Managing inventories with one-way substitution: A newsvendor analysis

► We present an insightful approach to analyze two-item periodic inventory systems with one-way substitution. ► We derive optimality conditions for the order-up-to levels in both single-period and infinite horizon settings. ► We discuss the optimality of a “borderline case” in which the order-up-to level of the inflexible item is reduced to zero. This paper presents an insightful approach to analyze two-item periodic inventory systems with one-way substitution. The objective is to minimize the expected total cost per period, which consists of expected purchasing costs, expected inventory holding costs, expected shortage costs, and expected adjustment costs. This approach helps derive the optimality conditions in both single-period and infinite horizon settings and yields useful insights into the impact of substitution on the service level, the optimality of a borderline case in which the order-up-to level of the inflexible item is reduced to zero, and the pivotal role of the purchasing cost.