An inventory system with two types of customers and retrial demands

Abstract

We consider a continuous review (s, S) inventory system in which the arriving customers belong to any one of the two types (type-1 or type-2). When the inventory level is above s, the customers are not distinguished as to their type and their demanded items are delivered immediately to them. Once the inventory level drops to s(≥ 0), an order for Q items is placed and thereafter the demands of type-2 customers alone are satisfied. The type-1 customers are sent to a place called orbit which is of infinite size. These orbiting demands retry for their demand after a random time which is assumed to have exponential distribution. The arrivals of customers are assumed to follow a Markovian arrival process and the lead time is assumed to have phase-type distribution. The joint probability distribution of the number of customers in the orbit and the inventory level is obtained in the steady-state case. Various system performance measures in the steady state are derived and total expected cost rate is calculated.