Analysis is a discrete time queueing-inventory model with back-order of items

This paper analyses a discrete-time (s, S) queueing inventory model with service time and back-order in inventory. The arrival of customers is assumed to be the Bernoulli process. Service time follows a geometric distribution. As soon as the inventory level reaches a pre-assigned level due to demands, an order for replenishment is placed. Replenishment time also follows a geometric distribution. When the inventory level reduces to zero due to the service of customers or non-replenishment of items, a maximum of k customers are allowed in the system and the remaining customers are assumed to be completely lost till the replenishment. Matrix-Analytic Method (MAM) is used to analyze the model. Stability conditions, various performance measures of the system, waiting-time distribution and reorder-time distribution are obtained. Numerical experiments are also incorporated.