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On the Asymptotic Optimality of a Simple On-Line Algorithm for the Stochastic Single-Machine Weighted Completion Time Problem and Its Extensions

Author

Listed:
  • Mabel C. Chou

    (Department of Decision Sciences, National University of Singapore, 117591 Singapore)

  • Hui Liu

    (Verizon Laboratories, Boston, Massachusetts)

  • Maurice Queyranne

    (Sauder School of Business, University of British Columbia, Vancouver, British Columbia, Canada)

  • David Simchi-Levi

    (Engineering Systems Division and the Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

We consider the stochastic single-machine problem, when the objective is to minimize the expected total weighted completion time of a set of jobs that are released over time. We assume that the existence and the parameters of each job including its release date, weight, and expected processing times are not known until its release date. The actual processing times are not known until processing is completed. We analyze the performance of the on-line nonpreemptive weighted shortest expected processing time among available jobs (WSEPTA) heuristic. When a scheduling decision needs to be made, this heuristic assigns, among the jobs that have arrived but not yet processed, one with the largest ratio of its weight to its expected processing time. We prove that when the job weights and processing times are bounded and job processing times are mutually independent random variables, WSEPTA is asymptotically optimal for the single-machine problem. This implies that WSEPTA generates a solution whose relative error approaches zero as the number of jobs increases. This result can be extended to the stochastic flow shop and open shop problems, as well as models with stochastic job weights.

Suggested Citation

  • Mabel C. Chou & Hui Liu & Maurice Queyranne & David Simchi-Levi, 2006. "On the Asymptotic Optimality of a Simple On-Line Algorithm for the Stochastic Single-Machine Weighted Completion Time Problem and Its Extensions," Operations Research, INFORMS, vol. 54(3), pages 464-474, June.
    • Handle: RePEc:inm:oropre:v:54:y:2006:i:3:p:464-474
    DOI: 10.1287/opre.1060.0270
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    References listed on IDEAS

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    1. Michael H. Rothkopf, 1966. "Scheduling with Random Service Times," Management Science, INFORMS, vol. 12(9), pages 707-713, May.
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    5. Philip Kaminsky & David Simchi-Levi, 1998. "Probabilistic Analysis and Practical Algorithms for the Flow Shop Weighted Completion Time Problem," Operations Research, INFORMS, vol. 46(6), pages 872-882, December.
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    Cited by:

    1. Shen, Zuo-Jun Max & Xie, Jingui & Zheng, Zhichao & Zhou, Han, 2023. "Dynamic scheduling with uncertain job types," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1047-1060.
    2. Nicole Megow & Tjark Vredeveld, 2014. "A Tight 2-Approximation for Preemptive Stochastic Scheduling," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1297-1310, November.
    3. Manzhan Gu & Xiwen Lu & Jinwei Gu, 2017. "An asymptotically optimal algorithm for large-scale mixed job shop scheduling to minimize the makespan," Journal of Combinatorial Optimization, Springer, vol. 33(2), pages 473-495, February.
    4. Manzhan Gu & Xiwen Lu, 2011. "Asymptotical optimality of WSEPT for stochastic online scheduling on uniform machines," Annals of Operations Research, Springer, vol. 191(1), pages 97-113, November.
    5. Megow, N. & Vredeveld, T., 2009. "Approximating preemptive stochastic scheduling," Research Memorandum 054, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    6. Xiaoyan Zhang & Ran Ma & Jian Sun & Zan-Bo Zhang, 0. "Randomized selection algorithm for online stochastic unrelated machines scheduling," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-16.
    7. Vredeveld, T., 2009. "Stochastic Online Scheduling," Research Memorandum 052, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    8. Huiqiao Su & Guohua Wan & Shan Wang, 2019. "Online scheduling for outpatient services with heterogeneous patients and physicians," Journal of Combinatorial Optimization, Springer, vol. 37(1), pages 123-149, January.
    9. Megow, N. & Vredeveld, T., 2006. "Approximation results for preemptive stochastic online scheduling," Research Memorandum 053, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    10. Nicole Megow & Marc Uetz & Tjark Vredeveld, 2006. "Models and Algorithms for Stochastic Online Scheduling," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 513-525, August.
    11. Xiaoyan Zhang & Ran Ma & Jian Sun & Zan-Bo Zhang, 2022. "Randomized selection algorithm for online stochastic unrelated machines scheduling," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1796-1811, October.
    12. Martin Skutella & Maxim Sviridenko & Marc Uetz, 2016. "Unrelated Machine Scheduling with Stochastic Processing Times," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 851-864, August.
    13. Rowan Wang & Oualid Jouini & Saif Benjaafar, 2014. "Service Systems with Finite and Heterogeneous Customer Arrivals," Manufacturing & Service Operations Management, INFORMS, vol. 16(3), pages 365-380, July.

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