Two commodity coordinated inventory system with Markovian demand

This paper considers a two commodity continuous review inventory system. The demand points for each commodity are assumed to form Poisson processes. It is further assumed that the demand for the first commodity requires one unit of the second commodity in addition to the first commodity with probability p1. Similarly, the demand for the second commodity requires one unit of the first commodity in addition to the second commodity with probability p2. This assumption models the situation in which a buyer who intends to buy one particular commodity may also go for another commodity. The limiting probability distribution for the joint inventory levels is computed. Various operational characteristics, expression for the long run total expected cost rate is derived. The results are illusrated with numerical examples.