Stochastic Analysis of the (s,Q) Continuous Review Inventory System with Retrial Demands

Abstract

In this work, we analyzed via the Generalized Stochastic Petri Nets (GSPNs) approach, a continuous review inventory system according to the (s,Q) replenishment policy, with batch arrivals of demands with deterministic size n, following a Poisson process, which are served immediately, if the stock is available. In the case of out of stock situation, the demands are directed into a limited orbit, if this latter is not complete and repeat their requests after an exponentially distributed time. If the orbit is complete, these demands are definitively lost. Thus, we describe the dynamics of the system considered by a bidimensional continuous time Markov chain, which represents the inventory level and the number of demands in the orbit. Then, we find the stationary distribution, using a recursive algorithm, from which we derive various performance measures of the model.