup time in future studies. In order to limit the overall cost of the system, Fakher et al. [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e] presented an inspection procedure that was carried out on a single machine with defective maintenance. The approach took into account the machine's age, as well as other factors, including lot size and the quality decision. This inspected machine was used to study the hidden state of the system. According to their findings, the nonconformity rate and quality cost were shown to have an impact on the effective age of machines. In addition to this, they discovered that the best gap between non-integrated and joint models was reached to be between 0.2% and 17.1%. They recommended including the non-linear equation in the model for implementation in the future. Holi and Kumar [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e] address the effect of routing flexibility on JSSP with SDST using GA. The system\u0026rsquo;s performance was measured in terms of C\u003csub\u003emin\u003c/sub\u003e. They considered two case studies in their work, i.e., five machines with five-part types and ten machines with ten-part types. Their results indicated that routing flexibility level one for the first study and level two for the second case study provided the best results. They came to the conclusion that increasing the system's routing flexibility, after a certain degree, results in a decline in the system's performance.\u003c/p\u003e \u003cp\u003eAccording to Chen et al. [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], the reliability threshold for flexible JSSP utilising SdSt was 0.82. Corrective maintenance was shown to have the best success rate. It turned out that the strategy also made machines more reliable and available. They found that both the availability and dependability of the machines were enhanced by their approach. Gupta and Jain [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e] studied two reliability-oriented maintenance strategies in JSSP. They found that for the considered system. Their result showed that for considered system performance measures, 0.74%, 0.78%, and 0.82% reliability threshold limits provided the optimal result except for NOTJ and MT. Further, Gupta and Jain [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e] examined the impact of routing flexibility (RF) in conjunction with reliability-based preventive maintenance. They discovered that, up to a certain point, routing flexibility improved system performance. Further, Flexible JSSP with reliability-based preventative maintenance and machine failure was also investigated by Gupta and Jain [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e] in their multi-objective optimisation investigation. Rani et al. [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e] investigated the impact of RF in Flexible JSSP on order release policies with setup time and varied dispatching rules.\u003c/p\u003e \u003cp\u003eThe present study considered a case study from the Hibret Manufacturing and Machine Building Industry. The company's scenario depicts the shop as a job shop with scheduling problems, with 15 jobs and 10 machines. Further, the problem can be defined in the following mannerː\u003c/p\u003e \u003cp\u003e\u0026ldquo;There is a job shop consisting of \u0026ldquo;m\u0026rdquo; machines which can process \u0026ldquo;n\u0026rdquo; job types simultaneously. Job types arrive continuously over a period of time in the shop. Each job type requires several operations for completion, and each operation can be performed on more than one machine. The processing times of jobs on machines are stochastic in nature and known. The objective is to analyse and optimise the system performance measures, i.e., completion time (makespan) of the system using two different optimisation approaches, GA and SA, and performance measures, which are also compared with company exiting completion time.\u003c/p\u003e"},{"header":"3. Adopted Methodology","content":"\u003cp\u003eThis section presents the details of the adopted methodology. SA-based GA approaches have been adopted to optimise the case study. For constructing the model, various assumptions, such as pre-emption, are not permitted. The job can not process more than one machine concurrently, and the machine will not undergo any maintenance activity in line with the literature. [\u003cspan class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e28\u003c/span\u003e] are taken in the present work. Further, the details of SA and GA are given below.\u003c/p\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n \u003ch2\u003e3.1. Simulated Annealing (SA)\u003c/h2\u003e\n \u003cp\u003eThe SA algorithm is an optimisation tool that uses the concept of cooling metal behaviours to find solutions to difficult or impossible combinatorial optimisation problems. The SA technique is introduced as a model-free optimisation approach for solving NP-hard problems. Kirkpatrick et al. [\u003cspan class=\"CitationRef\"\u003e13\u003c/span\u003e] were the first to provide simulated annealing as a solution to optimisation difficulties. It has been effectively used to solve several combinatorial optimisation issues in various fields, including neural networks, code design, scheduling, image processing, and computer-aided design of integrated circuits. The concept of physical annealing of solids serves as an inspiration for SA [\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e]. Annealing is a heat treatment process in which a crystal structure is achieved with the least energy consumption and minimum defects by heating metal to high temperatures and cooling slowly [\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e].