Benders decomposition for the mixed no-idle permutation flowshop scheduling problem

[EN] The mixed no-idle flowshop scheduling problem arises in modern industries including integrated circuits, ceramic frit and steel production, among others, and where some machines are not allowed to remain idle between jobs. This paper describes an exact algorithm that uses Benders decomposition with a simple yet effective enhancement mechanism that entails the generation of additional cuts by using a referenced local search to help speed up convergence. Using only a single additional optimality cut at each iteration, and combined with combinatorial cuts, the algorithm can optimally solve instances with up to 500 jobs and 15 machines that are otherwise not within the reach of off-the-shelf optimization software, and can easily surpass ad-hoc existing metaheuristics. To the best of the authors' knowledge, the algorithm described here is the only exact method for solving the mixed no-idle permutation flowshop scheduling problem.This research project was partially supported by the Scientific and Technological Research Council of Turkey (TuBITAK) under Grant 1059B191600107. While writing this paper, Dr Hamzaday was a visiting researcher at the Southampton Business School at the University of Southampton. Ruben Ruiz is supported by the Spanish Ministry of Science, Innovation and Universities, under the Project 'OPTEP-Port Terminal Operations Optimization' (No. RTI2018-094940-B-I00) financed with FEDER funds. Thanks are due to two anonymous reviewers for their careful reading of the paper and helpful suggestions.Bektas, T.; Hamzadayi, A.; Ruiz García, R. (2020). Benders decomposition for the mixed no-idle permutation flowshop scheduling problem. Journal of Scheduling. 23(4):513-523. https://doi.org/10.1007/s10951-020-00637-8S513523234Adiri, I., & Pohoryles, D. (1982). Flowshop no-idle or no-wait scheduling to minimize the sum of completion times. Naval Research Logistics, 29(3), 495–504.Baker, K. R. (1974). Introduction to sequencing and scheduling. New York: Wiley.Baptiste, P., & Hguny, L. K. (1997). A branch and bound algorithm for the $$F$$/no-idle/$$C_{max}$$. In Proceedings of the international conference on industrial engineering and production management, IEPM’97, Lyon, France (Vol. 1, pp. 429–438).Benders, J. F. (1962). Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik, 4(1), 238–252.Cordeau, J. F., Pasin, F., & Solomon, M. (2006). An integrated model for logistics network design. Annals of Operations Research, 144(1), 59–82.Costa, A. M., Cordeau, J. F., Gendron, B., & Laporte, G. (2012). Accelerating benders decomposition with heuristic master problem solutions. Pesquisa Operacional, 32(1), 3–20.Deng, G., & Gu, X. (2012). A hybrid discrete differential evolution algorithm for the no-idle permutation flow shop scheduling problem with makespan criterion. Computers & Operations Research, 39(9), 2152–2160.Goncharov, Y., & Sevastyanov, S. (2009). The flow shop problem with no-idle constraints: A review and approximation. European Journal of Operational Research, 196(2), 450–456.Kalczynski, P. J., & Kamburowski, J. (2005). A heuristic for minimizing the makespan in no-idle permutation flow shops. Computers & Industrial Engineering, 49(1), 146–154.Magnanti, T. L., & Wong, R. T. (1981). Accelerating benders decomposition: Algorithmic enhancement and model selection criteria. Operations Research, 29(3), 464–484.Pan, Q. K., & Ruiz, R. (2014). An effective iterated greedy algorithm for the mixed no-idle flowshop scheduling problem. Omega, 44(1), 41–50.Pan, Q. K., Tasgetiren, M. F., & Liang, Y. C. (2008). A discrete differential evolution algorithm for the permutation flowshop scheduling problem. Computers & Industrial Engineering, 55(4), 795–816.Pan, Q. K., & Wang, L. (2008a). No-idle permutation flow shop scheduling based on a hybrid discrete particle swarm optimization algorithm. International Journal of Advanced Manufacturing Technology, 39(7–8), 796–807.Pan, Q. K., & Wang, L. (2008b). A novel differential evolution algorithm for no-idle permutation flow-shop scheduling problems. European Journal of Industrial Engineering, 2(3), 279–297.Papadakos, N. (2008). Practical enhancements to the Magnanti–Wong method. Operations Research Letters, 36(4), 444–449.Röck, H. (1984). The three-machine no-wait flow shop is NP-complete. Journal of the Association for Computing Machinery, 31(2), 336–345.Ruiz, R., & Maroto, C. (2005). A comprehensive review and evaluation of permutation flowshop heuristics. 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An Enhanced Discrete Artificial Bee Colony Algorithm to Minimize the Total Flow Time in Permutation Flow Shop Scheduling with Limited Buffers

