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Minimizing maximum cost for a single machine under uncertainty of processing times

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  • Fridman, Ilia
  • Pesch, Erwin
  • Shafransky, Yakov

Abstract

One of the most known results in the machine scheduling is Lawler’s algorithm to minimize the maximum cost of jobs processed by a single machine subject to precedence constraints. We consider an uncertain version of the same min-max cost scheduling problem. The cost function of each job depends on the job completion time and on an additional generalized numerical parameter, which may be a tuple of parameters. For each job, both, its processing time and the additional parameter are uncertain, only intervals of possible values of these parameters are known.

Suggested Citation

  • Fridman, Ilia & Pesch, Erwin & Shafransky, Yakov, 2020. "Minimizing maximum cost for a single machine under uncertainty of processing times," European Journal of Operational Research, Elsevier, vol. 286(2), pages 444-457.
    • Handle: RePEc:eee:ejores:v:286:y:2020:i:2:p:444-457
    DOI: 10.1016/j.ejor.2020.03.052
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    References listed on IDEAS

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    1. Chanas, Stefan & Kasperski, Adam, 2003. "On two single machine scheduling problems with fuzzy processing times and fuzzy due dates," European Journal of Operational Research, Elsevier, vol. 147(2), pages 281-296, June.
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    5. Nadia Brauner & Gerd Finke & Yakov Shafransky, 2017. "Lawler’s minmax cost problem under uncertainty," Journal of Combinatorial Optimization, Springer, vol. 34(1), pages 31-46, July.
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    Cited by:

    1. Dung-Ying Lin & Tzu-Yun Huang, 2021. "A Hybrid Metaheuristic for the Unrelated Parallel Machine Scheduling Problem," Mathematics, MDPI, vol. 9(7), pages 1-20, April.
    2. Matthew Bold & Marc Goerigk, 2025. "Recoverable robust single machine scheduling with polyhedral uncertainty," Journal of Scheduling, Springer, vol. 28(3), pages 269-287, June.

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