A stochastic inventory system with postponed demands

This article considers a continuous review perishable (s,S)(s,S) inventory system in which the demands arrive according to a Markovian arrival process (MAP). The life time of each item in the stock and the lead time of orders are assumed to be independently distributed as exponential. We assume that the demands that occur during stock-out periods either enter a pool of infinite capacity or are lost. The demands in the pool are selected one by one according to FCFS rule when the stock after replenishment is above a prefixed level, say N(1≤N≤s). The interval time between any two successive selections is assumed to be distributed as exponential. In addition to the regular demands, a second flow of negative demands following another MAP is also considered. The negative demand will remove one of the demands waiting in the pool. The joint probability distribution of the number of customers in the pool and the inventory level is obtained in the steady-state case. The measures of system performance in the steady state are calculated and the total expected cost is also considered. The results are illustrated numerically.