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Non-permutation flowshop scheduling problem with minimal and maximal time lags: theoretical study and heuristic

  • Multiple Objective Optimization
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Abstract

In this paper, we address the non-permutation flowshop scheduling problem with minimal and maximal time lags between successive operations of each job. For this problem, the set of permutation schedules is not a dominant set but not all non-permutation schedules are feasible because they are not always able to satisfy all time lag constraints. We present a theoretical study, limited to the two-machine case, and related to the change on one machine of the order of two successive jobs of a permutation schedule. This study gives first the necessary conditions to make such move with regard to the feasibility of the schedule; secondly the necessary conditions to make such move interesting with regard to either the makespan or the number of tardy jobs. Through this analysis, we obtain new properties of dominance of permutation schedules. The results of the study are incorporated into a heuristic algorithm which starts the search with optimal permutation schedules and tries to improve them so as to obtain better non-permutation schedules. We also propose a mixed integer linear programming model. The objective function is to minimize lexicographically the number of tardy jobs as primary criterion and the makespan as secondary one. Computational experiments are performed to compare permutation with non-permutation schedules.

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References

  • Artigues, C., Huguet, M.-J., & Lopez, P. (2011). Generalized disjunctive constraint propagation for solving the job shop with time lags. Engineering Applications of Artificial Intelligence, 24(2), 211–230.

    Article  Google Scholar 

  • Benavides, J., & Ritt, M. (2016). Two simple and effective heuristics for minimizing the makespan in non-permutation flow shops. Computers & Operations Research, 66, 160–169.

    Article  Google Scholar 

  • Bouquard, J. L., & Lenté, C. (2006). Two-machine flow shop scheduling problems with minimal and maximal delays. 4OR, 4(1), 15–28.

    Article  Google Scholar 

  • Brucker, P., Knust, S., Cheng, T. C. E., & Shakhlevich, N. V. (2004). Complexity results for flowshop and open shop scheduling problems with transportation delays. Annals of Operations Research, 129, 81–106.

    Article  Google Scholar 

  • Caumond, A., Lacomme, P., & Tchernev, N. (2008). A memetic algorithm for the job-shop with time lags. Computers & Operations Research, 35(7), 2331–2356.

    Article  Google Scholar 

  • Chu, C., & Proth, J.-M. (1996). Single machine scheduling with chain structured precedence constraints and separation time windows. IEEE Transactions on Robotics and Automation, 12(6), 835–844.

    Article  Google Scholar 

  • Dell’Amico, M. (1996). Shop problems with two machines and time lags. Operations Research, 44(5), 777–787.

    Article  Google Scholar 

  • Demirkol, E., Mehta, S., & Uzsoy, R. (1998). Benchmarks for shop scheduling problems. European Journal of Operational Research, 109, 137–141.

    Article  Google Scholar 

  • Deppner, F. (2004). Ordonnancement d’atelier avec contraintes temporelles entre opérations. Phd thesis, Institut National Polytechnique de Lorraine, France

  • Dhouib, E., Teghem, J., Tuyttens, D., & Loukil, T. (2013). Metaheuristic for Production Scheduling 1. In B. Jarboui, P. Siarry, & J. Teghem (Eds.), Chapter comparison of local search metaheuristics for a hierarchical flow shop optimization problem with time lags. New York: Wiley & ISTE.

  • Dhouib, E., Teghem, J., & Loukil, T. (2013). Lexicographic optimization of a permutation flowshop with time lag constraints. International Transactions in Operational Research, 20(2), 213–232.

    Article  Google Scholar 

  • Dhouib, E. (2013). Exact and metaheuristic methods to solve flowshop scheduling problems with time lags. Phd thesis, Faculté des Sciences Economiques et de Gestion de Sfax, Tunisie–Univerité de Mons, Belgique.

  • Fondrevelle, J., Oulamara, A., & Portmann, M.-C. (2006). Permutation flowshop scheduling problems with maximal and minimal time lags. Computers and Operations Research, 33(6), 1540–1556.

    Article  Google Scholar 

  • Fondrevelle, J., Oulamara, A., & Portmann, M.-C. (2008). Permutation flowshop scheduling problems with time lags to minimize the weighted sum of machine completion times. International Journal of Production Economics, 112, 168–176.

    Article  Google Scholar 

  • González, M. A., Oddi, A., Rasconi, R., & Valera, R. (2015). Scatter search with path relinking for the job shop with time lags and setup times. Computers and Operations Research, 60, 37–54.

    Article  Google Scholar 

  • Grimes, D., & Hebrard, E. (2011). Models and strategies for variants of the job shop scheduling problem. Lecture Notes in Computer Science, (Vol. 6876, pp. 356–372). Berlin: Springer.

  • Gupta, J. N. D., Hennig, K., & Werner, F. (2002). Local search heuristics for two-stage flow shop problems with secondary criterion. Computers and Operations Research, 29, 123–149.

    Article  Google Scholar 

  • Hariri, A. M. A., & Potts, C. N. (1989). A branch and bound algorithm to minimize the number of late jobs in a permutation flowshop. European Journal of Operational Research, 38, 228–237.

