A Two-Commodity Continuous Review Inventory System with Substitutable Items

This article considers a two commodity continuous review inventory system with Markovian demands. The two commodities are assumed to be substitutable, that is, if the inventory level of one commodity reaches zero, then a demand for this commodity will be satisfied by an item of the other commodity. Reordering for supply is initiated as soon as the sum of the on-hand inventory levels of the two commodities reaches a certain level s, and there is a lead time until the reorder arrives. For this model, an associated Markovian model is derived which is then investigated in detail. The limiting probability distribution for the joint inventory levels is computed, and various operational characteristics are derived. The results are illustrated with numerical examples.