• A NEW APPROACH FOR QUEUE-INVENTORY NETWORK MODEL USING EXTENSION GRAPH ELIMINATION THEOREM WITH ENHANCED PERFORMANCE IN TIME

Abstract

To develop a supply network model for a service facility system with inventory which takes as input the number of customers and the on hand inventory. In return the model generates the steady state probabilities. The inter-arrival time to the service station is assumed to be exponentially distributed with mean 1/λ. The maximum inventory level is S and the maximum capacity of the waiting space is N. The replenishment process is assumed to be instantaneous i.e. (0, S) policy, and the service time for each customer is exponentially distributed with mean 1/ µ. The steady state probability distribution for the system states are obtained by graph elimination method and the classical iteration method. The elimination ordering of variables is found to greatly affect the time and space complexity of the solution process if M is sparse. A numerical example is presented to validate the model and to illustrate its various features.