• TWO SERVER (s, S) INVENTORY SYSTEM WITH POSITIVE SERVICE TIME, LEAD TIME, RETRIAL OF CUSTOMERS AND ORBITAL SEARCH

Abstract

This paper deals with a two server (s, S) inventory system with positive service time, lead time, retrial of customers and orbital search where the arrival of customers is Poisson and service times are exponential. The system starts with S units of inventory. Each arriving customer is served a single unit by one of the servers. The customer who arrives when the inventory level is zero or when both the servers are busy, joins the pool of retrial customers called the orbit. A retrial customer who finds the inventory level zero or both the servers busy returns to the orbit. Lead times follow an exponential distribution. This model also includes the concept of orbital search. This is a situation where each server immediately after a service completion, goes in search of a customer (with a negligible search time) in the orbit with a known probability p. The probability of not going for the search becomes 1-p which means the sever remains idle. If the server does not pick up the next customer to be served from the orbit, then whoever comes first either a primary customer or an orbital customer gets into service. Using matrix-analytic method, some measures of the system performance in the steady state are derived. A suitable cost function is defined. Numerical results are also provided.