Dynamic pricing via dynamic programming

Dynamic pricing via dynamic programming

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Article ID: iaor20061386
Country: Germany
Volume: 127
Issue: 3
Start Page Number: 565
End Page Number: 577
Publication Date: Dec 2005
Journal: Journal of Optimization Theory and Applications
Authors: , ,
Keywords: control processes
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.

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