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An approximation scheme for the bi-scenario sum of completion times trade-off problem

Author

Listed:
  • Miri Gilenson

    (Ben Gurion University)

  • Hussein Naseraldin

    (ORT Braude College of Engineering)

  • Liron Yedidsion

    (Technion)

Abstract

An influential aspect of any scheduling problem is the processing time of the tasks (jobs), which can be deterministic, stochastic, or even uncertain. Scheduling according to unique and known processing times (a.k.a. nominal values) may be naïve, since many production systems are subject to inherent uncertainty. We offer a novel approach for scheduling under uncertainty, inspired by scenario-based optimization. This new approach copes with uncertainty by simultaneously optimizing a given scheduling criterion under two different scenarios of processing times. We term the new problem the bi-scenario trade-off problem. We study the sum of completion times criterion for which we develop a 2-approximation algorithm and show that it is asymptotically tight. We use this approximation to develop the polynomial time approximation scheme that approximates the Pareto-optimal set of solutions and introduce data-dependent analysis to examine the sensitivity of the model parameters.

Suggested Citation

  • Miri Gilenson & Hussein Naseraldin & Liron Yedidsion, 2019. "An approximation scheme for the bi-scenario sum of completion times trade-off problem," Journal of Scheduling, Springer, vol. 22(3), pages 289-304, June.
    • Handle: RePEc:spr:jsched:v:22:y:2019:i:3:d:10.1007_s10951-018-0588-7
    DOI: 10.1007/s10951-018-0588-7
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    References listed on IDEAS

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    1. Hoogeveen, Han, 2005. "Multicriteria scheduling," European Journal of Operational Research, Elsevier, vol. 167(3), pages 592-623, December.
    2. Wayne E. Smith, 1956. "Various optimizers for single‐stage production," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 59-66, March.
    3. Shashi Mittal & Andreas S. Schulz, 2013. "A General Framework for Designing Approximation Schemes for Combinatorial Optimization Problems with Many Objectives Combined into One," Operations Research, INFORMS, vol. 61(2), pages 386-397, April.
    4. Jian Yang & Gang Yu, 2002. "On the Robust Single Machine Scheduling Problem," Journal of Combinatorial Optimization, Springer, vol. 6(1), pages 17-33, March.
    5. Leslie A. Hall & Andreas S. Schulz & David B. Shmoys & Joel Wein, 1997. "Scheduling to Minimize Average Completion Time: Off-Line and On-Line Approximation Algorithms," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 513-544, August.
    6. Michael Masin & Yossi Bukchin, 2008. "Diversity Maximization Approach for Multiobjective Optimization," Operations Research, INFORMS, vol. 56(2), pages 411-424, April.
    7. Uttarayan Bagchi, 1989. "Simultaneous Minimization of Mean and Variation of Flow Time and Waiting Time in Single Machine Systems," Operations Research, INFORMS, vol. 37(1), pages 118-125, February.
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