Two-Commodity Markovian Inventory System with Set of Reorders

Abstract

This article examines a two commodity substitutable inventory system—two different brands of super computers under continuous review. The demand points for each commodity are assumed to form independent Poisson processes. The reordering policy is to place orders for both the commodities when the total net inventory level drops to any one of the prefixed levels with prescribed probability distribution. Lost sales are assumed during the stock out period. The lead time for a reorder is exponentially distributed with parameter(, depending on the size of the ordering quantity. The limiting probability distribution for the joint inventory levels is also evaluated. Various operational characteristics and total expected cost rate are derived. Numerical examples are provided to find optimal reorder quantity and band width .