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A combination of flow shop scheduling and the shortest path problem

Author

Listed:
  • Kameng Nip

    (Tsinghua University)

  • Zhenbo Wang

    (Tsinghua University)

  • Fabrice Talla Nobibon

    (KU Leuven)

  • Roel Leus

    (KU Leuven)

Abstract

This paper studies a combinatorial optimization problem which is obtained by combining the flow shop scheduling problem and the shortest path problem. The objective of the obtained problem is to select a subset of jobs that constitutes a feasible solution to the shortest path problem, and to execute the selected jobs on the flow shop machines to minimize the makespan. We argue that this problem is NP-hard even if the number of machines is two, and is NP-hard in the strong sense for the general case. We propose an intuitive approximation algorithm for the case where the number of machines is an input, and an improved approximation algorithm for fixed number of machines.

Suggested Citation

  • Kameng Nip & Zhenbo Wang & Fabrice Talla Nobibon & Roel Leus, 2015. "A combination of flow shop scheduling and the shortest path problem," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 36-52, January.
    • Handle: RePEc:spr:jcomop:v:29:y:2015:i:1:d:10.1007_s10878-013-9670-4
    DOI: 10.1007/s10878-013-9670-4
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    References listed on IDEAS

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    1. Teofilo Gonzalez & Sartaj Sahni, 1978. "Flowshop and Jobshop Schedules: Complexity and Approximation," Operations Research, INFORMS, vol. 26(1), pages 36-52, February.
    2. Arthur Warburton, 1987. "Approximation of Pareto Optima in Multiple-Objective, Shortest-Path Problems," Operations Research, INFORMS, vol. 35(1), pages 70-79, February.
    3. Bo Chen & Celia A. Glass & Chris N. Potts & Vitaly A. Strusevich, 1996. "A New Heuristic for Three-Machine Flow Shop Scheduling," Operations Research, INFORMS, vol. 44(6), pages 891-898, December.
    4. 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.
    5. 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.
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    Cited by:

    1. Yang, Fan & Davari, Morteza & Wei, Wenchao & Hermans, Ben & Leus, Roel, 2022. "Scheduling a single parallel-batching machine with non-identical job sizes and incompatible job families," European Journal of Operational Research, Elsevier, vol. 303(2), pages 602-615.
    2. Li Guan & Jianping Li & Weidong Li & Junran Lichen, 2019. "Improved approximation algorithms for the combination problem of parallel machine scheduling and path," Journal of Combinatorial Optimization, Springer, vol. 38(3), pages 689-697, October.

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