Dynamic Pricing with Time-Dependent Elasticities

Abstract

Many stochastic dynamic sales applications are characterized by time-dependent price elasticities of demand. However, in general, such problems cannot be solved analytically. To determine smart pricing heuristics for general time-dependent dynamic pricing models, we solve a general class of deterministic dynamic pricing problems for perishable and durable goods. The continuous time model has several time-dependent parameters, e.g., discount rate, marginal unit costs, and price elasticity. We show how to derive the value function and optimal pricing policies. On the basis of the feedback solution to the deterministic model, we propose a method for constructing heuristics to be applied to general stochastic models. For the case of isoelastic demand, we analytically verify the excellent performance of this approach for both small and large inventory levels.

Keywords: dynamic pricing, optimal control, time-dependent price elasticity, perishable and durable goods, holding costs, feedback heuristics