Incremental quantity discounts in a periodic-review stochastic inventory model with a general demand distribution

Abstract

We examine a periodic–review stochastic inventory model in which the buyer places orders to meet stochastic demands under an incremental quantity discount schedule with a single price–break point. With a general demand distribution, we prove the optimality of a state–dependent base–stock policy for the single–period problem and provide simple bounds on the optimal order–up–to levels for the multiple–period problem. We also solve the infinite horizon problem by using the policy iteration method. Our computational results suggest that a state–dependent base–stock policy is also optimal for the multiple–period and infinite–horizon problems.