A two-commodity perishable inventory system

Abstract

We present a two-commodity perishable stochastic inventory system under continuous review at a service facility with a finite waiting room. The maximum storage capacity for the i–th item is fixed as Si (i = 1, 2). We assume that a demand for the i–th commodity is of unit size. The arrival instants of customers to the service station constitutes a Poisson process with parameter lambda. The customer demands for these commodities are assumed to be in the ratio p1:p2. An individual customer is issued a demanded item after a random time of service with a negative exponential distribution. The items are perishable in nature and the life time of items of each commodity is assumed to be exponentially distributed. Both commodities are supposed to be substitutable in the sense that at the instant of any zero-stock, the other item may be used to meet the demand. A joint reordering policy is adopted with a random lead time for orders with exponential distribution. The joint probability distribution of the number of customers in the system and the inventory levels are obtained in both the transient and steady states. We also derive some stationary performance measures. The results are illustrated by means of a numerical example.