Two-Commodity Markovian Inventory System with Compliment and Retrial Demand

Abstract

In this article, we consider a stochastic inventory system with two different items in stock, one is major item (I- commodity) and other is gift item (II- commodity). The maximum storage capacity for the th commodity is  The demand time points for each commodity are assumed to form a independent Poisson processes. The second commodity is supplied as a gift whenever the demand occurs for the first commodity, but no major item is provided as a gift for demanding a second commodity.  type control policy for the first commodity, with random lead time but instantaneous replenishment for the second commodity are considered. If the inventory position of first commodity (major item) is zero then any arriving primary demand for the first commodity enters into an orbit of finite size .  These orbiting customers compete for service by sending out signals that are exponentially distributed. The joint probability distribution for both commodities 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. The results are illustrated with numerical examples.In this article, we consider a stochastic inventory system with two different items in stock, one is major item (I- commodity) and other is gift item (II- commodity). The maximum storage capacity for the th commodity is  The demand time points for each commodity are assumed to form a independent Poisson processes. The second commodity is supplied as a gift whenever the demand occurs for the first commodity, but no major item is provided as a gift for demanding a second commodity.  type control policy for the first commodity, with random lead time but instantaneous replenishment for the second commodity are considered. If the inventory position of first commodity (major item) is zero then any arriving primary demand for the first commodity enters into an orbit of finite size .  These orbiting customers compete for service by sending out signals that are exponentially distributed. The joint probability distribution for both commodities 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. The results are illustrated with numerical examples.