    Article  Google Scholar 

  • Hamdi, I., & Loukil, T. (2015). Upper and lower bounds for the permutation flowshop scheduling problem with minimal time lags. Optimization Letters, 19(3), 465–482.

    Article  Google Scholar 

  • Hamdi, I., Oulamara, A., & Loukil, T. (2015). A branch and bound algorithm to minimise the total tardiness in the two-machine permutation flowshop scheduling problem with minimal time lags. International Journal of Operational Research, 23(4), 387–405.

    Article  Google Scholar 

  • Hodson, A., Muhlemann, A. P., & Price, D. H. R. (1985). A microcomputer based solution to a practical scheduling problem. Journal of Operational Research Society, 36(10), 903–914.

    Article  Google Scholar 

  • Liao, L.-M., & Huang, C.-J. (2010). Tabu search for non-permutation flowshop scheduling problem with minimizing total tardiness. Applied Mathematics and Computation, 217, 557–567.

    Article  Google Scholar 

  • Mehravaran, Y., & Logendran, R. (2012). Non-permutation flowshop scheduling in a supply chain with sequence-dependent setup times. International Journal of Production Economics, 135, 953–963.

    Article  Google Scholar 

  • Nagar, A., Haddock, J., & Heragu, S. (1995). Multiple and bicriteria scheduling: A literature survey. European Journal of Operational Research, 81, 88–104.

    Article  Google Scholar 

  • Neppalli, V. R., Chen, C. L., & Gupta, J. N. D. (1996). Genetic algorithms for the two-stage bicriteria flowshop problem. European Journal of Operational Research, 95, 356–373.

    Article  Google Scholar 

  • Potts, C. N., Shmoys, D. B., & Williamson, D. P. (1991). Permutation vs. non-permutation flow shop schedules. Operations Research Letters, 10, 281–284.

    Article  Google Scholar 

  • Pugazhendhi, S., Thiagarajan, S., Rajendran, C., & Anantharaman, N. (2004). Relative performance evaluation of permutation and non-permutation schedules in flowline-based manufacturing systems with flowtime objective. International Journal of Advanced Manufacturing Technology, 23, 820–830.

    Google Scholar 

  • Rajendran, C. (1992). Two-stage flowshop scheduling problem with bicriteria. Journal of the Operational Research Society, 43, 871–884.

    Article  Google Scholar 

  • Rossi, A., & Lanzetta, M. (2013). Scheduling flow lines with buffers by ant colony digraph. Expert Systems with Applications, 40, 3328–3340.

    Article  Google Scholar 

  • Rossi, A., & Lanzetta, M. (2014). Native metaheuristics for non-permutation flowshop scheduling. Journal of Intellingent Manufacturing, 25(6), 1221–1233.

    Article  Google Scholar 

  • Taillard, E. (1993). Benchmarks for basic scheduling problems. European Journal of Operational Research, 64, 278–285.

    Article  Google Scholar 

  • Tandon, M., Cummings, P. T., & Levan, M. D. (1991). Flowshop sequencing with non-permutation schedules. Computers and Chemical Engineering, 15(8), 601–607.

    Article  Google Scholar 

  • T’Kindt, V., & Billaut, J.-C. (2001). Multicriteria scheduling problems: A survey. RAIRO/Operations Research, 35, 143–163.

    Article  Google Scholar 

  • T’Kindt, V., & Billaut, J.-C. (2006). Multicriteria scheduling (2nd ed.). Berlin: Springer.

    Google Scholar 

  • T’Kindt, V., Gupta, J. N. D., & Billaut, J.-C. (2003). Two-machine flowshop scheduling with a secondary criterion. Computers and Operations Research, 30, 505–526.

    Article  Google Scholar 

  • Vahedi-Nouria, B., Fattahia, P., & Ramezanianb, R. (2013). Minimizing total flow time for the non-permutation flow shop scheduling problem with learning effects and availability constraints. Journal of Manufacturing Systems, 32, 167–173.

    Article  Google Scholar 

  • Yang, D. L., & Chern, M. S. (1995). A two-machine flowshop sequencing problem with limited waiting time constraints. Computers and Industrial Engineering, 28(1), 63–70.

    Article  Google Scholar 

  • Yu, W. (1996). The two-machine flow shop problem with delays and the one-machine total tardiness problem. Phd thesis, Technische Universiteit, Eindhoven.

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Authors and Affiliations

  1. Unité de recherche LOgistique Gestion Industrielle et de la Qualité (LOGIQ), Institut Supérieur de Gestion Industrielle de Sfax, Université de Sfax, Route de Tunis km 10.5, Technopole de Sfax 3021, 1164, Sfax, Tunisia

    E. Dhouib & T. Loukil

  2. Service de Mathématique et de Recherche Opérationnelle (MathRO), Université de Mons/Faculté Polytechnique, 21, Place du Parc, 7000, Mons, Belgium

    J. Teghem

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  1. E. Dhouib
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  2. J. Teghem
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  3. T. Loukil
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Correspondence to E. Dhouib.

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Dhouib, E., Teghem, J. & Loukil, T. Non-permutation flowshop scheduling problem with minimal and maximal time lags: theoretical study and heuristic. Ann Oper Res 267, 101–134 (2018). https://doi.org/10.1007/s10479-018-2775-5

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