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Solving Permutation Flow Shop Scheduling Problem with Sequence‐Independent Setup Time

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Listed:
  • Jabrane Belabid
  • Said Aqil
  • Karam Allali

Abstract

In this paper, we study the resolution of a permutation flow shop problem with sequence‐independent setup time. The objective is to minimize the maximum of job completion time, also called the makespan. In this contribution, we propose three methods of resolution, a mixed‐integer linear programming (MILP) model; two heuristics, the first based on Johnson’s rule and the second based on the NEH algorithm; and finally two metaheuristics, the iterative local search algorithm and the iterated greedy algorithm. A set of test problems is simulated numerically to validate the effectiveness of our resolution approaches. For relatively small‐size problems, it has been revealed that the adapted NEH heuristic has the best performance than that of the Johnson‐based heuristic. For the relatively medium and large problems, the comparative study between the two metaheuristics based on the exploration of the neighborhood shows that the iterated greedy algorithm records the best performances.

Suggested Citation

  • Jabrane Belabid & Said Aqil & Karam Allali, 2020. "Solving Permutation Flow Shop Scheduling Problem with Sequence‐Independent Setup Time," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnljam:v:2020:y:2020:i:1:n:7132469
    DOI: 10.1155/2020/7132469
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    References listed on IDEAS

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    2. Koulamas, Christos, 1998. "A new constructive heuristic for the flowshop scheduling problem," European Journal of Operational Research, Elsevier, vol. 105(1), pages 66-71, February.
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    6. Ruiz, Rubén & Maroto, Concepciøn & Alcaraz, Javier, 2006. "Two new robust genetic algorithms for the flowshop scheduling problem," Omega, Elsevier, vol. 34(5), pages 461-476, October.
    7. 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.
    8. 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.
    9. Ruiz, Rubén & Pan, Quan-Ke & Naderi, Bahman, 2019. "Iterated Greedy methods for the distributed permutation flowshop scheduling problem," Omega, Elsevier, vol. 83(C), pages 213-222.
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    Cited by:

    1. Boris Kupriyanov & Alexander Lazarev & Alexander Roschin & Frank Werner, 2025. "On the Recursive Representation of the Permutation Flow and Job Shop Scheduling Problems and Some Extensions," Mathematics, MDPI, vol. 13(19), pages 1-28, October.
    2. Achraf Sayah & Said Aqil & Mohamed Lahby, 2025. "Advanced Metaheuristics for Bi-criteria Optimization in a Distributed Blocking Flow Shop Problem with Setup Times," SN Operations Research Forum, Springer, vol. 6(4), pages 1-63, December.

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