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The Flow Shop Scheduling Polyhedron with Setup Times

Author

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  • Roger Z. Ríos-Mercado

    (Universidad Autónoma de Nuevo León, AP 111—F, Cd. Universitaria)

  • Jonathan F. Bard

    (University of Texas at Austin)

Abstract

This paper addresses the problem of improving the polyhedral representation of a certain class of machine scheduling problems. Despite the poor polyhedral representation of many such problems in general, it is shown that notably tighter linear programming representations can be obtained for many important models. In particular, we study the polyhedral structure of two different mixed-integer programming formulations of the flow shop scheduling problem with sequence-dependent setup times, denoted by SDST flow shop. The first is related to the asymmetric traveling salesman problem (ATSP) polytope. The second is less common and is derived from a model proposed by Srikar and Ghosh based on the linear ordering problem (LOP) polytope. The main contribution of this work is the proof that any facet-defining inequality (facet) of either of these polytopes (ATSP and LOP) induces a facet for the corresponding SDST flow shop polyhedron. The immediate benefit of this result is that all developments to date on facets and valid inequalities for both the ATSP and the LOP can be applied directly to the machine scheduling polytope. In addition, valid mixed-integer inequalities based on variable upper-bound flow inequalities for either model are developed as well. The derived cuts are evaluated within a branch-and-cut framework.

Suggested Citation

  • Roger Z. Ríos-Mercado & Jonathan F. Bard, 2003. "The Flow Shop Scheduling Polyhedron with Setup Times," Journal of Combinatorial Optimization, Springer, vol. 7(3), pages 291-318, September.
    • Handle: RePEc:spr:jcomop:v:7:y:2003:i:3:d:10.1023_a:1027372722187
    DOI: 10.1023/A:1027372722187
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    References listed on IDEAS

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    1. Allahverdi, Ali & Gupta, Jatinder N. D. & Aldowaisan, Tariq, 1999. "A review of scheduling research involving setup considerations," Omega, Elsevier, vol. 27(2), pages 219-239, April.
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    7. Gupta, Jatinder N. D. & Darrow, William P., 1986. "The two-machine sequence dependent flowshop scheduling problem," European Journal of Operational Research, Elsevier, vol. 24(3), pages 439-446, March.
    8. Rios-Mercado, Roger Z. & Bard, Jonathan F., 1998. "Heuristics for the flow line problem with setup costs," European Journal of Operational Research, Elsevier, vol. 110(1), pages 76-98, October.
    9. Burton D. Corwin & Augustine O. Esogbue, 1974. "Two machine flow shop scheduling problems with sequence dependent setup times: A dynamic programming approach," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 21(3), pages 515-524, September.
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    Cited by:

    1. Allahverdi, Ali & Ng, C.T. & Cheng, T.C.E. & Kovalyov, Mikhail Y., 2008. "A survey of scheduling problems with setup times or costs," European Journal of Operational Research, Elsevier, vol. 187(3), pages 985-1032, June.
    2. Ruiz, Ruben & Stutzle, Thomas, 2008. "An Iterated Greedy heuristic for the sequence dependent setup times flowshop problem with makespan and weighted tardiness objectives," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1143-1159, June.
    3. Ciavotta, Michele & Minella, Gerardo & Ruiz, Rubén, 2013. "Multi-objective sequence dependent setup times permutation flowshop: A new algorithm and a comprehensive study," European Journal of Operational Research, Elsevier, vol. 227(2), pages 301-313.
    4. Yunhe Wang & Xiangtao Li & Zhiqiang Ma, 2017. "A Hybrid Local Search Algorithm for the Sequence Dependent Setup Times Flowshop Scheduling Problem with Makespan Criterion," Sustainability, MDPI, vol. 9(12), pages 1-35, December.
    5. V. Anjana & R. Sridharan & P. N. Ram Kumar, 2020. "Metaheuristics for solving a multi-objective flow shop scheduling problem with sequence-dependent setup times," Journal of Scheduling, Springer, vol. 23(1), pages 49-69, February.

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