This paper presents an enhanced discrete artificial bee colony algorithm for minimizing the total flow time in the flow shop scheduling problem with buffer capacity. First, the solution in the algorithm is represented as discrete job permutation to directly convert to active schedule. Then, we present a simple and effective scheme called best insertion for the employed bee and onlooker bee and introduce a combined local search exploring both insertion and swap neighborhood. To validate the performance of the presented algorithm, a computational campaign is carried out on the Taillard benchmark instances, and computations and comparisons show that the proposed algorithm is not only capable of solving the benchmark set better than the existing discrete differential evolution algorithm and iterated greedy algorithm, but also capable of performing better than two recently proposed discrete artificial bee colony algorithms

An Enhanced Discrete Artificial Bee Colony Algorithm to Minimize the Total Flow Time in Permutation Flow Shop Scheduling with Limited Buffers

This paper presents an enhanced discrete artificial bee colony algorithm for minimizing the total flow time in the flow shop scheduling problem with buffer capacity. First, the solution in the algorithm is represented as discrete job permutation to directly convert to active schedule. Then, we present a simple and effective scheme called best insertion for the employed bee and onlooker bee and introduce a combined local search exploring both insertion and swap neighborhood. To validate the performance of the presented algorithm, a computational campaign is carried out on the Taillard benchmark instances, and computations and comparisons show that the proposed algorithm is not only capable of solving the benchmark set better than the existing discrete differential evolution algorithm and iterated greedy algorithm, but also capable of performing better than two recently proposed discrete artificial bee colony algorithms

An Enhanced Estimation of Distribution Algorithm for Energy-Efficient Job-Shop Scheduling Problems with Transportation Constraints

[EN] Nowadays, the manufacturing industry faces the challenge of reducing energy consumption and the associated environmental impacts. Production scheduling is an effective approach for energy-savings management. During the entire workshop production process, both the processing and transportation operations consume large amounts of energy. To reduce energy consumption, an energy-efficient job-shop scheduling problem (EJSP) with transportation constraints was proposed in this paper. First, a mixed-integer programming model was established to minimize both the comprehensive energy consumption and makespan in the EJSP. Then, an enhanced estimation of distribution algorithm (EEDA) was developed to solve the problem. In the proposed algorithm, an estimation of distribution algorithm was employed to perform the global search and an improved simulated annealing algorithm was designed to perform the local search. Finally, numerical experiments were implemented to analyze the performance of the EEDA. The results showed that the EEDA is a promising approach and that it can solve EJSP effectively and efficiently.This work was supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 17KJB460018), the Innovation Foundation for Science and Technology of Yangzhou University (No. 2016CXJ020 and No. 2017CXJ018), Science and Technology Project of Yangzhou under (No. YZ2017278), Research Topics of Teaching Reform of Yangzhou University under (No. YZUJX2018-28B), and the Spanish Government (No. TIN2016-80856-R and No. TIN2015-65515-C4-1-R).Dai, M.; Zhang, Z.; Giret Boggino, AS.; Salido, MA. (2019). An Enhanced Estimation of Distribution Algorithm for Energy-Efficient Job-Shop Scheduling Problems with Transportation Constraints. Sustainability. 11(11):1-23. https://doi.org/10.3390/su11113085S1231111Wu, X., & Sun, Y. (2018). 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Journal of Manufacturing Systems, 37, 126-140. doi:10.1016/j.jmsy.2015.08.002Akbar, M., & Irohara, T. (2018). Scheduling for sustainable manufacturing: A review. Journal of Cleaner Production, 205, 866-883. doi:10.1016/j.jclepro.2018.09.100Che, A., Wu, X., Peng, J., & Yan, P. (2017). Energy-efficient bi-objective single-machine scheduling with power-down mechanism. Computers & Operations Research, 85, 172-183. doi:10.1016/j.cor.2017.04.004Lee, S., Do Chung, B., Jeon, H. W., & Chang, J. (2017). A dynamic control approach for energy-efficient production scheduling on a single machine under time-varying electricity pricing. Journal of Cleaner Production, 165, 552-563. doi:10.1016/j.jclepro.2017.07.102Rubaiee, S., & Yildirim, M. B. (2019). An energy-aware multiobjective ant colony algorithm to minimize total completion time and energy cost on a single-machine preemptive scheduling. Computers & Industrial Engineering, 127, 240-252. doi:10.1016/j.cie.2018.12.020Zhang, M., Yan, J., Zhang, Y., & Yan, S. (2019). Optimization for energy-efficient flexible flow shop scheduling under time of use electricity tariffs. Procedia CIRP, 80, 251-256. doi:10.1016/j.procir.2019.01.062Li, J., Sang, H., Han, Y., Wang, C., & Gao, K. (2018). Efficient multi-objective optimization algorithm for hybrid flow shop scheduling problems with setup energy consumptions. Journal of Cleaner Production, 181, 584-598. doi:10.1016/j.jclepro.2018.02.004Lu, C., Gao, L., Li, X., Pan, Q., & Wang, Q. (2017). Energy-efficient permutation flow shop scheduling problem using a hybrid multi-objective backtracking search algorithm. Journal of Cleaner Production, 144, 228-238. doi:10.1016/j.jclepro.2017.01.011Fu, Y., Tian, G., Fathollahi-Fard, A. M., Ahmadi, A., & Zhang, C. (2019). Stochastic multi-objective modelling and optimization of an energy-conscious distributed permutation flow shop scheduling problem with the total tardiness constraint. Journal of Cleaner Production, 226, 515-525. doi:10.1016/j.jclepro.2019.04.046Schulz, S., Neufeld, J. S., & Buscher, U. (2019). A multi-objective iterated local search algorithm for comprehensive energy-aware hybrid flow shop scheduling. Journal of Cleaner Production, 224, 421-434. doi:10.1016/j.jclepro.2019.03.155Liu, Y., Dong, H., Lohse, N., Petrovic, S., & Gindy, N. (2014). An investigation into minimising total energy consumption and total weighted tardiness in job shops. Journal of Cleaner Production, 65, 87-96. doi:10.1016/j.jclepro.2013.07.060Liu, Y., Dong, H., Lohse, N., & Petrovic, S. (2016). A multi-objective genetic algorithm for optimisation of energy consumption and shop floor production performance. 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Scheduling flexible job-shops with transportation times: Mathematical models and a hybrid imperialist competitive algorithm. Applied Mathematical Modelling, 41, 667-682. doi:10.1016/j.apm.2016.09.022Liu, Z., Guo, S., & Wang, L. (2019). Integrated green scheduling optimization of flexible job shop and crane transportation considering comprehensive energy consumption. Journal of Cleaner Production, 211, 765-786. doi:10.1016/j.jclepro.2018.11.231Tang, D., & Dai, M. (2015). Energy-efficient approach to minimizing the energy consumption in an extended job-shop scheduling problem. Chinese Journal of Mechanical Engineering, 28(5), 1048-1055. doi:10.3901/cjme.2015.0617.082Hao, X., Lin, L., Gen, M., & Ohno, K. (2013). Effective Estimation of Distribution Algorithm for Stochastic Job Shop Scheduling Problem. Procedia Computer Science, 20, 102-107. doi:10.1016/j.procs.2013.09.246Wang, L., Wang, S., Xu, Y., Zhou, G., & Liu, M. (2012). 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On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

