This paper presents a perishable type inventory model in discrete time for the products with different life times. Arrival of customers constitutes a Bernoulli process. Replenishment rate, perishability of items and service time are geometrically distributed. The items are replenished according to (s, S) policy. Maximum storage of inventory is S. Considering positive lead time, we construct a multi-dimensional Markov chain to model the inventory-level process. When the level of inventory downs to s due to decay or service the items are replenished to the maximum level S. Using Matrix Analytic Method, we obtain steady state probability vector of the system. Various system performance measures in the steady state and expected total cost are obtained. Certain important numerical calculations were made and the results are illustrated graphically.