A comparative study on replenishment policies of inventory system with postponed demands

Abstract

We consider a continuous review inventory system in which demands arrive according to a Markovian arrival process. The demands that occur during stock-out periods enter a finite pool. Once the pool is full, subsequent demands will be lost. We use (s, S) ordering policy and variable ordering policy for replenishing the inventory. The lead time is assumed to follow a phase-type distribution. When the on-hand inventory level is above s, the demand in the pool is selected one by one with first come first serve discipline. The time interval between any two successive selections of demand from the pool is assumed to have exponential distribution. The joint probability distribution of on-hand inventory level, number of demands in the pool and number of ordered items are obtained in the steady-state case. The measures of system performance in the steady state and total expected cost are derived for both policies. Finally, these two policies are numerically compared, and we obtain results that show the total expected cost rate and the mean waiting time of pooled demands with variable ordering policy are minimal when comparing with (s, S) policy.