Modeling and Analysis of Stochastic Perishable Inventory System with Impatient Customers at Service Facility

Abstract

In this paper, we consider a two-commodity stochastic s,S perishable inventory system of the multiqueue Jackson network at a service facility with reneging and jockeying of the customers. The waiting room capacity of the first queue is M/M/1/∞ and the second queue is M/M/1/C2, where C2<∞. In this network, different queues have different service rates. Service times are exponentially distributed. Customers join the system at a rate of λi;i=1,2 using a Poisson process. We assumed that some customers maybe impatient due to the long waiting time in the queue and can leave the system without service or may switch from the longest queue to the shortest queue to reduce the waiting time. If the inventory levels of the items from the warehouse i at any time reaches below or reorder level si, an order Qi=Si-si>0;i=1,2 units is placed to bring the inventory level up to Si. The joint probability distribution of the number of customers in the system and also the stock level of the warehouse is determined in the equilibrium case. Several important measures of steady-state system performance are derived. Several examples are presented to demonstrate the reneging and jockeying behavior of the customers for this system. A sensitivity analysis is performed to investigate the effect of changing the parameters on the total expected cost of the system