Modelling, performance evaluation and optimisation of (s, Q) retrial inventory system with partial backlogging demands: a GSPN approach

In this article, we model and analyse by using generalised stochastic Petri nets (GSPNs), an inventory system according to the (s, Q) replenishment policy, Poissonian batch arrivals in deterministic size n, immediate batch service and retrials. In out-of-stock situation, the arriving demands at the system join a limited orbit, if it is not full, and retry again after a random time exponentially distributed, following the classic retrial policy. However, in the case of a full orbit, these demands are definitively rejected from the system. We describe the dynamic of this inventory system using a two-dimensional continuous time Markov chain (CTMC), which expresses the inventory level and the number of demands in the orbit. Then, we recover the stationary distribution, using a recursive algorithm, from which we derive various performance measures. Finally, we investigate some numerical analysis of the reward-cost function induced by this model.