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Dynamic Optimization and Learning: How Should a Manager set Prices when the Demand Function is Unknown ?

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  • Alexandre X. Carvalho
  • Martin L. Puterman

Abstract

This paper considers the problem of changing prices over time to maximize expectedrevenues in the presence of unknown demand distribution parameters. It providesand compares several methods that use the sequence of past prices and observeddemands to set price in the current period. A Taylor series expansion of the futurereward function explicitly illustrates the tradeoff between short term revenuemaximization and future information gain and suggests a promising pricing policyreferred to as a one-step look-ahead rule. An in-depth Monte Carlo study comparesseveral different pricing strategies and shows that the one-step look-ahead rulesdominate other heuristic policies and produce good short term performance. Thereasons for the observed bias of parameter estimates are also investigated.

Suggested Citation

  • Alexandre X. Carvalho & Martin L. Puterman, 2005. "Dynamic Optimization and Learning: How Should a Manager set Prices when the Demand Function is Unknown ?," Discussion Papers 1117, Instituto de Pesquisa Econômica Aplicada - IPEA.
    • Handle: RePEc:ipe:ipetds:1117
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    References listed on IDEAS

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    1. William S. Lovejoy, 1990. "Myopic Policies for Some Inventory Models with Uncertain Demand Distributions," Management Science, INFORMS, vol. 36(6), pages 724-738, June.
    2. 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.
    3. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
    4. Easley, David & Kiefer, Nicholas M, 1989. "Optimal Learning with Endogenous Data," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(4), pages 963-978, November.
    5. Martin A. Lariviere & Evan L. Porteus, 1999. "Stalking Information: Bayesian Inventory Management with Unobserved Lost Sales," Management Science, INFORMS, vol. 45(3), pages 346-363, March.
    6. Xiaomei Ding & Martin L. Puterman & Arnab Bisi, 2002. "The Censored Newsvendor and the Optimal Acquisition of Information," Operations Research, INFORMS, vol. 50(3), pages 517-527, June.
    7. James T. Treharne & Charles R. Sox, 2002. "Adaptive Inventory Control for Nonstationary Demand and Partial Information," Management Science, INFORMS, vol. 48(5), pages 607-624, May.
    8. Balvers, Ronald J & Cosimano, Thomas F, 1990. "Actively Learning about Demand and the Dynamics of Price Adjustment," Economic Journal, Royal Economic Society, vol. 100(402), pages 882-898, September.
    9. Kiefer, Nicholas M & Nyarko, Yaw, 1989. "Optimal Control of an Unknown Linear Process with Learning," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(3), pages 571-586, August.
    10. Silver, Edward A. & Rahnama, Mina Rasty, 1987. "Biased selection of the inventory reorder point when demand parameters are statistically estimated," Engineering Costs and Production Economics, Elsevier, vol. 12(1-4), pages 283-292, July.
    11. Chuanpu Hu & William S. Lovejoy & Steven L. Shafer, 1996. "Comparison of Some Suboptimal Control Policies in Medical Drug Therapy," Operations Research, INFORMS, vol. 44(5), pages 696-709, October.
    12. Kirthi Kalyanam, 1996. "Pricing Decisions Under Demand Uncertainty: A Bayesian Mixture Model Approach," Marketing Science, INFORMS, vol. 15(3), pages 207-221.
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    Cited by:

    1. den Boer, Arnoud V., 2015. "Tracking the market: Dynamic pricing and learning in a changing environment," European Journal of Operational Research, Elsevier, vol. 247(3), pages 914-927.
    2. Arnoud V. den Boer, 2014. "Dynamic Pricing with Multiple Products and Partially Specified Demand Distribution," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 863-888, August.

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