A discrete time inventory system with postponed demands

Abstract

In this article, we consider a discrete-time inventory model in which demands arrive according to a discrete Markovian arrival process. The inventory is replenished according to an (s,S) policy and the lead time is assumed to follow a discrete phase-type distribution. The demands that occur during stock-out periods either enter a pool which has a finite capacity N(<∞) or leave the system with a predefined probability. Any demand that arrives 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 on-hand inventory level is above s+1, and the interval time between any two successive selections is assumed to have discrete phase-type distribution. 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 derived and the total expected cost rate is also calculated. The results are illustrated numerically.