Optimal Inventory Policies when Purchase Price and Demand Are Stochastic

In this paper we consider the problem of a firm that faces a stochastic (Poisson) demand and must replenish from a market in which prices fluctuate, such as a commodity market. We describe the price evolution as a continuous stochastic process and we focus on commonly used processes suggested by the financial literature, such as the geometric Brownian motion and the Ornstein-Uhlenbeck process. It is well-known that under variable purchase price, a price-dependent base-stock policy is optimal. Using the single-unit decomposition approach, we explicitly characterize the optimal base-stock level using a series of threshold prices. We show that the base-stock level is first increasing and then decreasing in the current purchase price. We provide a procedure for calculating the thresholds, which yields closed-form solutions when price follows a geometric Brownian motion and implicit solutions under the Ornstein-Uhlenbeck price model. In addition, our numerical study shows that the opti...

• Type: Journal
• Year: 2011
• Where: IOR
• Authors: Peter Berling, Victor Martínez-de-Albéniz
• Keywords: Geometric Brownian Motion, IOR 2011, Price Evolution, Purchase Price