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A mixed integer linear programming modelling for the flexible cyclic jobshop problem

  • Félix Quinton
  • Idir Hamaz
  • Laurent HoussinEmail author
S.I.: Project Management and Scheduling 2018
  • 57 Downloads

Abstract

This paper addresses the Cyclic Jobshop Problem in a flexible context. The flexibility feature means that machines are able to perform several kinds of tasks. Hence, a solution of the scheduling problem does not only concern the starting times of the elementary tasks, but also the assignment of these tasks to a unique machine. The objective considered in this paper is the minimisation of the cycle time of a periodic schedule. We formulate the problem as a Mixed Integer Linear Problem and propose a Benders decomposition method along with a heuristic procedure to speed up the solving of large instances. It consists in reducing the number of machines available for each task. Results of numerical experiments on randomly generated instances show that the MILP modelling has trouble solving difficult instances, while our decomposition method is more efficient for solving such instances. Our heuristic procedure provides good estimates for difficult instances.

Keywords

Cyclic scheduling Flexible scheduling Mixed integer programming 

Notes

References

  1. Benders, J. F. (1962). Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik, 4(1), 238–252.CrossRefGoogle Scholar
  2. Błażewicz, J., Domschke, W., & Pesch, E. (1996). The job shop scheduling problem: Conventional and new solution techniques. European Journal of Operational Research, 93(1), 1–33.CrossRefGoogle Scholar
  3. Bożejko, W., Gnatowski, A., Klempous, R., Affenzeller, M., Beham, A. (2016). Cyclic scheduling of a robotic cell. In Cognitive Infocommunications (CogInfoCom), 2016 7th IEEE international conference on, IEEE, pp. 000379–000384.Google Scholar
  4. Bożejko, W., Pempera, J., & Wodecki, M. (2017). A fine-grained parallel algorithm for the cyclic flexible job shop problem. Archives of Control Sciences, 27(2), 169–181.CrossRefGoogle Scholar
  5. Brucker, P., & Kampmeyer, T. (2008a). Cyclic job shop scheduling problems with blocking. Annals of Operations Research, 159(1), 161–181.CrossRefGoogle Scholar
  6. Brucker, P., & Kampmeyer, T. (2008b). A general model for cyclic machine scheduling problems. Discrete Applied Mathematics, 156(13), 2561–2572.CrossRefGoogle Scholar
  7. Brucker, P., Burke, E. K., & Groenemeyer, S. (2012). A mixed integer programming model for the cyclic job-shop problem with transportation. Discrete Applied Mathematics, 160(13–14), 1924–1935.CrossRefGoogle Scholar
  8. Carlier, J., & Chrétienne, P. (1988). Problèmes d’ordonnancement: modélisation, complexité, algorithmes. Paris: Masson.Google Scholar
  9. Chretienne, P., et al. (1991). The basic cyclic scheduling problem with deadlines. Discrete Applied Mathematics, 30(2–3), 109–123.CrossRefGoogle Scholar
  10. Dell’Amico, M., & Trubian, M. (1993). Applying tabu search to the job-shop scheduling problem. Annals of Operations Research, 41(3), 231–252.CrossRefGoogle Scholar
  11. Draper, D. L., Jonsson, A. K., Clements, D. P., Joslin, D. E. (1999). Cyclic scheduling. In IJCAI, Citeseer, pp. 1016–1021.Google Scholar
  12. Elmi, A., & Topaloglu, S. (2017). Cyclic job shop robotic cell scheduling problem: Ant colony optimization. Computers & Industrial Engineering, 111, 417–432.CrossRefGoogle Scholar
  13. Fink, M., Rahhou, T. B., & Houssin, L. (2012). A new procedure for the cyclic job shop problem. IFAC Proceedings Volumes, 45(6), 69–74.CrossRefGoogle Scholar
  14. Gao, J., Sun, L., & Gen, M. (2008). A hybrid genetic and variable neighborhood descent algorithm for flexible job shop scheduling problems. Computers & Operations Research, 35(9), 2892–2907.CrossRefGoogle Scholar
  15. Garey, M., & Johnson, D. (1979). Computers and intractability. New York: WII Freeman and Company.Google Scholar
  16. Gomes, M., Barbosa-Povoa, A., & Novais, A. (2005). Optimal scheduling for flexible job shop operation. International Journal of Production Research, 43(11), 2323–2353.Google Scholar
  17. Hamaz, I., Houssin, L., & Cafieri, S. (2018a). A robust basic cyclic scheduling problem. EURO Journal on Computational Optimization, 6(3), 291–313.CrossRefGoogle Scholar
  18. Hamaz, I., Houssin, L., & Cafieri, S. (2018b). The Cyclic Job Shop Problem with uncertain processing times. In 16th International conference on project management and scheduling (PMS 2018), Rome, Italy.Google Scholar
  19. Hanen, C. (1994). Study of a NP-hard cyclic scheduling problem: The recurrent job-shop. European Journal of Operational Research, 72(1), 82–101.CrossRefGoogle Scholar
