( s , S ) stochastic inventory system in Jackson network

In this work, we develop and analyse an (s, S) stochastic perishable inventory system at each node into Jackson network with a service facility in which the waiting hall of first queue has infinite capacity and second queue has finite capacity for the customers. Service times are exponentially distributed. We assume that demands arrive in the system according to a Poisson process with rate λi(> 0, ∀i) and demands only single unit item at a time. The maximum storage capacity of the ith warehouse is fixed as Si; i = 1, 2. Whenever the inventory level reaches the reorder level si(0 ≤ si < Si), an order Qi(= Si – si) units is placed to bring the level to Si. The lead-time is exponentially distributed. The items of inventory have exponential life times. The joint probability distribution of the number of customers in the system and the inventory level is obtained in the steady state case. Matrix analytical method is applied to solve for the steady state occupancy probabilities. Various system performance measures in the steady state are derived. A suitable cost function is defined and the long-run total expected cost rate is calculated. Sensitivity analysis has been carried out to study the effect of variation of parameters. Numerical examples and graphical illustrations are provided to illustrate the proposed model.