Optimal Inventory Control and Pricing of Perishable Items Without Shortages

Abstract

In this paper, we consider a joint pricing and dynamic production policy for perishable items without shortages. A unimodal time-varying demand function is assumed to be convex nonincreasing in sales price. We propose a dynamic optimization model to maximize total profit by allocating a limited production capacity and setting a suitable sales price. For a given sales price, the optimal production rate can be obtained by solving a dynamic optimization problem with Pontryagin’s maximum principle. By virtue of the relationships between price intervals and the corresponding optimal production policies, an effective algorithm is designed to generate the joint policy for a system with a general nonlinear demand function of price. For a linear demand function, it is shown that the objective function is concave in price and that there exists a unique optimal joint policy. Numerical examples are presented to illustrate the validity of the theoretical results, and several managerial implications in terms of the production and pricing of perishable items are provided.