\u003c/p\u003e\n \u003cp\u003eA local search method known as simulated annealing is used to replicate the melting and cooling processes that occur during the processing of metals. It exhibits a changing starting temperature that is first set at a very high level and then progressively decreases over time. The temperature is slowly reduced so that the search space becomes smaller for the metropolis simulation. The system will be settled into the most favourable state when the temperature is low enough. The SA optimization algorithm utilizes a closely resembling \u0026quot;controlled cooling\u0026quot; handle for nonphysical optimization issues. The fitness function of the optimisation problem is the adjustment of the low vitality bonds at the warming stages of the improvement issue. SA will seek out its neighbours in order to obtain an optimal solution, since it only has one option for a solution. \u0026quot;The temperature\u0026quot; determines how long SA will spend looking for the optimal answer. In the present scheduling problem makespan is considered as shop performance measure [\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e].\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n \u003ch2\u003e3.2. Genetic Algorithm (GA)\u003c/h2\u003e\n \u003cp\u003eGA-based strategy was also used in this current study. The initial stage in the GA process is encoding. In the work that is being presented here, an operation-oriented representation is considered. Here, the design of a chromosomal bit (gene) is accomplished by a number process plan (i.e. numeric) [\u003cspan class=\"CitationRef\"\u003e12\u003c/span\u003e]. The fixed sequence/order of the chromosomal bits represents a part type\u0026apos;s associated process plan. Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e shows the example sets of chromosomes. As an example, let\u0026apos;s say that there are three distinct part types x, y, and z. Each has multiple process plans (MPP). Any MPPs assigned to a certain component type may process that type. Here is an example of how this data might be encoded: {3, 6, 5}. Where 3 denotes processing part-type x according to its subsequent process plan, 6 denotes processing part-type y according to its initial process plan, and 5 denotes processing part-type z according to its process plan [\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e]. The study uses a randomly generated initial population. The linear ranking approach is used for selection, with stochastic universal sampling. To implement this strategy, individuals within the population are ranked according to their level of fitness, and the anticipated value of each individual is determined not by their level of fitness but rather by their particular rank [\u003cspan class=\"CitationRef\"\u003e39\u003c/span\u003e]. After assigning the anticipated value, use the stochastic universal sampling technique to choose parents. Therefore, a mating pool that is comprised of people who have been chosen is created. Further, in the next step, the two-point crossover method is applied to individuals in the mating pool. In the two-point crossover method, randomly, two strings are selected to make a pair from the mating pool. The crossover probability (pc\u0026thinsp;=\u0026thinsp;0.8) is used to estimate the essentiality of carrying out the crossover for each pair [\u003cspan class=\"CitationRef\"\u003e11\u003c/span\u003e]. Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e depicts the crossover step. After that, in the subsequent stage, which is known as a mutation, a mutation operator of the reciprocal exchange type is applied to the offspring that were formed as a result of the crossover operation, with the amount of mutation probability being equal to 0.2 (i.e., pm\u0026thinsp;=\u0026thinsp;0.2) [\u003cspan class=\"CitationRef\"\u003e7\u003c/span\u003e]. The mutation point, from the beginning to the end, is chosen at random twice, and the process plans at these locations are switched while the rest of the bits remain the same. Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e demonstrates the mutation of the procedure. Following the mutation process, all of the individuals that are subjected to the mutation operation are examined via the application of a mutation strategy. This is done to guarantee that no part type surpasses the set of process plans that have been provided. In addition, a repair method randomly selects a process plan from the provided range to replace anyone that surpasses the set number of concerned process plans of the component type at any particular location or site of the string. The elitist method is ingrained in linear ranking selection for reproduction. Elitism is responsible for the transmission of just a few numbers of the most admirable people from the previous population to the subsequent generation. In the present work, in order to transfer the best individual form from the previous population to the next generation, a 0.9 elitism rate is considered. The termination criteria in this study are considered as a maximum number of generations, i.e., corresponding to the number of jobs (n) multiplied by the number of machines (m) [\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e12\u003c/span\u003e].