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A combinatorial analysis of the permutation and non-permutation flow shop scheduling problems

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  • Rossit, Daniel A.
  • Vásquez, Óscar C.
  • Tohmé, Fernando
  • Frutos, Mariano
  • Safe, Martín D.

Abstract

In this paper we introduce a novel approach to the combinatorial analysis of flow shop scheduling problems for the case of two jobs, assuming that processing times are unknown. The goal is to determine the dominance properties between permutation flow shop (PFS) and non-permutation flow shop (NPFS) schedules. In order to address this issue we develop a graph-theoretical approach to describe the sets of operations that define the makespan of feasible PFS and NPFS schedules (critical paths). The cardinality of these sets is related to the number of switching machines at which the sequence of the previous operations of the two jobs becomes reversed. This, in turn, allows us to uncover structural and dominance properties between the PFS and NPFS versions of the scheduling problem. We also study the case in which the ratio between the shortest and longest processing times, denoted ρ, is the only information known about those processing times. A combinatorial argument based on ρ leads to the identification of the NPFS schedules that are dominated by PFS ones, restricting the space of feasible solutions to the NPFS problem. We also extend our analysis to the comparison of NPFS schedules (with different number of switching machines). Again, based on the value of ρ, we are able to identify NPFS schedules dominated by other NPFS schedules.

Suggested Citation

  • Rossit, Daniel A. & Vásquez, Óscar C. & Tohmé, Fernando & Frutos, Mariano & Safe, Martín D., 2021. "A combinatorial analysis of the permutation and non-permutation flow shop scheduling problems," European Journal of Operational Research, Elsevier, vol. 289(3), pages 841-854.
    • Handle: RePEc:eee:ejores:v:289:y:2021:i:3:p:841-854
    DOI: 10.1016/j.ejor.2019.07.055
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    References listed on IDEAS

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    1. Waldherr, Stefan & Knust, Sigrid, 2017. "Decomposition algorithms for synchronous flow shop problems with additional resources and setup times," European Journal of Operational Research, Elsevier, vol. 259(3), pages 847-863.
    2. Sheldon B. Akers, 1956. "Letter to the Editor---A Graphical Approach to Production Scheduling Problems," Operations Research, INFORMS, vol. 4(2), pages 244-245, April.
    3. Viswanath Nagarajan & Maxim Sviridenko, 2009. "Tight Bounds for Permutation Flow Shop Scheduling," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 417-427, May.
    4. Sheldon B. Akers & Joyce Friedman, 1955. "A Non-Numerical Approach to Production Scheduling Problems," Operations Research, INFORMS, vol. 3(4), pages 429-442, November.
    5. Rossit, Daniel Alejandro & Tohmé, Fernando & Frutos, Mariano, 2018. "The Non-Permutation Flow-Shop scheduling problem: A literature review," Omega, Elsevier, vol. 77(C), pages 143-153.
    6. Vallada, Eva & Ruiz, Rubén & Framinan, Jose M., 2015. "New hard benchmark for flowshop scheduling problems minimising makespan," European Journal of Operational Research, Elsevier, vol. 240(3), pages 666-677.
    7. Anis Gharbi & Mohamed Labidi & Mohamed Aly Louly, 2014. "The Nonpermutation Flowshop Scheduling Problem: Adjustment and Bounding Procedures," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-14, November.
    8. S. M. Johnson, 1954. "Optimal two‐ and three‐stage production schedules with setup times included," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 1(1), pages 61-68, March.
    9. M. R. Garey & D. S. Johnson & Ravi Sethi, 1976. "The Complexity of Flowshop and Jobshop Scheduling," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 117-129, May.
    10. Shabtay, Dvir & Zofi, Moshe, 2018. "Single machine scheduling with controllable processing times and an unavailability period to minimize the makespan," International Journal of Production Economics, Elsevier, vol. 198(C), pages 191-200.
    11. Bultmann, Matthias & Knust, Sigrid & Waldherr, Stefan, 2018. "Synchronous flow shop scheduling with pliable jobs," European Journal of Operational Research, Elsevier, vol. 270(3), pages 943-956.
    12. Nowicki, Eugeniusz & Smutnicki, Czeslaw, 1996. "A fast tabu search algorithm for the permutation flow-shop problem," European Journal of Operational Research, Elsevier, vol. 91(1), pages 160-175, May.
    13. James E. Kelley, 1961. "Critical-Path Planning and Scheduling: Mathematical Basis," Operations Research, INFORMS, vol. 9(3), pages 296-320, June.
    14. Choi, Byung-Cheon & Yoon, Suk-Hun & Chung, Sung-Jin, 2007. "Minimizing maximum completion time in a proportionate flow shop with one machine of different speed," European Journal of Operational Research, Elsevier, vol. 176(2), pages 964-974, January.
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    2. Marcello Urgo & Massimo Manzini, 2024. "An upper bound for the inter-exit time of two jobs in an m-machine flow shop," Annals of Operations Research, Springer, vol. 338(1), pages 379-405, July.

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