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Scheduling with Random Service Times

Author

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  • Michael H. Rothkopf

    (Massachusetts Institute of Technology)

Abstract

This paper considers the problem scheduling of m immediately available tasks with random variable service times. It is shown that certain such problems can be reduced to equivalent deterministic problems. The existence of optimal schedules not involving the removal from service of incompletely processed tasks for some problems is proved and for other problems is disproved.

Suggested Citation

  • Michael H. Rothkopf, 1966. "Scheduling with Random Service Times," Management Science, INFORMS, vol. 12(9), pages 707-713, May.
    • Handle: RePEc:inm:ormnsc:v:12:y:1966:i:9:p:707-713
    DOI: 10.1287/mnsc.12.9.707
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    Cited by:

    1. Santiago R. Balseiro & David B. Brown, 2019. "Approximations to Stochastic Dynamic Programs via Information Relaxation Duality," Operations Research, INFORMS, vol. 67(2), pages 577-597, March.
    2. Baker, Kenneth R., 2014. "Minimizing earliness and tardiness costs in stochastic scheduling," European Journal of Operational Research, Elsevier, vol. 236(2), pages 445-452.
    3. Marbán Sebastián & Rutten Cyriel & Vredeveld Tjark, 2010. "Asymptotic optimality of SEPT in Bayesian Scheduling," Research Memorandum 051, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    4. Szmerekovsky, Joseph G., 2007. "Single machine scheduling under market uncertainty," European Journal of Operational Research, Elsevier, vol. 177(1), pages 163-175, February.
    5. Ruben Hoeksma & Marc Uetz, 2016. "Optimal Mechanism Design for a Sequencing Problem with Two-Dimensional Types," Operations Research, INFORMS, vol. 64(6), pages 1438-1450, December.
    6. V. Rattini, 2016. "Managing the Workload: an Experiment on Individual Decision Making and Performance," Working Papers wp1080, Dipartimento Scienze Economiche, Universita' di Bologna.
    7. 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.
    8. Xiaoqiang Cai & Xiaoqian Sun & Xian Zhou, 2004. "Stochastic scheduling subject to machine breakdowns: The preemptive‐repeat model with discounted reward and other criteria," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(6), pages 800-817, September.
    9. Uetz, M.J., 2002. "When greediness fails: examples from stochastic scheduling," Research Memorandum 067, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    10. Bertsimas, Dimitris., 1995. "The achievable region method in the optimal control of queueing systems : formulations, bounds and policies," Working papers 3837-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    11. 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.
    12. Marban, S. & Rutten, C. & Vredeveld, T., 2010. "Asymptotic optimality of SEPT in Bayesian scheduling," Research Memorandum 050, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    13. 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.
    14. José Niño-Mora, 2000. "Beyond Smith's rule: An optimal dynamic index, rule for single machine stochastic scheduling with convex holding costs," Economics Working Papers 514, Department of Economics and Business, Universitat Pompeu Fabra.
    15. Carlo Meloni & Marco Pranzo, 2020. "Expected shortfall for the makespan in activity networks under imperfect information," Flexible Services and Manufacturing Journal, Springer, vol. 32(3), pages 668-692, September.
    16. Megow, N. & Vredeveld, T., 2009. "Approximating preemptive stochastic scheduling," Research Memorandum 054, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    17. Brian C. Dean & Michel X. Goemans & Jan Vondrák, 2008. "Approximating the Stochastic Knapsack Problem: The Benefit of Adaptivity," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 945-964, November.
    18. Mandelbaum, Marvin & Hlynka, Myron, 2003. "Job sequencing using an expert," International Journal of Production Economics, Elsevier, vol. 85(3), pages 389-401, September.
    19. Vredeveld, T., 2009. "Stochastic Online Scheduling," Research Memorandum 052, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    20. 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.
    21. Marban, S. & Rutten, C. & Vredeveld, T., 2010. "Tight performance in Bayesian scheduling," Research Memorandum 052, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    22. Forst, Frank G., 1995. "Bicriterion stochastic scheduling on one or more machines," European Journal of Operational Research, Elsevier, vol. 80(2), pages 404-409, January.
    23. 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.
    24. José Niño-Mora, 2007. "Dynamic priority allocation via restless bandit marginal productivity indices," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(2), pages 161-198, December.

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