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Optimal Dynamic Pricing Policies for an M / M / s Queue

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  • David W. Low

    (IBM Scientific Center, Los Angeles, California)

Abstract

We consider the problem of maximizing the long-run average expected reward per unit time in a queuing-reward system, which we formulate as a semi-Markov decision process. Control of the system is effected by increasing or decreasing the price charged for the facility's service in order to discourage or encourage the arrival of customers. We assume that the arrival process is Poisson with arrival rate a strictly decreasing function of the currently advertized price, and that the service times are independent exponentially distributed random variables. The reward structure consists of customer payments and holding costs (possibly nonlinear). At each transition (customer arrival or service completion), the manager of the facility must choose one of a finite number of prices to advertize until the next transition. We show that there exist optimal stationary policies and that each possesses the monotonicity property: the optimal price to advertize is a nondecreasing function of the number of customers in the system. An efficient computational algorithm is developed that, in a finite number of steps, produces a stationary policy that is optimal.

Suggested Citation

  • David W. Low, 1974. "Optimal Dynamic Pricing Policies for an M / M / s Queue," Operations Research, INFORMS, vol. 22(3), pages 545-561, June.
    • Handle: RePEc:inm:oropre:v:22:y:1974:i:3:p:545-561
    DOI: 10.1287/opre.22.3.545
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    Cited by:

    1. Xinchang Wang & Sigrún Andradóttir & Hayriye Ayhan, 2019. "Optimal pricing for tandem queues with finite buffers," Queueing Systems: Theory and Applications, Springer, vol. 92(3), pages 323-396, August.
    2. Baric{s} Ata & Shiri Shneorson, 2006. "Dynamic Control of an M/M/1 Service System with Adjustable Arrival and Service Rates," Management Science, INFORMS, vol. 52(11), pages 1778-1791, November.
    3. Jae‐Dong Son & Yaghoub Khojasteh Ghamari, 2008. "Optimal admission and pricing control problems in service industries with multiple servers and sideline profit," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(4), pages 325-342, July.
    4. Sriram Somanchi & Idris Adjerid & Ralph Gross, 2022. "To Predict or Not to Predict: The Case of the Emergency Department," Production and Operations Management, Production and Operations Management Society, vol. 31(2), pages 799-818, February.
    5. Balcıõglu, Barış & Varol, Yãgız, 2022. "Fair and profitable: How pricing and lead-time quotation policies can help," European Journal of Operational Research, Elsevier, vol. 299(3), pages 977-986.
    6. Omar Besbes & Costis Maglaras, 2009. "Revenue Optimization for a Make-to-Order Queue in an Uncertain Market Environment," Operations Research, INFORMS, vol. 57(6), pages 1438-1450, December.
    7. Vibhanshu Abhishek & Mustafa Dogan & Alexandre Jacquillat, 2021. "Strategic Timing and Dynamic Pricing for Online Resource Allocation," Management Science, INFORMS, vol. 67(8), pages 4880-4907, August.
    8. Constantinos Maglaras, 2006. "Revenue Management for a Multiclass Single-Server Queue via a Fluid Model Analysis," Operations Research, INFORMS, vol. 54(5), pages 914-932, October.
    9. Aktaran-KalaycI, Tûba & Ayhan, Hayriye, 2009. "Sensitivity of optimal prices to system parameters in a steady-state service facility," European Journal of Operational Research, Elsevier, vol. 193(1), pages 120-128, February.
    10. Philipp Afèche & Opher Baron & Yoav Kerner, 2013. "Pricing Time-Sensitive Services Based on Realized Performance," Manufacturing & Service Operations Management, INFORMS, vol. 15(3), pages 492-506, July.
    11. Son, Jae-Dong, 2007. "Customer selection problem with profit from a sideline," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1084-1102, January.
    12. Benioudakis, Myron & Burnetas, Apostolos & Ioannou, George, 2021. "Lead-time quotations in unobservable make-to-order systems with strategic customers: Risk aversion, load control and profit maximization," European Journal of Operational Research, Elsevier, vol. 289(1), pages 165-176.
    13. S. D. Deshmukh & Wayne Winston, 1976. "Stochastic Control of Competition Through Prices," Discussion Papers 205, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    14. Eugene A. Feinberg & Fenghsu Yang, 2016. "Optimal pricing for a GI/M/k/N queue with several customer types and holding costs," Queueing Systems: Theory and Applications, Springer, vol. 82(1), pages 103-120, February.
    15. Noah Gans & Sergei Savin, 2007. "Pricing and Capacity Rationing for Rentals with Uncertain Durations," Management Science, INFORMS, vol. 53(3), pages 390-407, March.
    16. Chen-An Lin & Kevin Shang & Peng Sun, 2023. "Wait Time–Based Pricing for Queues with Customer-Chosen Service Times," Management Science, INFORMS, vol. 69(4), pages 2127-2146, April.

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