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Dynamic Pricing via Dynamic Programming1

Author

Listed:
  • Y. Y. Fan

    (University of California)

  • H. K. Bhargava

    (University of California)

  • H. H. Natsuyama

    (California State University)

Abstract

This article specifies an efficient numerical scheme for computing optimal dynamic prices in a setting where the demand in a given period depends on the price in that period, cumulative sales up to the current period, and remaining market potential. The problem is studied in a deterministic and monopolistic context with a general form of the demand function. While traditional approaches produce closed-form equations that are difficult to solve due to the boundary conditions, we specify a computationally tractable numerical procedure by converting the problem to an initial-value problem based on a dynamic programming formulation. We find also that the optimal price dynamics preserves certain properties over the planning horizon: the unit revenue is linearly proportional to the demand elasticity of price; the unit revenue is constant over time when the demand elasticity is constant; and the sales rate is constant over time when the demand elasticity is linear in the price.

Suggested Citation

  • Y. Y. Fan & H. K. Bhargava & H. H. Natsuyama, 2005. "Dynamic Pricing via Dynamic Programming1," Journal of Optimization Theory and Applications, Springer, vol. 127(3), pages 565-577, December.
    • Handle: RePEc:spr:joptap:v:127:y:2005:i:3:d:10.1007_s10957-005-7503-z
    DOI: 10.1007/s10957-005-7503-z
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    Cited by:

    1. Yanwu Yang & Baozhu Feng & Joni Salminen & Bernard J. Jansen, 2022. "Optimal advertising for a generalized Vidale–Wolfe response model," Electronic Commerce Research, Springer, vol. 22(4), pages 1275-1305, December.

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