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Robust Scheduling to Hedge Against Processing Time Uncertainty in Single-Stage Production

Author

Listed:
  • Richard L. Daniels

    (School of Management, Georgia Institute of Technology, Atlanta, Georgia 30332-0520)

  • Panagiotis Kouvelis

    (Fuqua School of Business, Duke University, Durham, North Carolina 27706)

Abstract

Schedulers confronted with significant processing time uncertainty often discover that a schedule which is optimal with respect to a deterministic or stochastic scheduling model yields quite poor performance when evaluated relative to the actual processing times. In these environments, the notion of schedule robustness, i.e., determining the schedule with the best worst-case performance compared to the corresponding optimal solution over all potential realizations of job processing times, is a more appropriate guide to schedule selection. In this paper, we formalize the robust scheduling concept for scheduling situations with uncertain or variable processing times. To illustrate the development of solution approaches for a robust scheduling problem, we consider a single-machine environment where the performance criterion of interest is the total flow time over all jobs. We define two measures of schedule robustness, formulate the robust scheduling problem, establish its complexity, describe properties of the optimal schedule, and present exact and heuristic solution procedures. Extensive computational results are reported to demonstrate the efficiency and effectiveness of the proposed solution procedures.

Suggested Citation

  • Richard L. Daniels & Panagiotis Kouvelis, 1995. "Robust Scheduling to Hedge Against Processing Time Uncertainty in Single-Stage Production," Management Science, INFORMS, vol. 41(2), pages 363-376, February.
  • Handle: RePEc:inm:ormnsc:v:41:y:1995:i:2:p:363-376
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    File URL: http://dx.doi.org/10.1287/mnsc.41.2.363
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    Citations

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    Cited by:

    1. Ng, Tsan Sheng, 2013. "Robust regret for uncertain linear programs with application to co-production models," European Journal of Operational Research, Elsevier, vol. 227(3), pages 483-493.
    2. Kimms, A, 1998. "Stability Measures for Rolling Schedules with Applications to Capacity Expansion Planning, Master Production Scheduling, and Lot Sizing," Omega, Elsevier, vol. 26(3), pages 355-366, June.
    3. Cao, Qidong & Patterson, J. Wayne & Bai, Xue, 2005. "Reexamination of processing time uncertainty," European Journal of Operational Research, Elsevier, vol. 164(1), pages 185-194, July.
    4. Choi, Byung-Cheon & Chung, Kwanghun, 2016. "Min–max regret version of a scheduling problem with outsourcing decisions under processing time uncertainty," European Journal of Operational Research, Elsevier, vol. 252(2), pages 367-375.
    5. Briskorn, Dirk & Leung, Joseph & Pinedo, Michael, 2008. "Robust scheduling on a single machine usinge time buffers," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 639, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    6. Vairaktarakis, George L., 2000. "Robust multi-item newsboy models with a budget constraint," International Journal of Production Economics, Elsevier, vol. 66(3), pages 213-226, July.
    7. Mausser, Helmut E. & Laguna, Manuel, 1999. "A heuristic to minimax absolute regret for linear programs with interval objective function coefficients," European Journal of Operational Research, Elsevier, vol. 117(1), pages 157-174, August.
    8. Xiong, Jian & Xing, Li-ning & Chen, Ying-wu, 2013. "Robust scheduling for multi-objective flexible job-shop problems with random machine breakdowns," International Journal of Production Economics, Elsevier, vol. 141(1), pages 112-126.
    9. Al-Hinai, Nasr & ElMekkawy, T.Y., 2011. "Robust and stable flexible job shop scheduling with random machine breakdowns using a hybrid genetic algorithm," International Journal of Production Economics, Elsevier, vol. 132(2), pages 279-291, August.
    10. Kimms, Alf, 1996. "Stability measures for rolling schedules with applications to capacity expansion planning, master production scheduling, and lot sizing," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 418, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    11. Aytug, Haldun & Lawley, Mark A. & McKay, Kenneth & Mohan, Shantha & Uzsoy, Reha, 2005. "Executing production schedules in the face of uncertainties: A review and some future directions," European Journal of Operational Research, Elsevier, vol. 161(1), pages 86-110, February.
    12. Abdelhamid Boudjelida, 0. "On the robustness of joint production and maintenance scheduling in presence of uncertainties," Journal of Intelligent Manufacturing, Springer, vol. 0, pages 1-16.
    13. Cowling, Peter & Johansson, Marcus, 2002. "Using real time information for effective dynamic scheduling," European Journal of Operational Research, Elsevier, vol. 139(2), pages 230-244, June.
    14. Wang, Juite, 2004. "A fuzzy robust scheduling approach for product development projects," European Journal of Operational Research, Elsevier, vol. 152(1), pages 180-194, January.
    15. Averbakh, Igor, 2006. "The minmax regret permutation flow-shop problem with two jobs," European Journal of Operational Research, Elsevier, vol. 169(3), pages 761-766, March.
    16. Herroelen, Willy & Leus, Roel, 2005. "Project scheduling under uncertainty: Survey and research potentials," European Journal of Operational Research, Elsevier, vol. 165(2), pages 289-306, September.
    17. Lin, Jun & Ng, Tsan Sheng, 2011. "Robust multi-market newsvendor models with interval demand data," European Journal of Operational Research, Elsevier, vol. 212(2), pages 361-373, July.
    18. Kasperski, Adam & Kurpisz, Adam & Zieliński, Paweł, 2012. "Approximating a two-machine flow shop scheduling under discrete scenario uncertainty," European Journal of Operational Research, Elsevier, vol. 217(1), pages 36-43.
    19. Chang, Zhiqi & Song, Shiji & Zhang, Yuli & Ding, Jian-Ya & Zhang, Rui & Chiong, Raymond, 2017. "Distributionally robust single machine scheduling with risk aversion," European Journal of Operational Research, Elsevier, vol. 256(1), pages 261-274.
    20. repec:spr:annopr:v:248:y:2017:i:1:d:10.1007_s10479-016-2251-z is not listed on IDEAS
    21. Conde, Eduardo, 2012. "On a constant factor approximation for minmax regret problems using a symmetry point scenario," European Journal of Operational Research, Elsevier, vol. 219(2), pages 452-457.
    22. Şeker, Merve & Noyan, Nilay, 2012. "Stochastic optimization models for the airport gate assignment problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(2), pages 438-459.
    23. 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.

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