Dynamic Pricing via Dynamic Programming1
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.
KeywordsDynamic pricing dynamic programming optimal control
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- 1.Robinson, B., Lakhani, C. 1975Dynamic Price Models for New-Product PlanningManagement Science2111131122Google Scholar
- 2.Dockner, E.J., Jorgensen, S. 1988Optimal Pricing Strategies for New Products in Dynamic OligopoliesMarketing Science7315334Google Scholar
- 7.Kalish, S. 1983Monopolist Pricing with Dynamic Demand and Production CostMarketing Science2135159Google Scholar
- 9.Krishnan, T.V., Bass, F.M., Jain, D.C. 1999Optimal Pricing Strategies for New ProductsManagement Science4516501663Google Scholar
- 11.Bellman, R.E., Kalaba, R.E. 1965Dynamic Programming and Modern Control TheoryMcGraw-HillNew York, NYGoogle Scholar