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Dynamic Pricing Strategies for Multi-Product Revenue Management Problems


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  • Constantinos Maglaras

    (Graduate School of Business, Columbia University)

  • Joern Meissner

    (Department of Management Science, Lancaster University Management School)


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.

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Bibliographic Info

Paper provided by Department of Management Science, Lancaster University in its series Working Papers with number MRG/0002.

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Length: 13 pages
Date of creation: Jul 2003
Date of revision: Nov 2005
Publication status: Published in Manufacturing and Service Operations Management (MSOM) Vol 8, No 2 (Spring 2006), pp 136-148.
Handle: RePEc:lms:mansci:mrg-0002

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

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  1. 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.
  2. 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.
  3. 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.
  4. 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.
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Cited by:
  1. Sumit Kunnumkal & Kalyan Talluri, 2014. "On the Tractability of the Piecewiselinear Approximation for General Discrete-Choice Network Revenue Management," Working Papers 749, Barcelona Graduate School of Economics.
  2. Berk, Emre & Gürler, Ülkü & YIldIrIm, Gonca, 2009. "On pricing of perishable assets with menu costs," International Journal of Production Economics, Elsevier, vol. 121(2), pages 678-699, October.
  3. Weaver, Robert D. & Moon, Yongma, 2011. "Pricing Perishables," 2011 International European Forum, February 14-18, 2011, Innsbruck-Igls, Austria 122007, International European Forum on Innovation and System Dynamics in Food Networks.
  4. Kuo, Chia-Wei & Huang, Kwei-Long, 2012. "Dynamic pricing of limited inventories for multi-generation products," European Journal of Operational Research, Elsevier, vol. 217(2), pages 394-403.
  5. Grigoriev Alexander & Hiller Benjamin & Marbán Sebastián & Vredeveld Tjark & Zwaan Ruben van der, 2010. "Dynamic Pricing Problems with Elastic Demand," Research Memorandum 053, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  6. Burkart, Wolfgang R. & Klein, Robert & Mayer, Stefan, 2012. "Product line pricing for services with capacity constraints and dynamic substitution," European Journal of Operational Research, Elsevier, vol. 219(2), pages 347-359.
  7. Sumit Kunnumkal & Kalyan Talluri, 2014. "On the tractability of the piecewise-linear approximation for general discrete-choice network revenue management," Economics Working Papers 1409, Department of Economics and Business, Universitat Pompeu Fabra.


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