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 need to be set for all periods. The objective is to find an optimal price and ordering decisions simultaneously. In 1973 Kunreuther and Schrage proposed an 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.

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Keywords inventory, lot-sizing, pricing, production
JEL Production, Pricing, and Market Structure; Size Distribution of Firms (jel L11), Business Administration and Business Economics; Marketing; Accounting (jel M), Production Management (jel M11), Transportation Systems (jel R4)
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Series ERIM Top-Core Articles , Econometric Institute Reprint Series
Journal European Journal of Operational Research
van den Heuvel, W, & Wagelmans, A.P.M. (2006). A polynomial time algorithm for a deterministic joint pricing and inventory model. European Journal of Operational Research, 170(2), 463–480. doi:10.1016/j.ejor.2004.06.027