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Heuristic algorithms for the minmax regret flow-shop problem with interval processing times

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  • Michał Ćwik

    (Wroclaw University of Science and Technology)

  • Jerzy Józefczyk

    (Wroclaw University of Science and Technology)

Abstract

An uncertain version of the permutation flow-shop with unlimited buffers and the makespan as a criterion is considered. The investigated parametric uncertainty is represented by given interval-valued processing times. The maximum regret is used for the evaluation of uncertainty. Consequently, the minmax regret discrete optimization problem is solved. Due to its high complexity, two relaxations are applied to simplify the optimization procedure. First of all, a greedy procedure is used for calculating the criterion’s value, as such calculation is NP-hard problem itself. Moreover, the lower bound is used instead of solving the internal deterministic flow-shop. The constructive heuristic algorithm is applied for the relaxed optimization problem. The algorithm is compared with previously elaborated other heuristic algorithms basing on the evolutionary and the middle interval approaches. The conducted computational experiments showed the advantage of the constructive heuristic algorithm with regards to both the criterion and the time of computations. The Wilcoxon paired-rank statistical test confirmed this conclusion.

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  • Michał Ćwik & Jerzy Józefczyk, 2018. "Heuristic algorithms for the minmax regret flow-shop problem with interval processing times," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(1), pages 215-238, March.
    • Handle: RePEc:spr:cejnor:v:26:y:2018:i:1:d:10.1007_s10100-017-0485-8
    DOI: 10.1007/s10100-017-0485-8
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