A postponed inventory system with modified M vacation policy

In this article, we analyse a postponed inventory system with a single server under modified M vacation policy, where the server can take atmost M inactive mode. We assume that the demand process follows a Markovian arrival process and (s, S) ordering policy with exponential lead time. During the inactive mode, the server can be idle or go on vacation, which occurs due to the depletion of inventory. In every inactive mode, server avails the inactive idle period first followed by a vacation period. Inactive idle period and vacation period follow independent phase type distribution. The demand that arrives during the server inactive mode enters the pool of infinite size. The server selects a demand one by one on FCFS rule from the pool, as long as the inventory level is greater than the reorder point and inter selection time follows exponential distribution. A quasi birth and death process is formulated to analyse the system and solved by using the matrix-geometric method. We explicit some system performance measures on the steady state and some illustrative examples are discussed numerically.