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Stochastic scheduling to minimize expected maximum lateness

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  • Wu, Xianyi
  • Zhou, Xian

Abstract

This paper is concerned with the problems in scheduling a set of jobs associated with random due dates on a single machine so as to minimize the expected maximum lateness in stochastic environment. This is a difficult problem and few efforts have been reported on its solution in the literature. In this paper, we first derive a deterministic equivalent to the expected maximum lateness and then propose a dynamic programming algorithm to obtain the optimal solutions. The procedures to compute optimal solutions are initially developed in the case of deterministic processing times, and then extended to stochastic processing times following arbitrary probability distributions. Moreover, several heuristic rules are suggested to compute near-optimal solutions, which are shown to be highly efficient and accurate by computer-based experiments.

Suggested Citation

  • Wu, Xianyi & Zhou, Xian, 2008. "Stochastic scheduling to minimize expected maximum lateness," European Journal of Operational Research, Elsevier, vol. 190(1), pages 103-115, October.
    • Handle: RePEc:eee:ejores:v:190:y:2008:i:1:p:103-115
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    References listed on IDEAS

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    1. Sartaj Sahni, 1979. "Preemptive Scheduling with Due Dates," Operations Research, INFORMS, vol. 27(5), pages 925-934, October.
    2. Slowinski, Roman, 1984. "Preemptive scheduling of independent jobs on parallel machines subject to financial constraints," European Journal of Operational Research, Elsevier, vol. 15(3), pages 366-373, March.
    3. E. L. Lawler, 1973. "Optimal Sequencing of a Single Machine Subject to Precedence Constraints," Management Science, INFORMS, vol. 19(5), pages 544-546, January.
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    Cited by:

    1. Chang, Zhiqi & Ding, Jian-Ya & Song, Shiji, 2019. "Distributionally robust scheduling on parallel machines under moment uncertainty," European Journal of Operational Research, Elsevier, vol. 272(3), pages 832-846.
    2. Guhlich, Hendrik & Fleischmann, Moritz & Mönch, Lars & Stolletz, Raik, 2018. "A clearing function based bid-price approach to integrated order acceptance and release decisions," European Journal of Operational Research, Elsevier, vol. 268(1), pages 243-254.
    3. Senay Solak & Gustaf Solveling & John-Paul B. Clarke & Ellis L. Johnson, 2018. "Stochastic Runway Scheduling," Transportation Science, INFORMS, vol. 52(4), pages 917-940, August.
    4. Sun, Jing & Yamamoto, Hisashi & Matsui, Masayuki, 2020. "Horizontal integration management: An optimal switching model for parallel production system with multiple periods in smart supply chain environment," International Journal of Production Economics, Elsevier, vol. 221(C).
    5. Pei, Zhi & Lu, Haimin & Jin, Qingwei & Zhang, Lianmin, 2022. "Target-based distributionally robust optimization for single machine scheduling," European Journal of Operational Research, Elsevier, vol. 299(2), pages 420-431.
    6. M. Urgo & J. Váncza, 2019. "A branch-and-bound approach for the single machine maximum lateness stochastic scheduling problem to minimize the value-at-risk," Flexible Services and Manufacturing Journal, Springer, vol. 31(2), pages 472-496, June.
    7. 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.

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