A polynomial time algorithm for a deterministic joint pricing and inventory model

In this paper we consider the uncapacitated economic lot-size model, where demand is a deterministic function of price. In the model a single price needs to be set for all periods. The objective is to find the optimal price and ordering decisions simultaneously. In 1973 Kunreuther and Schrage proposed a heuristic algorithm to solve this problem. The contribution of our paper is twofold. First, we derive an exact algorithm to determine the optimal price and lot-sizing decisions. Moreover, we show that our algorithm boils down to solving a number of lot-sizing problems that is quadratic in the number of periods, i.e., the problem can be solved in polynomial time.