A stochastic queueing - inventory system with renewal demands and positive lead time

This article analyses a stochastic inventory system with a service facility. This is an extended work of Yadavalli et al. (2008) by including the positive lead time. The customer arrives according to a renewal process and demanded item is delivered to the customer after performing an exponentially distributed service time. An (s, S) type ordering policy is adopted with exponentially distributed lead times. The stationary probability distribution for number of customers in the system and inventory level at arrival epoch and at arbitrary time point are derived. Some system performance measures in the steady state are computed and using these system performance measures the long-run expected cost rate is calculated. Since the long run expected cost rate is highly complex, the mixed integer distributed ant colony optimisation is used to obtain the optimal values. A sensitivity analysis to illustrate the effects of parameters and cost on the optimal values is also carried out in this work. [Received: 13 December 2018; Accepted: 10 October 2019]