A comparative study of the inventory system with service facility and postponed demands

In this article,we present a continuous review(s,S)inventory system with a service facility consisting of finite buffer(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.When the inventory level drops to s an order for Q(=S-s)items is placed.The lead time of reorder is assumed to be exponential distribution.An arriving customer,who finds the buffer is full,enters into the pool of infinite size or leaves the system according to a Bernolli trial.At the time of service completion,if the buffer size drops to a preassigned level L(1LN)or below and the inventory level is above s,we select the customers from the pool according to two different policy:in first policy,with probability p(0P1)we select the customer from the head of the pool and we place the customer at the end of the buffer;in the second policy,with p(0p1)the customer from the pool is transferred to the buffer for immediate service and after completion of his service we provide service to the customer who is in the buffer with probability one.If at a service completion epoch the buffer turns out to be empty,there is at least one customer in the pool and the inventory level is positive,then the one ahead of all waiting in the pool gets transferred to the buffer,and his service starts immediately.The joint probability distribution of the number of customers in the pool,number of customers in the buffer 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.A comparative result of two models is illustrate numerically.