A substitutable two-product inventory system with joint-ordering policy and common demand

A substitutable two-product inventory system with joint-ordering policy is considered in this paper. Common demands occur according to a Poisson process. A demand is satisfied either with an item of product 1 with probability p1 or with an item of product 2 with probability p2 (p1 + p2 = 1). When one of the products is out of stock, the demand is satisfied with the other available product with probability 1. Analyzing the imbedded renewal process describing the system, expressions for the stationary distribution of the inventory level and the stationary rates of the replenishments, the re-orders placed, the lost demands, and the units replenished are obtained. A cost analysis is also provided. Numerical example illustrated the results obtained.