Inventory Model At Service Facility With Negative Arrivals

The purpose of this paper is to analyze an inventory management systemat service facility with negative arrivals in both general and perishable inventoryitems cases.Queueing model with negative customers is a new branch of queueing theory.Negative customers can be considered as removal signal, inhibitor signal in neuralnetworks or virus of system and so on. They will remove some regular customersafter arriving at system. Inventory model at service facility is also a new branch ofclassic inventory theory. The di?erence between the model and classic inventorytheory is that inventory items is necessary to perform some kind of service beforedelivered to customers.In the paper we introduce negative customers to inventory system with servicefacility and extend the existing literatures which only deal with a single server case.Under the assumption with independent exponential service time and lead time, (s, S)ordering policy. Regular and negative customers arrive at system according toPossion process. negative customers don't join the queue and remove some regularcostumes if present from the system, the number of removals is a random variabledepending on the number of waiting customers in the system. For the stable case,the matrix-analytic formalism is used to study the joint probability distributionof the inventory level and number of customers in the queue. Our analysis alsoyields various system performance measures. Based on these measures we getlong-run expected cost rate, furthermore, the optimal values of S is obtained tominimize the expected cost rate. In perishable inventory items case, consideringthe in?uence of these items on the system, we get some performance measures andexpected cost rate via similar method to regular items case.