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 ðs; SÞ 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 an infinite capacity or leave the system with a predefined probability. The demands in the pool are selected one by one, if the on-hand inventory level is above s þ 1; and the interval time between any two successive selections is assumed to have a 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.We derive the system performance measures under steady state and using these measures, the total expected cost rate of the system is calculated. The impacts of arrival rate on the performance measures are graphically illustrated. Finally, we study the impact of cost on the optimal values of the total expected cost rate, inventory level and the reorder point.

Key words: (s, S) Policy , Discrete-time inventory system  , Discrete Markovian arrival process , Discrete phase-type distribution,  Postponed demands