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Solution algorithms for unrelated machines minmax regret scheduling problem with interval processing times and the total flow time criterion

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  • Marcin Siepak
  • Jerzy Józefczyk

Abstract

An uncertain version of the task scheduling problem on unrelated machines to minimize the total flow time is considered. It is assumed that processing times are not known a priori, but they belong to intervals of known bounds. The absolute regret is applied to evaluate the uncertainty, and minmax regret task scheduling problem is solved. A simple 2-approximate middle intervals time efficient algorithm is proposed. More time consuming but better in terms of the quality of solutions scatter search based heuristic algorithm is described. Its usefulness is justified via computational experiments. Copyright The Author(s) 2014

Suggested Citation

  • Marcin Siepak & Jerzy Józefczyk, 2014. "Solution algorithms for unrelated machines minmax regret scheduling problem with interval processing times and the total flow time criterion," Annals of Operations Research, Springer, vol. 222(1), pages 517-533, November.
    • Handle: RePEc:spr:annopr:v:222:y:2014:i:1:p:517-533:10.1007/s10479-014-1538-1
    DOI: 10.1007/s10479-014-1538-1
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    References listed on IDEAS

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    1. W. A. Horn, 1973. "Technical Note—Minimizing Average Flow Time with Parallel Machines," Operations Research, INFORMS, vol. 21(3), pages 846-847, June.
    2. Nowicki, Eugeniusz & Smutnicki, Czeslaw, 2006. "Some aspects of scatter search in the flow-shop problem," European Journal of Operational Research, Elsevier, vol. 169(2), pages 654-666, March.
    3. Kasperski, Adam & Zielinski, Pawel, 2010. "Minmax regret approach and optimality evaluation in combinatorial optimization problems with interval and fuzzy weights," European Journal of Operational Research, Elsevier, vol. 200(3), pages 680-687, February.
    4. Aissi, Hassene & Bazgan, Cristina & Vanderpooten, Daniel, 2009. "Min-max and min-max regret versions of combinatorial optimization problems: A survey," European Journal of Operational Research, Elsevier, vol. 197(2), pages 427-438, September.
    5. A Corberán & E Fernández & M Laguna & R Martí, 2002. "Heuristic solutions to the problem of routing school buses with multiple objectives," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(4), pages 427-435, April.
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    Cited by:

    1. Zhi Pei & Mingzhong Wan & Ziteng Wang, 2020. "A new approximation algorithm for unrelated parallel machine scheduling with release dates," Annals of Operations Research, Springer, vol. 285(1), pages 397-425, February.
    2. 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.

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