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Greed Works—Online Algorithms for Unrelated Machine Stochastic Scheduling

Author

Listed:
  • Varun Gupta

    (Booth School of Business, University of Chicago, Chicago, Illinois 60637)

  • Benjamin Moseley

    (Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

  • Marc Uetz

    (Department of Applied Mathematics, University of Twente, 7522 NB Enschede, Netherlands)

  • Qiaomin Xie

    (Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

Abstract

This paper establishes performance guarantees for online algorithms that schedule stochastic, nonpreemptive jobs on unrelated machines to minimize the expected total weighted completion time. Prior work on unrelated machine scheduling with stochastic jobs was restricted to the offline case and required linear or convex programming relaxations for the assignment of jobs to machines. The algorithms introduced in this paper are purely combinatorial. The performance bounds are of the same order of magnitude as those of earlier work and depend linearly on an upper bound on the squared coefficient of variation of the jobs’ processing times. Specifically for deterministic processing times, without and with release times, the competitive ratios are 4 and 6, respectively. As to the technical contribution, this paper shows how dual fitting techniques can be used for stochastic and nonpreemptive scheduling problems.

Suggested Citation

  • Varun Gupta & Benjamin Moseley & Marc Uetz & Qiaomin Xie, 2020. "Greed Works—Online Algorithms for Unrelated Machine Stochastic Scheduling," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 497-516, May.
    • Handle: RePEc:inm:ormoor:v:45:y:2020:i:2:p:497-516
    DOI: 10.1287/moor.2019.0999
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    References listed on IDEAS

    as
    1. Michael H. Rothkopf, 1966. "Scheduling with Random Service Times," Management Science, INFORMS, vol. 12(9), pages 707-713, May.
    2. Megow, N. & Vredeveld, T., 2009. "Approximating preemptive stochastic scheduling," Research Memorandum 054, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    3. 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.
    4. José R. Correa & Maurice Queyranne, 2012. "Efficiency of equilibria in restricted uniform machine scheduling with total weighted completion time as social cost," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(5), pages 384-395, August.
    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. 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.
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    Cited by:

    1. Tugba Saraç & Feristah Ozcelik & Mehmet Ertem, 2023. "Unrelated parallel machine scheduling problem with stochastic sequence dependent setup times," Operational Research, Springer, vol. 23(3), pages 1-19, September.

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