Performance Analysis of Queuing-Inventory System with Catastrophes Under (s, Q) Policy

Abstract

We discuss the single-server queuing-inventory system with possible catastrophes in warehouse and negative customers. Consumer customers arrive in the system according to Poisson process and their service times follow exponential distribution. The customers can be queued in an infinite buffer. Upon arrival of catastrophe all inventory of the system is destroyed but consumer customers in the system (on server or in buffer) continue to waiting for replenishment of stocks. One consumer customer is pushed out from the system, if a negative customer arrives to the system. In the system (s, Q) inventory policy is used. When the inventory level drops to s, an order quantity of Q = S - s is placed and upon replenishment the level becomes sum of the current items and order quantity. If upon arrival of the consumer customer, the inventory level is zero, this customer is either lost (lost sale) or joins to the queue (backorder sale). Mathematical model of the system is constructed via two-dimensional Markov chain. Steady-state probabilities are obtained using the matrix-geometric method and ergodicity condition is established in closed-form. Numerical results are presented about the behavior of performance measures and the optimum inventory policy to minimize the expected total cost.