A Finite Source Two Commodity Inventory System with Retrial Demands and Multiple Server Vacation

Abstract

Consider a two commodity continuous review inventory system with a finite number of homogeneous sources generating demands. The maximum storage capacity for the commodity - i is S i (i = 1, 2). We adopt a joint reordering policy for placing orders. The lead time for the delivery of orders is assumed to have an exponential distribution. An arriving demand receives either commodity - 1 or commodity - 2 according to a Bernoulli trial. The commodities are assumed to be substitutable in the sense that during the zero stock of any commodity, the demand for that commodity can be met by the unit of the other commodity. The server goes for a vacation of an exponentially distributed duration whenever the inventory level of both commodities reaches zero. If the server finds empty stock when he returns to the system, he immediately takes another vacation. The demands that occur during stock-out period or during the server vacation period enter into the orbit of finite size. These orbiting demands retry for their demand after a random time, which is assumed to be an exponential distribution. The joint probability distribution of the inventory level and the number of demands in the orbit is obtained in the steady state case. Various system performance measures in the steady state are derived and the long-run total expected cost rate is calculated.