Substitutable Inventory System with Partial Backlogging under Continuous Review

Abstract

Consider a two-commodity substitutable inventory system with storage capacity Si for commodity i, (i=1,2) under continuous review. The demand time points for each commodity are assumed to form independent Poisson processes. The two commodities are assumed to be substitutable. That is when any one of the commodity's inventory level reaches zero, then the demand for that commodity will be satisfied by the other commodity. If no substitute is available, then this demand is backlogged up to the level Ni, for commodity i, (i=1,2). The reordering policy is to place an order for both the commodities, when both inventory levels are less than or equal to their respective reorder levels. If the inventory level drops to N1 or N2, then both inventory levels are pulled back to their maximum levels S1 and S2 immediately and the previous order gets canceled. The lead time is assumed to follow negative exponential distribution. Various stationary measures of system performances have been derived and total expected cost rate is computed. Numerical examples are provided.