A continuous review (<i>s</i>, <i>S</i>) inventory system with postponed demands at service facility

Abstract

In this article, we present a continuous review (s, S) inventory system with a service facility consisting of finite waiting hall (capacity N) and a single server. The customers arrive according to a Poisson process. The individual customer's unit demand is satisfied after a random time of service, which is assumed to be exponential. An arriving customer, who finds the waiting hall is full, enters into the pool of infinite size or leaves the system which is according to a Bernolli trial. The joint probability distribution of the number of customers in the pool, number of customers in the waiting hall and the inventory level is obtained in the steady-state case. Various stationary system performance measures are computed and total expected cost rate is calculated. The results are illustrated numerically. [Received: 8 January 2017; Revised: 28 February 2018; Accepted: 30 July 2018]