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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Suganthan, S. Das, & S. S. Dash (Eds.), Swarm, evolutionary, and memetic computing (pp. 24–34). Cham: Springer.Vachajitpan, P. (1982). Job sequencing with continuous machine operation. Computers & Industrial Engineering, 6(3), 255–259

A local search heuristic with self-tuning parameter for permutation flow-shop scheduling problem

In this paper, a new local search metaheuristic is proposed for the permutation flow-shop scheduling problem. In general, metaheuristics are widely used to solve this problem due to its NP-completeness. Although these heuristics are quite effective to solve the problem, they suffer from the need to optimize parameters. The proposed heuristic, named STLS, has a single self-tuning parameter which is calculated and updated dynamically based on both the response surface information of the problem field and the performance measure of the method throughout the search process. Especially, application simplicity of the algorithm is attractive for the users. Results of the experimental study show that STLS generates high quality solutions and outperforms the basic tabu search, simulated annealing, and record-to-record travel algorithms which are well-known local search based metaheuristics

Efficient heuristics for the parallel blocking flow shop scheduling problem

We consider the NP-hard problem of scheduling n jobs in F identical parallel flow shops, each consisting of a series of m machines, and doing so with a blocking constraint. The applied criterion is to minimize the makespan, i.e., the maximum completion time of all the jobs in F flow shops (lines). The Parallel Flow Shop Scheduling Problem (PFSP) is conceptually similar to another problem known in the literature as the Distributed Permutation Flow Shop Scheduling Problem (DPFSP), which allows modeling the scheduling process in companies with more than one factory, each factory with a flow shop configuration. Therefore, the proposed methods can solve the scheduling problem under the blocking constraint in both situations, which, to the best of our knowledge, has not been studied previously. In this paper, we propose a mathematical model along with some constructive and improvement heuristics to solve the parallel blocking flow shop problem (PBFSP) and thus minimize the maximum completion time among lines. The proposed constructive procedures use two approaches that are totally different from those proposed in the literature. These methods are used as initial solution procedures of an iterated local search (ILS) and an iterated greedy algorithm (IGA), both of which are combined with a variable neighborhood search (VNS). The proposed constructive procedure and the improved methods take into account the characteristics of the problem. The computational evaluation demonstrates that both of them –especially the IGA– perform considerably better than those algorithms adapted from the DPFSP literature.Peer ReviewedPostprint (author's final draft

