An inventory system with service facility and finite orbit size for feedback customers

In this article, we consider a continuous review inventory system with service facility consisting of finite waiting hall and a single server. The customers arrive according to a Poisson process and any arriving customer, who finds the waiting hall is full, is considered to be lost. The individual customer’s unit demand is satisfied after a random time of service, which is assumed to be exponential distribution. After a customer is served, he/she will decide either to join the retrial group, which is of finite size, called orbit, for another service or leave the system according to a Bernoulli trial. The customers in the orbit, called feedback customers, compete for service according to classical retrial policy. The service times for these feedback customers are assumed to be independent and exponential distribution. The inventory is replenished according to an (s, S) inventory policy, and the replenishing times are assumed to be exponential. The joint probability distribution of the inventory level, the number of customers in the orbit, number of customers in the waiting hall and the status of the server is obtained in the steady state. Some important system performance measures in the steady state are derived, and the long-run total expected cost rate is also calculated. We have derived the Laplace-Stieljes transforms of waiting time distribution of both primary as well as the feedback customers. The sensitivity analysis has been carried out to examine the effect of different parameters and cost in the system. © 2014, Operational Research Society of India.