Perishable Inventory System with Postponed Demands and Negative Customers

This article considers a continuous review perishable (s,S) inventory system in which the demands arrive according to aMarkovian arrival process (MAP). The lifetime of items in thestock and the lead time of reorder are assumed to be independentlydistributed as exponential. Demands that occur during the stock-outperiods either enter a pool which has capacity N(<∞) or are lost. Any demand that takes place when the pool is full andthe inventory level is zero is assumed to be lost. The demands in thepool are selected one by one, if the replenished stock is above s, with time interval between any two successive selections distributed as exponential with parameter depending on the numberof customers in the pool. The waiting demands in the poolindependently may renege the system after an exponentiallydistributed amount of time. In addition to the regular demands, asecond flow of negative demands following MAP is also consideredwhich will remove one of the demands waiting in the pool. Thejoint probability distribution of the number of customers in thepool and the inventory level is obtained in the steady state case.The measures of system performance in the steady state arecalculated and the total expected cost per unit time is alsoconsidered. The results are illustrated numerically