A stochastic inventory system with replacement of perishable items

This article presents a continuous review perishable inventory system in which the perished items will be replaced by the supplier at a later time. Demands occur according to a Markov arrival process. The items in the inventory have exponential life times and these perished items are stored in a place, called pool for replacement. The (s, S) ordering policy is adopted. At the time of placing an order, the ordering quantity is adjusted with number of items in the pool. The lead time is assumed to have phase type distribution. The joint probability distribution of the inventory level and the number of pooled items is obtained in the steady state case using the matrix-geometric methods. Various system performance measures in the steady state are derived and the total expected cost rate is calculated under a prefixed cost structure. The results derived in this work are numerically illustrated.