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Minimizing worst-case and average-case makespan over scenarios

Author

Listed:
  • Esteban Feuerstein

    (Universidad de Buenos Aires)

  • Alberto Marchetti-Spaccamela

    (Sapienza Università di Roma)

  • Frans Schalekamp

    (Cornell University)

  • René Sitters

    (Vrije Universiteit & CWI)

  • Suzanne Ster

    (Technische Universität München)

  • Leen Stougie

    (Vrije Universiteit & CWI)

  • Anke Zuylen

    (College of William and Mary)

Abstract

We consider scheduling problems over scenarios where the goal is to find a single assignment of the jobs to the machines which performs well over all scenarios in an explicitly given set. Each scenario is a subset of jobs that must be executed in that scenario. The two objectives that we consider are minimizing the maximum makespan over all scenarios and minimizing the sum of the makespans of all scenarios. For both versions, we give several approximation algorithms and lower bounds on their approximability. We also consider some (easier) special cases. Combinatorial optimization problems under scenarios in general, and scheduling problems under scenarios in particular, have seen only limited research attention so far. With this paper, we make a step in this interesting research direction.

Suggested Citation

  • Esteban Feuerstein & Alberto Marchetti-Spaccamela & Frans Schalekamp & René Sitters & Suzanne Ster & Leen Stougie & Anke Zuylen, 2017. "Minimizing worst-case and average-case makespan over scenarios," Journal of Scheduling, Springer, vol. 20(6), pages 545-555, December.
    • Handle: RePEc:spr:jsched:v:20:y:2017:i:6:d:10.1007_s10951-016-0484-y
    DOI: 10.1007/s10951-016-0484-y
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    References listed on IDEAS

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    1. Patrick Jaillet, 1988. "A Priori Solution of a Traveling Salesman Problem in Which a Random Subset of the Customers Are Visited," Operations Research, INFORMS, vol. 36(6), pages 929-936, December.
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    Cited by:

    1. Shabtay, Dvir & Gilenson, Miri, 2023. "A state-of-the-art survey on multi-scenario scheduling," European Journal of Operational Research, Elsevier, vol. 310(1), pages 3-23.
    2. Haimin Lu & Zhi Pei, 2024. "A distributionally robust approach for the two-machine permutation flow shop scheduling," Annals of Operations Research, Springer, vol. 338(1), pages 709-739, July.
    3. Zhang, Xiechen & Angel, Eric & Chu, Feng & Regnault, Damien, 2025. "Minimizing total completion time and makespan for a multi-scenario bi-criteria parallel machine scheduling problem," European Journal of Operational Research, Elsevier, vol. 321(2), pages 397-406.
    4. Attila Bódis & János Balogh, 2019. "Bin packing problem with scenarios," 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. 27(2), pages 377-395, June.

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