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Monotone Optimal Policies for a Transient Queueing Staffing Problem

Author

Listed:
  • Michael C. Fu

    (Robert H. Smith School of Business, University of Maryland, College Park, Maryland 20742)

  • Steven I. Marcus

    (Department of Electrical Engineering, University of Maryland, College Park, Maryland 20742)

  • I-Jeng Wang

    (The Johns Hopkins University Applied Physics Laboratory, Laurel, Maryland 20723)

Abstract

We consider the problem of determining the optimal policy for staffing a queueing system over multiple periods, using a model that takes into account transient queueing effects. Formulating the problem in a dynamic programming setting, we show that the optimal policy follows a monotone optimal control by establishing the submodularity of the objective function with respect to the staffing level and initial queue size in a period. In particular, this requires proving that the system occupancy in a G/M/s queue is submodular in the number of servers and initial system occupancy.

Suggested Citation

  • Michael C. Fu & Steven I. Marcus & I-Jeng Wang, 2000. "Monotone Optimal Policies for a Transient Queueing Staffing Problem," Operations Research, INFORMS, vol. 48(2), pages 327-331, April.
    • Handle: RePEc:inm:oropre:v:48:y:2000:i:2:p:327-331
    DOI: 10.1287/opre.48.2.327.13375
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    Cited by:

    1. Nasuh Buyukkaramikli & Henny Ooijen & J. Bertrand, 2015. "Integrating inventory control and capacity management at a maintenance service provider," Annals of Operations Research, Springer, vol. 231(1), pages 185-206, August.
    2. Niyirora, Jerome & Zhuang, Jun, 2017. "Fluid approximations and control of queues in emergency departments," European Journal of Operational Research, Elsevier, vol. 261(3), pages 1110-1124.
    3. Gabriel Zayas-Cabán & Mark E. Lewis, 2020. "Admission control in a two-class loss system with periodically varying parameters and abandonments," Queueing Systems: Theory and Applications, Springer, vol. 94(1), pages 175-210, February.
    4. Li Xiao & Susan H. Xu & David D. Yao & Hanqin Zhang, 2022. "Optimal staffing for ticket queues," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 309-351, October.
    5. Jerome Niyirora & Jamol Pender, 2016. "Optimal staffing in nonstationary service centers with constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(8), pages 615-630, December.
    6. Nasuh Buyukkaramikli & J. Bertrand & Henny Ooijen, 2013. "Flexible hiring in a make to order system with parallel processing units," Annals of Operations Research, Springer, vol. 209(1), pages 159-178, October.
    7. Noah Gans & Ger Koole & Avishai Mandelbaum, 2003. "Telephone Call Centers: Tutorial, Review, and Research Prospects," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 79-141, September.
    8. Zhe George Zhang, 2009. "Performance Analysis of a Queue with Congestion-Based Staffing Policy," Management Science, INFORMS, vol. 55(2), pages 240-251, February.
    9. Defraeye, Mieke & Van Nieuwenhuyse, Inneke, 2016. "Staffing and scheduling under nonstationary demand for service: A literature review," Omega, Elsevier, vol. 58(C), pages 4-25.

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