Technical Note—Joint Inventory and Pricing Control with General Additive Demand

Abstract

This paper analyzes a periodic-review, joint inventory and pricing control problem for a firm that faces stochastic, price-sensitive demand under a nonstationary environment with fixed ordering costs. Any unsatisfied demand is backlogged. The objective is to maximize expected profit over a finite selling horizon by coordinating the inventory and pricing decisions in each period. We show that for an additive demand model, an (s, S, p) policy is optimal when the expected revenue is quasi-concave in price, the inventory cost (of holding and/or backlogging) is quasi-convex, and the nonnegative random demand has a Pólya or uniform density function. For the special case with no fixed ordering cost, the optimality of a base stock list price policy is demonstrated for more general demand distributions and convex inventory cost. These sets of sufficient conditions generalize the existing conditions in the literature that require, for example, the demand and/or revenue functions to be concave or the model parameters to be stationary in time. Our generalization makes the structural results applicable to models broadly supported by economic theory and empirical data. In addition, our proof uses a distinct sequential optimization technique for iteratively establishing the quasi-K-concavity of dynamic optimal value functions.