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. European Journal of Operational Research, 165(2), 479–494.Ruiz, R., Vallada, E., & Fernández-Martínez, C. (2009). Scheduling in flowshops with no-idle machines. In U. Chakraborty (Ed.), Computational intelligence in flow shop and job shop scheduling, chap 2 (pp. 21–51). New York: Springer.Saadani, N. E. H., Guinet, A., & Moalla, M. (2003). Three stage no-idle flow-shops. Computers & Industrial Engineering, 44(3), 425–434.Saharidis, G., & Ierapetritou, M. (2013). Speed-up Benders decomposition using maximum density cut (MDC) generation. Annals of Operations Research, 210, 101–123.Shao, W., Pi, D., & Shao, Z. (2017). Memetic algorithm with node and edge histogram for no-idle flow shop scheduling problem to minimize the makespan criterion. Applied Soft Computing, 54, 164–182.Tasgetiren, M. F., Buyukdagli, O., Pan, Q. K., & Suganthan, P. N. (2013). A general variable neighborhood search algorithm for the no-idle permutation flowshop scheduling problem. In B. K. Panigrahi, P. N. 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 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

An effective iterated greedy algorithm for the mixed no-idle flowshop scheduling problem

In the no-idle flowshop, machines cannot be idle after finishing one job and before starting the next one. Therefore, start times of jobs must be delayed to guarantee this constraint. In practice machines show this behavior as it might be technically unfeasible or uneconomical to stop a machine in between jobs. This has important ramifications in the modern industry including fiber glass processing, foundries, production of integrated circuits and the steel making industry, among others. However, to assume that all machines in the shop have this no-idle constraint is not realistic. To the best of our knowledge, this is the first paper to study the mixed no-idle extension where only some machines have the no-idle constraint. We present a mixed integer programming model for this new problem and the equations to calculate the makespan. We also propose a set of formulas to accelerate the calculation of insertions that is used both in heuristics as well as in the local search procedures. An effective iterated greedy (IG) algorithm is proposed. We use an NEH-based heuristic to construct a high quality initial solution. A local search using the proposed accelerations is employed to emphasize intensification and exploration in the IG. A new destruction and construction procedure is also shown. To evaluate the proposed algorithm, we present several adaptations of other well-known and recent metaheuristics for the problem and conduct a comprehensive set of computational and statistical experiments with a total of 1750 instances. The results show that the proposed IG algorithm outperforms existing methods in the no-idle and in the mixed no-idle scenarios by a significant margin.Quan-Ke Pan is partially supported by the National Science Foundation of China 61174187, Program for New Century Excellent Talents in University (NCET-13-0106), Science Foundation of Liaoning Province in China (2013020016), Basic scientific research foundation of Northeast University under Grant N110208001, Starting foundation of Northeast University under Grant 29321006, and Shandong Province Key Laboratory of Intelligent Information Processing and Network Security (Liaocheng University). Ruben Ruiz is partially supported by the Spanish Ministry of Economy and Competitiveness, under the project "RESULT - Realistic Extended Scheduling Using Light Techniques" with reference DPI2012-36243-C02-01 co-financed by the European Union and FEDER funds and by the Universitat Politecnica de Valencia, for the project MRPIV with reference PAID/2012/202.Pan, Q.; Ruiz García, R. (2014). An effective iterated greedy algorithm for the mixed no-idle flowshop scheduling problem. Omega. 44:41-50. https://doi.org/10.1016/j.omega.2013.10.002S41504

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

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 efficient discrete artificial bee colony algorithm for the blocking flow shop problem with total flowtime minimization

This paper presents a high performing Discrete Artificial Bee Colony algorithm for the blocking flow shop problem with flow time criterion. To develop the proposed algorithm, we considered four strategies for the food source phase and two strategies for each of the three remaining phases (employed bees, onlookers and scouts). One of the strategies tested in the food source phase and one implemented in the employed bees phase are new. Both have been proved to be very effective for the problem at hand. The initialization scheme named HPF2(¿, µ) in particular, which is used to construct the initial food sources, is shown in the computational evaluation to be one of the main procedures that allow the DABC_RCT to obtain good solutions for this problem. To find the best configuration of the algorithm, we used design of experiments (DOE). This technique has been used extensively in the literature to calibrate the parameters of the algorithms but not to select its configuration. Comparing it with other algorithms proposed for this problem in the literature demonstrates the effectiveness and superiority of the DABC_RCTPeer ReviewedPostprint (author’s final draft