Abstract
This article considers a continuous review perishable (s,S) inventory system in which the demands arrive according to a Markovian arrival process (MAP). The lifetime of items in the stock and the lead time of reorder are assumed to be independently distributed as exponential. Demands that occur during the stock-out periods either enter a pool which has capacity N(<∞) or are lost. Any demand that takes place when the pool is full and the inventory level is zero is assumed to be lost. The demands in the pool 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 number of customers in the pool. The waiting demands in the pool independently may renege the system after an exponentially distributed amount of time. In addition to the regular demands, a second flow of negative demands following MAP is also considered which 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 per unit time is also considered. The results are illustrated numerically.
Highlights
In most of the inventory models considered in the literature, the demanded items are directly delivered from the stock
This article considers a continuous review perishable (s,S) inventory system in which the demands arrive according to a Markovian arrival process (MAP)
In this work we have extended the work of Krishnamoorthy and Islam [10] by assuming that the items are perishable in nature, the demands occur according to a MAP, and that the lead times are distributed as exponential
Summary
In most of the inventory models considered in the literature, the demanded items are directly delivered from the stock (if available). In this work we have extended the work of Krishnamoorthy and Islam [10] by assuming that the items are perishable in nature, the demands occur according to a MAP, and that the lead times are distributed as exponential. In addition to the regular demands, we consider a second flow of negative customers following MAP who will remove one of the waiting customers in the pool. These negative customers may be viewed as the touts of competing organizations, who take away prospective customers.
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