Journal of Applied Mathematics and Decision Sciences
Volume 2007 (2007), Article ID 94850, 12 pages
Research Article

Perishable Inventory System with Postponed Demands and Negative Customers

Paul Manuel,1 B. Sivakumar,2 and G. Arivarignan2

1Department of Information Science, Kuwait University, Safat 13060, Kuwait
2Department of Applied Mathematics and Statistics, Madurai Kamaraj University, Madurai 625021, India

Received 19 October 2006; Accepted 23 May 2007

Academic Editor: Mahyar A. Amouzegar

Copyright © 2007 Paul Manuel et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.