Journal of Applied Mathematics and Decision Sciences
Volume 2007 (2007), Article ID 94850, 12 pages
doi:10.1155/2007/94850
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.