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A Partially Observed Markov Decision Process for Dynamic Pricing

Author

Listed:
  • Yossi Aviv

    (Olin School of Business, Washington University, St. Louis, Missouri 63130)

  • Amit Pazgal

    (Olin School of Business, Washington University, St. Louis, Missouri 63130)

Abstract

In this paper, we develop a stylized partially observed Markov decision process (POMDP) framework to study a dynamic pricing problem faced by sellers of fashion-like goods. We consider a retailer that plans to sell a given stock of items during a finite sales season. The objective of the retailer is to dynamically price the product in a way that maximizes expected revenues. Our model brings together various types of uncertainties about the demand, some of which are resolvable through sales observations. We develop a rigorous upper bound for the seller's optimal dynamic decision problem and use it to propose an active-learning heuristic pricing policy. We conduct a numerical study to test the performance of four different heuristic dynamic pricing policies in order to gain insight into several important managerial questions that arise in the context of revenue management.

Suggested Citation

  • Yossi Aviv & Amit Pazgal, 2005. "A Partially Observed Markov Decision Process for Dynamic Pricing," Management Science, INFORMS, vol. 51(9), pages 1400-1416, September.
  • Handle: RePEc:inm:ormnsc:v:51:y:2005:i:9:p:1400-1416
    DOI: 10.1287/mnsc.1050.0393
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    References listed on IDEAS

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    1. William S. Lovejoy, 1991. "Computationally Feasible Bounds for Partially Observed Markov Decision Processes," Operations Research, INFORMS, vol. 39(1), pages 162-175, February.
    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. Lode Li, 1988. "A Stochastic Theory of the Firm," Mathematics of Operations Research, INFORMS, vol. 13(3), pages 447-466, August.
    4. 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.
    5. Richard D. Smallwood & Edward J. Sondik, 1973. "The Optimal Control of Partially Observable Markov Processes over a Finite Horizon," Operations Research, INFORMS, vol. 21(5), pages 1071-1088, October.
    6. 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.
    7. Jing-Sheng Song & Paul Zipkin, 1993. "Inventory Control in a Fluctuating Demand Environment," Operations Research, INFORMS, vol. 41(2), pages 351-370, April.
    8. George E. Monahan, 1982. "State of the Art---A Survey of Partially Observable Markov Decision Processes: Theory, Models, and Algorithms," Management Science, INFORMS, vol. 28(1), pages 1-16, January.
    9. William S. Lovejoy, 1993. "Suboptimal Policies, with Bounds, for Parameter Adaptive Decision Processes," Operations Research, INFORMS, vol. 41(3), pages 583-599, June.
    10. Awi Federgruen & Aliza Heching, 1999. "Combined Pricing and Inventory Control Under Uncertainty," Operations Research, INFORMS, vol. 47(3), pages 454-475, June.
    11. Suresh P. Sethi & Feng Cheng, 1997. "Optimality of ( s , S ) Policies in Inventory Models with Markovian Demand," Operations Research, INFORMS, vol. 45(6), pages 931-939, December.
    12. White, Chelsea C. & White, Douglas J., 1989. "Markov decision processes," European Journal of Operational Research, Elsevier, vol. 39(1), pages 1-16, March.
    13. Gabriel R. Bitran & Susana V. Mondschein, 1997. "Periodic Pricing of Seasonal Products in Retailing," Management Science, INFORMS, vol. 43(1), pages 64-79, January.
    14. Chelsea C. White & William T. Scherer, 1989. "Solution Procedures for Partially Observed Markov Decision Processes," Operations Research, INFORMS, vol. 37(5), pages 791-797, October.
    15. David J. Braden & Shmuel S. Oren, 1994. "Nonlinear Pricing to Produce Information," Marketing Science, INFORMS, vol. 13(3), pages 310-326.
    16. 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.
    17. Serhan Ziya & Hayriye Ayhan & Robert D. Foley, 2004. "Relationships Among Three Assumptions in Revenue Management," Operations Research, INFORMS, vol. 52(5), pages 804-809, October.
    18. 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.
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