Matrix analytic solution to an inventory with service, reneging of customers and shortage

This article analyses an (s, S) inventory system with reneging of customers and finite shortage. Arrival of customers forms a Poisson process, service times are exponentially distributed and lead-time is zero. Customers renege according to an exponentially distributed inter-occurrence time. Shortage is permitted and shortage cost is finite. Using Matrix Analytic Method we perform the steady state analysis of the inventory model. Some measures of the system performance in the steady state are derived. A suitable cost function is defined and analyzed. Some graphical illustrations are also presented.