Abstract
A continuous review (s; S) inventory system at a service facility with nite homogeneous sources of demands and retrial is analysed. The lifetime of each item is assumed to be exponential. Before items are delivered to the customers, some basic service on the item must be performed. It is known as a regular or main service. The service may get interrupted according to a Poisson process and it restarts after an exponentially distributed time. If the server is idle at the time of arrival of a customer and the inventory level is positive, then the service begins immediately. After the completion of regular service, a customer may either abandon the system forever or demand for a second service from the same server, which is multi-optional. If any arriving customer nds that the server is busy or inventory level is zero, he/she either enters into the orbit with probability p or balks (does not enter) with probability 1 - p. The stationary distribution of the number of customers in the system, server status and the inventory level is obtained by the matrix method. The Laplace-Stieltjes transform of the waiting time of the tagged customer is derived. Various system performance measures are derived and the total expected cost rate is computed under a suitable cost structure. A numerical illustration is given. Key words : (s; S) policy, service interruption, nite source, retrial, repair, essential and optional service.
Highlights
In recent years, there has been a considerable interest in the stochastic inventory system in which an item demanded by the customer is not immediately delivered
106 VSS Yadavalli, K Jeganathan, T Venkatesan, S Padmasekaran, S Jehoashan Kingsly arises when the items in the inventory needs some time for preparation and it is considered as having positive service time
They assumed that the service time follows an arbitrary distribution and the customers arrive according to a Poisson process wherein the demand is for a single item per customer
Summary
There has been a considerable interest in the stochastic inventory system in which an item demanded by the customer is not immediately delivered. Maike Schwarz et al [16] have considered a M/M/1 queueing system with attached inventory They assumed a Poisson demand, exponentially distributed lead times and lost sales for infinite and finite waiting rooms. Yadavalli et al [22] analysed a finite source perishable inventory system with a service facility having two heterogeneous servers and repeated attempts They assumed that the first server is perfectly reliable and the second server is subject to interruptions. Jeganathan [9] investigated a continuous review perishable (s, S) inventory system with N optional services, in which some of the arriving customers asked for second optional service as soon as the completion of first essential service and the second service is multi-optional He assumed that the customer arrivals follow a Poisson process.
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