\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003cdiv align=\"left\" class=\"colspec\"\u003eIn order to prevent the population from converging too quickly, a restart method is used, drawing inspiration from a similar technique utilised by Ruiz and Maroto [\u003cspan class=\"CitationRef\"\u003e40\u003c/span\u003e]. Consequently, every generation saves the highest possible fitness value. The restart phase begins to renew the population if the best fitness value remains unchanged for longer than the pre-specified number of generations, i.e., best_generation. In the present investigation, the value of best_generation is set as 15, i.e. if the maximum fitness value in the population remains unchanged for more than 15 generations, the restart phase will be activated. The flow chart that illustrates how GA operates may be seen in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e [\u003cspan class=\"CitationRef\"\u003e12\u003c/span\u003e]. The procedure is as described below:\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eStep 1: Reduce the population by sorting its fitness values from highest to lowest.\u003c/p\u003e\n \u003cp\u003eStep 2: Eliminate the first 20% of individuals from the shorted list.\u003c/p\u003e\n \u003cp\u003eStep 3: To regenerate the remaining 80% of persons on the reduced list, we will use the following strategy: We will create 50% of the new chromosomes by exchanging mutations with the top 20% of individuals who were sent. We will also make an additional 50% of the chromosomes at random.\u003c/p\u003e\n \u003cp\u003eTo replace the 80% worst person in the prior population, freshly produced genetic material must outperform the fitness value of the 80% worst person in the population. Duplicating chromosomes is also forbidden in the freshly produced 80% of the population. The present work considers minimising makespan as a system performance measure.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"4. Results and Discussion","content":"\u003cp\u003eThe findings obtained after adopting the methods outlined before are presented in this section. Table \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e depicts the details of the case study,i.e., a job shop consisting of 10 machines and 15 jobs. Using makespan performance metrics for GA and SA optimisation strategies, we compare the shop\u0026apos;s performance to the current situation. The result of each approach is described below:\u003c/p\u003e\n\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\n \u003ch2\u003e4.1 Simulated Annealing Result:\u003c/h2\u003e\n \u003cp\u003eThis sub-section presents the optimisation result of the considered case study for makespan performance measures using simulated annealing. The optimisation test was conducted using MATLAB\u0026reg; 2020a. Figure \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e depicts the convergence curve opted using the SA optimisation approach. Table \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e shows the optimisation results using SA with the best chromosome setting for optimal performance value. The optimisation results show that the optimum makespan value using the simulated annealing optimisation approach is 1247 at the best chromosome set, as shown in Table \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n \u003ch2\u003e4.2 Genetic Algorithm Results\u003c/h2\u003e\n \u003cp\u003eThis sub-section presents the optimisation result of the considered case study for makespan performance measures using the GA approach. The optimisation test was conducted in MATLAB\u0026reg; 2020a. Figure \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e depicts the convergence curve opted using the GA optimisation approach. In the present study, the maximum number of iterations is set at 250. Table \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e shows the optimisation results using GA with the best chromosome setting for optimal performance value. The optimisation results show that the optimum makespan value using the genetic algorithm optimisation approach is 1225 at the best chromosome set, as demonstrated in Table \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\n \u003ch2\u003e4.3 Comparison Results:\u003c/h2\u003e\n \u003cp\u003eThis section presents the comparison results of considered optimisation techniques, i.e., SA and GA and the companies\u0026apos; current scenario. Table \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e shows comparative results between SA, GA, and company schedules with the chromosome setting and makespan value. It depicts that using SA and GA approaches, makespan values are 1247 and 1225, respectively. Further, the company\u0026apos;s current makespan value is 1808. This shows that using an SA optimisation technique, the makespan value can be reduced by up to 31.02%. However, using the GA optimisation approach, the makespan value can be reduced by up to 32.25%. Further, GA reduced makespan by 1.76% as compared to the SA approach. Figure \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e shows a comparative result between GA and SA. Table \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e and Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e show that the genetic algorithm outperforms SA and the company\u0026apos;s current scenario. Thus, it can be safely concluded that to improve makespan, a genetic algorithm showed setting should be used. Figure \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e represents a Gant chart of the optimal schedule using the GA approach. The present study will provide an optimal schedule to optimise the system performance measure, i.e., makespan, which will help the considered company to improve its overall production performance.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"5. Conclusions","content":"\u003cp\u003eThe present investigation presents a case study from a manufacturing industry to optimise the maximum completion time of jobs (\u003cem\u003ei.e.