  20. Hanen, C., & Munier, A. (1995). A study of the cyclic scheduling problem on parallel processors. Discrete Applied Mathematics, 57(2–3), 167–192.CrossRefGoogle Scholar
  21. Hillion, H. P., & Proth, J. M. (1989). Performance evaluation of job-shop systems using timed event-graphs. IEEE Transactions on Automatic Control, 34(1), 3–9.CrossRefGoogle Scholar
  22. Houssin, L. (2011). Cyclic jobshop problem and (max, plus) algebra. In World IFAC Congress (IFAC 2011), pp. 2717–2721.CrossRefGoogle Scholar
  23. Ioachim, I., & Soumis, F. (1995). Schedule efficiency in a robotic production cell. International Journal of Flexible Manufacturing Systems, 7(1), 5–26.CrossRefGoogle Scholar
  24. Jalilvand-Nejad, A., & Fattahi, P. (2015). A mathematical model and genetic algorithm to cyclic flexible job shop scheduling problem. Journal of Intelligent Manufacturing, 26(6), 1085–1098.CrossRefGoogle Scholar
  25. Jamili, A., Shafia, M. A., & Tavakkoli-Moghaddam, R. (2011). A hybrid algorithm based on particle swarm optimization and simulated annealing for a periodic job shop scheduling problem. The International Journal of Advanced Manufacturing Technology, 54(1–4), 309–322.CrossRefGoogle Scholar
  26. Kampmeyer, T. (2006). Cyclic scheduling problems.Google Scholar
  27. Karp, R. M., & Orlin, J. B. (1981). Parametric shortest path algorithms with an application to cyclic staffing. Discrete Applied Mathematics, 3(1), 37–45.CrossRefGoogle Scholar
  28. Kats, V., & Levner, E. (1996). Polynomial algorithms for scheduling of robots. Intelligent Scheduling of Robots and FMS, pp. 77–100.Google Scholar
  29. Kim, H. J., Lee, J. H. (2018). Cyclic robot scheduling for 3D printer-based flexible assembly systems. Annals of Operations Research, pp. 1–21.Google Scholar
  30. Korbaa, O., Camus, H., & Gentina, J. C. (2002). A new cyclic scheduling algorithm for flexible manufacturing systems. International Journal of Flexible Manufacturing Systems, 14(2), 173–187.CrossRefGoogle Scholar
  31. Levner, E., & Kats, V. (1998). A parametric critical path problem and an application for cyclic scheduling. Discrete Applied Mathematics, 87(1–3), 149–158.CrossRefGoogle Scholar
  32. Magnanti, T. L., & Wong, R. T. (1981). Accelerating benders decomposition: Algorithmic enhancement and model selection criteria. Operations research, 29(3), 464–484.CrossRefGoogle Scholar
  33. Papadakos, N. (2008). Practical enhancements to the Magnanti–Wong method. Operations Research Letters, 36(4), 444–449.CrossRefGoogle Scholar
  34. Quinton, F., Hamaz, I., & Houssin, L. (2018). Algorithms for the flexible cyclic jobshop problem. In 14th IEEE international conference on automation science and engineering, CASE 2018, Munich, Germany, August 20–24, 2018, pp. 945–950.Google Scholar
  35. Rossi, A., & Dini, G. (2007). Flexible job-shop scheduling with routing flexibility and separable setup times using ant colony optimisation method. Robotics and Computer-Integrated Manufacturing, 23(5), 503–516.CrossRefGoogle Scholar
  36. Roundy, R. (1992). Cyclic schedules for job shops with identical jobs. Mathematics of Operations Research, 17(4), 842–865.CrossRefGoogle Scholar
  37. Saidi-Mehrabad, M., & Fattahi, P. (2007). Flexible job shop scheduling with tabu search algorithms. The International Journal of Advanced Manufacturing Technology, 32(5–6), 563–570.CrossRefGoogle Scholar
  38. Schutten, J. M. (1998). Practical job shop scheduling. Annals of Operations Research, 83, 161–178.CrossRefGoogle Scholar
  39. Serafini, P., & Ukovich, W. (1989). A mathematical model for periodic scheduling problems. SIAM Journal on Discrete Mathematics, 2(4), 550–581.CrossRefGoogle Scholar
  40. Song, J. S., & Lee, T. E. (1998). Petri net modeling and scheduling for cyclic job shops with blocking. Computers & Industrial Engineering, 34(2), 281–295.CrossRefGoogle Scholar
  41. Thomalla, C. S. (2001). Job shop scheduling with alternative process plans. International Journal of Production Economics, 74(1), 125–134.CrossRefGoogle Scholar
  42. Xia, W., & Wu, Z. (2005). An effective hybrid optimization approach for multi-objective flexible job-shop scheduling problems. Computers & Industrial Engineering, 48(2), 409–425.CrossRefGoogle Scholar
  43. Zhang, H., Collart-Dutilleul, S., & Mesghouni, K. (2015). Cyclic scheduling of flexible job-shop with time window constraints and resource capacity constraints. IFAC-PapersOnLine, 48(3), 816–821.CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.LAAS-CNRS, Université de Toulouse, CNRS, UPSToulouseFrance
  2. 2.LIRMM UMR 5506Université de MontpellierMontpelier Cedex 5France

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