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Revenue Management for a Multiclass Single-Server Queue via a Fluid Model Analysis

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  • Constantinos Maglaras

    (Columbia Business School, Columbia University, 409 Uris Hall, 3022 Broadway, New York, New York 10027)

Abstract

Motivated by the recent adoption of tactical pricing strategies in manufacturing settings, this paper studies a problem of dynamic pricing for a multiproduct make-to-order system. Specifically, for a multiclass M n / M /1 queue with controllable arrival rates, general demand curves, and linear holding costs, we study the problem of maximizing the expected revenues minus holding costs by selecting a pair of dynamic pricing and sequencing policies. Using a deterministic and continuous (fluid model) relaxation of this problem, which can be justified asymptotically as the capacity and the potential demand grow large, we show the following: (i) greedy sequencing (i.e., the c (mu)-rule) is optimal, (ii) the optimal pricing and sequencing decisions decouple in finite time, after which (iii) the system evolution and thus the optimal prices depend only on the total workload. Building on (i)--(iii), we propose a one-dimensional workload relaxation to the fluid pricing problem that is simpler to analyze, and leads to intuitive and implementable pricing heuristics. Numerical results illustrate the near-optimal performance of the fluid heuristics and the benefits from dynamic pricing.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:54:y:2006:i:5:p:914-932
    DOI: 10.1287/opre.1060.0305
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    References listed on IDEAS

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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. A. Piunovskiy, 2009. "Random walk, birth-and-death process and their fluid approximations: absorbing case," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(2), pages 285-312, October.
    3. Shuo Wang & Xiuli Xu, 2021. "Equilibrium strategies of the fluid queue with working vacation," Operational Research, Springer, vol. 21(2), pages 1211-1228, June.
    4. Yiwei Chen & Vivek F. Farias, 2013. "Simple Policies for Dynamic Pricing with Imperfect Forecasts," Operations Research, INFORMS, vol. 61(3), pages 612-624, June.
    5. Jiaqi Zhou & Ilya O. Ryzhov, 2021. "Equilibrium analysis of observable express service with customer choice," Queueing Systems: Theory and Applications, Springer, vol. 99(3), pages 243-281, December.
    6. Constantinos Maglaras & Joern Meissner, 2006. "Dynamic Pricing Strategies for Multiproduct Revenue Management Problems," Manufacturing & Service Operations Management, INFORMS, vol. 8(2), pages 136-148, July.
    7. Sabri Çelik & Costis Maglaras, 2008. "Dynamic Pricing and Lead-Time Quotation for a Multiclass Make-to-Order Queue," Management Science, INFORMS, vol. 54(6), pages 1132-1146, June.
    8. 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.
    9. Mustafa Akan & Barı ş Ata & Tava Olsen, 2012. "Congestion-Based Lead-Time Quotation for Heterogenous Customers with Convex-Concave Delay Costs: Optimality of a Cost-Balancing Policy Based on Convex Hull Functions," Operations Research, INFORMS, vol. 60(6), pages 1505-1519, December.
    10. 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.
    11. Marketa Kubickova, 2022. "Revenue management in manufacturing: systematic review of literature," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 21(2), pages 147-152, April.

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