Dynamic Pricing via Dynamic Programming1

Y. Y. Fan, H. K. Bhargava and H. H. Natsuyama
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Y. Y. Fan: University of California
H. K. Bhargava: University of California
H. H. Natsuyama: California State University

Journal of Optimization Theory and Applications, 2005, vol. 127, issue 3, No 10, 565-577

Abstract: 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.

Keywords: Dynamic pricing; dynamic programming; optimal control (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10957-005-7503-z

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