Automatic Algorithm Design for Hybrid Flowshop Scheduling Problems

[EN] Industrial production scheduling problems are challenges that researchers have been trying to solve for decades. Many practical scheduling problems such as the hybrid flowshop are ATP-hard. As a result, researchers resort to metaheuristics to obtain effective and efficient solutions. The traditional design process of metaheuristics is mainly manual, often metaphor-based, biased by previous experience and prone to producing overly tailored methods that only work well on the tested problems and objectives. In this paper, we use an Automatic Algorithm Design (AAD) methodology to eliminate these limitations. AAD is capable of composing algorithms from components with minimal human intervention. We test the proposed MD for three different optimization objectives in the hybrid flowshop. Comprehensive computational and statistical testing demonstrates that automatically designed algorithms outperform specifically tailored state-of-the-art methods for the tested objectives in most cases.Pedro Alfaro-Fernandez and Ruben Ruiz are partially 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 and under grants BES-2013-064858 and EEBB-I-15-10089. This work was supported by the COMEX project (P7/36) within the Interuniversity Attraction Poles Programme of the Belgian Science Policy Office. Thomas Stiitzle acknowledges support from the Belgian F.R.S.-FNRS, of which he is a Research Director.Alfaro-Fernandez, P.; Ruiz García, R.; Pagnozzi, F.; Stützle, T. (2020). Automatic Algorithm Design for Hybrid Flowshop Scheduling Problems. 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An Exact Method for Solving the Multi-Processor Flow-Shop. RAIRO - Operations Research, 34(1), 1-25. doi:10.1051/ro:2000103Chung, T.-P., & Liao, C.-J. (2013). An immunoglobulin-based artificial immune system for solving the hybrid flow shop problem. Applied Soft Computing, 13(8), 3729-3736. doi:10.1016/j.asoc.2013.03.006Cui, Z., & Gu, X. (2015). An improved discrete artificial bee colony algorithm to minimize the makespan on hybrid flow shop problems. Neurocomputing, 148, 248-259. doi:10.1016/j.neucom.2013.07.056Ding, J.-Y., Song, S., Gupta, J. N. D., Zhang, R., Chiong, R., & Wu, C. (2015). An improved iterated greedy algorithm with a Tabu-based reconstruction strategy for the no-wait flowshop scheduling problem. Applied Soft Computing, 30, 604-613. doi:10.1016/j.asoc.2015.02.006Dubois-Lacoste, J., López-Ibáñez, M., & Stützle, T. (2011). A hybrid TP+PLS algorithm for bi-objective flow-shop scheduling problems. Computers & Operations Research, 38(8), 1219-1236. doi:10.1016/j.cor.2010.10.008Dubois-Lacoste, J., Pagnozzi, F., & Stützle, T. (2017). An iterated greedy algorithm with optimization of partial solutions for the makespan permutation flowshop problem. Computers & Operations Research, 81, 160-166. doi:10.1016/j.cor.2016.12.021Gupta, J. N. D. (1988). Two-Stage, Hybrid Flowshop Scheduling Problem. Journal of the Operational Research Society, 39(4), 359-364. doi:10.1057/jors.1988.63Gupta, J. N. D., & Stafford, E. F. (2006). Flowshop scheduling research after five decades. European Journal of Operational Research, 169(3), 699-711. doi:10.1016/j.ejor.2005.02.001Hidri, L., & Haouari, M. (2011). Bounding strategies for the hybrid flow shop scheduling problem. Applied Mathematics and Computation, 217(21), 8248-8263. doi:10.1016/j.amc.2011.02.108Hutter, F., Hoos, H. H., Leyton-Brown, K., & Stuetzle, T. (2009). ParamILS: An Automatic Algorithm Configuration Framework. 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An approach using particle swarm optimization and bottleneck heuristic to solve hybrid flow shop scheduling problem. Applied Soft Computing, 12(6), 1755-1764. doi:10.1016/j.asoc.2012.01.011Lopez-Ibanez, M., & Stutzle, T. (2012). The Automatic Design of Multiobjective Ant Colony Optimization Algorithms. IEEE Transactions on Evolutionary Computation, 16(6), 861-875. doi:10.1109/tevc.2011.2182651López-Ibáñez, M., Dubois-Lacoste, J., Pérez Cáceres, L., Birattari, M., & Stützle, T. (2016). The irace package: Iterated racing for automatic algorithm configuration. Operations Research Perspectives, 3, 43-58. doi:10.1016/j.orp.2016.09.002Marichelvam, M. K., Prabaharan, T., & Yang, X. S. (2014). A Discrete Firefly Algorithm for the Multi-Objective Hybrid Flowshop Scheduling Problems. IEEE Transactions on Evolutionary Computation, 18(2), 301-305. doi:10.1109/tevc.2013.2240304Marichelvam, M. K., Prabaharan, T., & Yang, X. S. (2014). Improved cuckoo search algorithm for hybrid flow shop scheduling problems to minimize makespan. Applied Soft Computing, 19, 93-101. doi:10.1016/j.asoc.2014.02.005Marichelvam, M. K., Prabaharan, T., Yang, X. S., & Geetha, M. (2013). Solving hybrid flow shop scheduling problems using bat algorithm. International Journal of Logistics Economics and Globalisation, 5(1), 15. doi:10.1504/ijleg.2013.054428Mascia, F., López-Ibáñez, M., Dubois-Lacoste, J., & Stützle, T. (2014). Grammar-based generation of stochastic local search heuristics through automatic algorithm configuration tools. Computers & Operations Research, 51, 190-199. doi:10.1016/j.cor.2014.05.020Nawaz, M., Enscore, E. E., & Ham, I. (1983). A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem. Omega, 11(1), 91-95. doi:10.1016/0305-0483(83)90088-9Pan, Q.-K., & Dong, Y. (2014). An improved migrating birds optimisation for a hybrid flowshop scheduling with total flowtime minimisation. 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A. (2010). The hybrid flow shop scheduling problem. European Journal of Operational Research, 205(1), 1-18. doi:10.1016/j.ejor.2009.09.024Sörensen, K. (2013). Metaheuristics-the metaphor exposed. International Transactions in Operational Research, 22(1), 3-18. doi:10.1111/itor.12001Vignier, A., Billaut, J.-C., & Proust, C. (1999). Les problèmes d’ordonnancement de type flow-shop hybride : état de l’art. RAIRO - Operations Research, 33(2), 117-183. doi:10.1051/ro:1999108Wang, S., Wang, L., Liu, M., & Xu, Y. (2013). An enhanced estimation of distribution algorithm for solving hybrid flow-shop scheduling problem with identical parallel machines. The International Journal of Advanced Manufacturing Technology, 68(9-12), 2043-2056. doi:10.1007/s00170-013-4819-yXu, Y., Wang, L., Wang, S., & Liu, M. (2013). An effective shuffled frog-leaping algorithm for solving the hybrid flow-shop scheduling problem with identical parallel machines. 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Iterated-greedy-based algorithms with beam search initialization for the permutation flowshop to minimize total tardiness

The permutation flow shop scheduling problem is one of the most studied operations research related problems. Literally, hundreds of exact and approximate algorithms have been proposed to optimise several objective functions. In this paper we address the total tardiness criterion, which is aimed towards the satisfaction of customers in a make-to-order scenario. Although several approximate algorithms have been proposed for this problem in the literature, recent contributions for related problems suggest that there is room for improving the current available algorithms. Thus, our contribution is twofold: First, we propose a fast beam-search-based constructive heuristic that estimates the quality of partial sequences without a complete evaluation of their objective function. Second, using this constructive heuristic as initial solution, eight variations of an iterated-greedy-based algorithm are proposed. A comprehensive computational evaluation is performed to establish the efficiency of our proposals against the existing heuristics and metaheuristics for the problem.Ministerio de Ciencia e Innovación DPI2013-44461-PMinisterio de Ciencia e Innovación DPI2016-80750-