\u003c/em\u003e, makespan) having job shop configuration. Two distinguished nature-inspired algorithms, viz Simulated Annealing (SA) and Genetic Algorithm (GA), have been applied to optimise the existing schedule. The results show that GA outperform the SA by a 1.76% increment in the makespan value. Also, GA and SA possessed better results than the company's existing production schedule by 32.25% and 31.02%, respectively. The present study can be extended by incorporating various real-time scenarios such as maintenance time, random machine failure, transportation time, and sudden cancellation of customer orders. The problem can also be optimised by considering various optimisation approaches with various system performance measures.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cul\u003e\n \u003cli\u003eFunding: This research received no external funding.\u003c/li\u003e\n \u003cli\u003eConflicts of interests/Competing interests: Authors do not have any conflict of interest with this manuscript’s content. The authors have followed all ethical responsibilities mentioned by the journal.\u003c/li\u003e\n \u003cli\u003eData availability statement: All enquiries about data and its availability should be directed to the authors.\u003c/li\u003e\n\u003c/ul\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eH. Zhang, G. Xu, R. Pan, and H. Ge, \u0026ldquo;A novel heuristic method for the energy-efficient flexible job-shop scheduling problem with sequence-dependent set-up and transportation time,\u0026rdquo; \u003cem\u003eEng. 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Res.\u003c/em\u003e, vol. 34, no. 11, pp. 3314\u0026ndash;3330, 2007, doi: 10.1016/j.cor.2005.12.007.\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Tables","content":"\u003cp\u003eTables 1 to 6 are available in the Supplementary Files section\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"international-journal-of-system-assurance-engineering-and-management","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ijsa","sideBox":"Learn more about [International Journal of System Assurance Engineering and Management](http://link.springer.com/journal/13198)","snPcode":"13198","submissionUrl":"https://www.editorialmanager.com/ijsa/default2.aspx","title":"International Journal of System Assurance Engineering and Management","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Production Scheduling, Job Shop Scheduling, Simulated Annealing, and Genetic Algorithm, Case Study","lastPublishedDoi":"10.21203/rs.3.rs-4762389/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4762389/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eProduction scheduling is an important activity within the manufacturing system to improve its performance. It is a process of assigning resources to the task or vice versa, which depends upon the configuration of the shop floor and the type of products to be manufactured. In job shops, scheduling is a very complex task since it involves a variety of products to process on a limited number of machines to cut down on the amount of time it takes to do tasks. In the present work, a case study from the manufacturing industry has been taken to maximise the amount of time it takes to do tasks (\u003cem\u003ei.e.,\u003c/em\u003emakespan) having job shop configuration. Two distinguished nature-inspired algorithms, viz Simulated Annealing (SA) and Genetic Algorithm (GA), have been pragmatic in optimising the existing schedule. The results show that GA outperform the SA by a 1.76% increment in the makespan value. Also, the GA and SA possessed better results than the company's existing production schedule by 32.23% and 31.02%, respectively.\u003c/p\u003e","manuscriptTitle":"Optimization of Job Shop Scheduling Problem Using Genetic Algorithm and Simulated Annealing: A Case Study of Manufacturing Industry","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-12-23 16:41:47","doi":"10.21203/rs.3.rs-4762389/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Accept","date":"2025-01-15T10:07:08+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-01-03T01:31:36+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"","date":"2024-12-19T16:33:21+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-12-19T16:31:08+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"International Journal of System Assurance Engineering and Management","date":"2024-12-19T05:17:04+00:00","index":"","fulltext":""},{"type":"submitted","content":"International Journal of System Assurance Engineering and Management","date":"2024-12-18T11:20:35+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"international-journal-of-system-assurance-engineering-and-management","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ijsa","sideBox":"Learn more about [International Journal of System Assurance Engineering and Management](http://link.springer.com/journal/13198)","snPcode":"13198","submissionUrl":"https://www.editorialmanager.com/ijsa/default2.aspx","title":"International Journal of System Assurance Engineering and Management","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"996c6c06-0229-4468-858b-7de23318377e","owner":[],"postedDate":"December 23rd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-01-27T16:05:39+00:00","versionOfRecord":{"articleIdentity":"rs-4762389","link":"https://doi.org/10.1007/s13198-025-02714-7","journal":{"identity":"international-journal-of-system-assurance-engineering-and-management","isVorOnly":false,"title":"International Journal of System Assurance Engineering and Management"},"publishedOn":"2025-01-25 15:57:21","publishedOnDateReadable":"January 25th, 2025"},"versionCreatedAt":"2024-12-23 16:41:47","video":"","vorDoi":"10.1007/s13198-025-02714-7","vorDoiUrl":"https://doi.org/10.1007/s13198-025-02714-7","workflowStages":[]},"version":"v1","identity":"rs-4762389","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4762389","identity":"rs-4762389","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}