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 require the one unit of second commodity in addition to the first commodity with probability pi. Similarly, the demand for the second commodity require the one unit of first commodity in addition to the second commodity with probability p(2). This assumption model 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 illustrated with numerical examples.