An estimation of distribution algorithm for lot-streaming flow shop problems with setup times

Lot-streaming flow shops have important applications in different industries including textile, plastic, chemical, semiconductor and many others. This paper considers an n-job m-machine lot-streaming flow shop scheduling problem with sequence-dependent setup times under both the idling and noidling production cases. The objective is to minimize the maximum completion time or makespan. To solve this important practical problem, a novel estimation of distribution algorithm (EDA) is proposed with a job permutation based representation. In the proposed EDA, an efficient initialization scheme based on the NEH heuristic is presented to construct an initial population with a certain level of quality and diversity. An estimation of a probabilistic model is constructed to direct the algorithm search towards good solutions by taking into account both job permutation and similar blocks of jobs. A simple but effective local search is added to enhance the intensification capability. A diversity controlling mechanism is applied to maintain the diversity of the population. In addition, a speed-up method is presented to reduce the computational effort needed for the local search technique and the NEH-based heuristics. A comparative evaluation is carried out with the best performing algorithms from the literature. The results show that the proposed EDA is very effective in comparison after comprehensive computational and statistical analyses.This research is partially supported by the National Science Foundation of China (60874075, 70871065), and Science Foundation of Shandong Province in China under Grant BS2010DX005, and Postdoctoral Science Foundation of China under Grant 20100480897. Ruben Ruiz is partially funded by the Spanish Ministry of Science and Innovation, under the project "SMPA-Advanced Parallel Multiobjective Sequencing: Practical and Theoretical Advances" with reference DPI2008-03511/DPI and by the IMPIVA-Institute for the Small and Medium Valencian Enterprise, for the project OSC with references IMIDIC/2008/137, IMIDIC/2009/198 and IMIDIC/2010/175.Pan, Q.; Ruiz García, R. (2012). An estimation of distribution algorithm for lot-streaming flow shop problems with setup times. Omega. 40(2):166-180. https://doi.org/10.1016/j.omega.2011.05.002S16618040

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). A green scheduling algorithm for flexible job shop with energy-saving measures. Journal of Cleaner Production, 172, 3249-3264. doi:10.1016/j.jclepro.2017.10.342Wang, Q., Tang, D., Li, S., Yang, J., Salido, M., Giret, A., & Zhu, H. (2019). An Optimization Approach for the Coordinated Low-Carbon Design of Product Family and Remanufactured Products. Sustainability, 11(2), 460. doi:10.3390/su11020460Meng, Y., Yang, Y., Chung, H., Lee, P.-H., & Shao, C. (2018). Enhancing Sustainability and Energy Efficiency in Smart Factories: A Review. Sustainability, 10(12), 4779. doi:10.3390/su10124779Gahm, C., Denz, F., Dirr, M., & Tuma, A. (2016). Energy-efficient scheduling in manufacturing companies: A review and research framework. European Journal of Operational Research, 248(3), 744-757. doi:10.1016/j.ejor.2015.07.017Giret, A., Trentesaux, D., & Prabhu, V. (2015). Sustainability in manufacturing operations scheduling: A state of the art review. 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. International Journal of Production Economics, 179, 259-272. doi:10.1016/j.ijpe.2016.06.019May, G., Stahl, B., Taisch, M., & Prabhu, V. (2015). Multi-objective genetic algorithm for energy-efficient job shop scheduling. International Journal of Production Research, 53(23), 7071-7089. doi:10.1080/00207543.2015.1005248Zhang, R., & Chiong, R. (2016). Solving the energy-efficient job shop scheduling problem: a multi-objective genetic algorithm with enhanced local search for minimizing the total weighted tardiness and total energy consumption. Journal of Cleaner Production, 112, 3361-3375. doi:10.1016/j.jclepro.2015.09.097Salido, M. A., Escamilla, J., Giret, A., & Barber, F. (2015). A genetic algorithm for energy-efficiency in job-shop scheduling. The International Journal of Advanced Manufacturing Technology, 85(5-8), 1303-1314. doi:10.1007/s00170-015-7987-0Masmoudi, O., Delorme, X., & Gianessi, P. (2019). Job-shop scheduling problem with energy consideration. 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A Neighborhood Search for Sequence-dependent Setup Time in Flow Shop Fabrics Making of Textile Industry

Abstract This paper proposes a neighborhood search to solve scheduling for fabrics making in a textile industry. The production process consists of three production stages from spinning, weaving, and dyeing. All stages have one processor. Setup time between two consecutive jobs with different color is considered. This paper also proposes attribute’s decomposition of a single job to classify available jobs to be processed and to consider setup time between two consecutive jobs. Neighborhood search (NS) algorithm is proposed in which the permutation of set of jobs with same attribute and the permutation among set of jobs is conducted. Solution obtained from neighborhood search, which might be trapped in local solution, then is compared with other known optimal methods