A finite-source inventory system with postponed demands and modified M vacation policy

Abstract

We study a finite source (s, S) inventory system with postponed demands and server vacation. We adopt a modified M vacation policy which is defined as: Whenever the inventory level reaches zero, the server goes to inactive period which comprises the inactive-idle and vacation period. If replenishment occurs during the inactive-idle period, the server becomes active immediately, or otherwise he goes for a vacation period. The server can take at most M inactive periods repeatedly until replenishment takes place. This inactive-idle time, the vacation time and lead time follow independent PH distributions. After the M t h inactive period, the server remains dormant in the system irrespective of the replenishment of order. Demands that occur during stock out or inactive periods, enter the pool and these demands are selected if the inventory level is above s. The inter-selection time follows exponential distribution. The joint distribution of the mode of the server, server status, the inventory level and the number of demands in the pool is obtained in the steady state. We have derived several system performance measures and total expected cost function. The results are illustrated numerically.