Technical Note—Dynamic Optimal Policy for an Inventory System of Two Substitutable Products with Positive Replenishment Lead Times

Abstract

We consider a periodic-review inventory system of two products with positive replenishment lead times, assuming that downward substitution is allowed and that replenishment is capped. We aim to characterize the structures of the optimal policies for product replenishment and substitution that minimize the expected total discounted cost over a finite horizon. With a Markovian decision programming formulation and an appropriate relaxation of constraints on the substitution quantity, we show that the objective function is L♮-convex. We then explore various structural properties of the optimal policy through sensitivity analysis.

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