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Dynamic Pricing Strategies for Multi-Product Revenue Management Problems

Author

Listed:
  • Constantinos Maglaras

    (Graduate School of Business, Columbia University)

  • Joern Meissner

    (Department of Management Science, Lancaster University Management School)

Abstract

Consider a firm that owns a fixed capacity of a resource that is consumed in the production or delivery of multiple products. The firm's problem is to maximize its total expected revenues over a finite horizon either by choosing a dynamic pricing strategy for each product, or, if prices are fixed, by selecting a dynamic rule that controls the allocation of capacity to requests for the different products. This paper shows how these well-studied revenue management problems can be reduced to a common formulation where the firm controls the aggregate rate at which all products jointly consume resource capacity. Product-level controls are then chosen to maximize the instantaneous revenues subject to the constraint that they jointly consume capacity at the desired rate. This highlights the common structure of these two problems, and in some cases leads to algorithmic simplifications through the reduction in the control dimension of the associated optimization problems. In addition, we show that this reduction leads to a closed-form solutions of the associated deterministic (fluid) formulation of these problems, which, in turn, suggest several natural static and dynamic pricing heuristics that we analyze asymptotically and through an extensive numerical study. In the context of the former, we show that "resolving" the fluid heuristic achieves asymptotically optimal performance under fluid scaling.

Suggested Citation

  • Constantinos Maglaras & Joern Meissner, 2003. "Dynamic Pricing Strategies for Multi-Product Revenue Management Problems," Working Papers MRG/0002, Department of Management Science, Lancaster University, revised Nov 2005.
  • Handle: RePEc:lms:mansci:mrg-0002
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    References listed on IDEAS

    as
    1. Guillermo Gallego & Garrett van Ryzin, 1994. "Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons," Management Science, INFORMS, vol. 40(8), pages 999-1020, August.
    2. Kalyan Talluri & Garrett van Ryzin, 2004. "Revenue Management Under a General Discrete Choice Model of Consumer Behavior," Management Science, INFORMS, vol. 50(1), pages 15-33, January.
    3. Gabriel Bitran & René Caldentey, 2003. "An Overview of Pricing Models for Revenue Management," Manufacturing & Service Operations Management, INFORMS, vol. 5(3), pages 203-229, August.
    4. Wen Zhao & Yu-Sheng Zheng, 2000. "Optimal Dynamic Pricing for Perishable Assets with Nonhomogeneous Demand," Management Science, INFORMS, vol. 46(3), pages 375-388, March.
    5. Youyi Feng & Baichun Xiao, 2000. "A Continuous-Time Yield Management Model with Multiple Prices and Reversible Price Changes," Management Science, INFORMS, vol. 46(5), pages 644-657, May.
    6. Gustavo Vulcano & Garrett van Ryzin & Costis Maglaras, 2002. "Optimal Dynamic Auctions for Revenue Management," Manufacturing & Service Operations Management, INFORMS, vol. 4(1), pages 7-11.
    7. Gustavo Vulcano & Garrett van Ryzin & Costis Maglaras, 2002. "Optimal Dynamic Auctions for Revenue Management," Management Science, INFORMS, vol. 48(11), pages 1388-1407, November.
    8. Wedad Elmaghraby & P{i}nar Keskinocak, 2003. "Dynamic Pricing in the Presence of Inventory Considerations: Research Overview, Current Practices, and Future Directions," Management Science, INFORMS, vol. 49(10), pages 1287-1309, October.
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    More about this item

    Keywords

    revenue management; dynamic pricing; capacity controls; fluid approximations; efficient frontier;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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