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Stochastic Prices in a Single-Item Inventory Purchasing Model

This paper studies a single-item multi-period inventory model in which future prices of the purchased item are assumed to be determined by a Markovian stochastic process instead of being known with certainty. Convex holding and shortage costs and a set-up charge for ordering are assumed. Such a model applies to purchasing a commodity whose price fluctuates widely because of speculative activity and large variations in supply or demand. For both a finite and infinite planning horizon, the paper determines the form and bounds of optimal policies and discusses computational approaches exploiting structure.