A computational evaluation of constructive and improvement heuristics for the blocking flow shop to minimize total flowtime

This paper focuses on the blocking flow shop scheduling problem with the objective of total flowtime minimisation. This problem assumes that there are no buffers between machines and, due to its application to many manufacturing sectors, it is receiving a growing attention by researchers during the last years. Since the problem is NP-hard, a large number of heuristics have been proposed to provide good solutions with reasonable computational times. In this paper, we conduct a comprehensive evaluation of the available heuristics for the problem and for related problems, resulting in the implementation and testing of a total of 35 heuristics. Furthermore, we propose an efficient constructive heuristic which successfully combines a pool of partial sequences in parallel, using a beam-search-based approach. The computational experiments show the excellent performance of the proposed heuristic as compared to the best-so-far algorithms for the problem, both in terms of quality of the solutions and of computational requirements. In fact, despite being a relative fast constructive heuristic, new best upper bounds have been found for more than 27% of Taillard’s instances.Ministerio de Ciencia e Innovación DPI2013-44461-P/DP

A new vision of approximate methods for the permutation flowshop to minimise makespan: State-of-the-art and computational evaluation

[EN] The permutation flowshop problem is a classic machine scheduling problem where n jobs must be processed on a set of m machines disposed in series and where each job must visit all machines in the same order. Many production scheduling problems resemble flowshops and hence it has generated much interest and had a big impact in the field, resulting in literally hundreds of heuristic and metaheuristic methods over the last 60 years. However, most methods proposed for makespan minimisation are not properly compared with existing procedures so currently it is not possible to know which are the most efficient methods for the problem regarding the quality of the solutions obtained and the computational effort required. In this paper, we identify and exhaustively compare the best existing heuristics and metaheuristics so the state-of-the-art regarding approximate procedures for this relevant problem is established. (C) 2016 Elsevier B.V. All rights reserved.The authors are sincerely grateful to the anonymous referees, who provide very valuable comments on the earlier version of the paper. This research has been funded by the Spanish Ministry of Science and Innovation, under projects "ADDRESS" (DPI2013-44461-P/DPI) and "SCHEYARD" (DPI2015-65895-R) co-financed by FEDER funds.Fernandez-Viagas, V.; Ruiz García, R.; Framinan, J. (2017). A new vision of approximate methods for the permutation flowshop to minimise makespan: State-of-the-art and computational evaluation. European Journal of Operational Research. 257(3):707-721. https://doi.org/10.1016/j.ejor.2016.09.055S707721257