G. Arivarignan

In this paper, we consider an inventory system with two heterogeneous servers and multiple vacations. We have assumed that the customers arrive according to a Markovian arrival process and two parallel servers who provide heterogeneous phase type services to customers. The inventory is replenished according to an (s, S) policy and the replenishing time is assumed to follow exponential distribution. The vacation times of both severs are assumed to be independent and identically distributed exponential random variables. The joint probability distribution of the number of customers in the system, inventory level and server status is obtained in the steady state. Some important performance measures are obtained and the optimality of an expected total cost rate is shown through numerical illustration.

In this article, we consider a perishable inventory system with postponed demand and single server. The server is allowed to take multiple vacations during stock out period. The demands that arrive during a stock out period or server vacation period either postponed their demand or considered to be lost according to a Bernoulli distribution. The postponed demands are sent to a place called pool and its capacity is finite. When the server is not in vacation and the inventory level is above s, the demands in the pool are selected one by one with FCFS discipline. The waiting time distribution for demands in the pool is derived for both (s, S) and the variable ordering policy. System performance measures for model with variable ordering policy and (s, S) policy are also computed under steady-state case. And these performance measures are used to calculate the total expected cost rate for both policies. Finally, using numerical results, we compare the optimal total cost rate corresponding to two policies and also we compare the expected waiting time of the pooled demands.

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.

TWO-COMMODITY PERISHABLE INVENTORY SYSTEM WITH BULK DEMAND FOR ONE COMMODITY

In this work, we consider a continuous review ( 5, S ) inventory system in which the arriving customers belong to any one of two types such that the type-1 customer would be willing to wait for delivery of the demanded item and the type-2 customers would not be willing to do so. When the stock is more than 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 (= S - s ) items is placed and thereafter the demand of type-2 customers alone are satisfied. The type-1 customers are asked to wait until the ordered items are received. The maximum number of type-1 customers allowed to wait is fixed as M( < Q - s ). The arrivals of both types of customers are assumed to follow a Markovian arrival process (MAP) and the lead time has exponential distribution. The life time of each item is assumed to have exponential distribution. Further we assume that the demand, the lead time and the life time of each items are mutually independent. The limiting distribution of inventory level is computed and the measures of system performance in the steady state are derived. The results are illustrated numerically.