Numerical investigation of a PH/PH/1 inventory system with positive service time and shortage

The aim of this paper is to numerically investigate a PH/PH/1 inventory model with reneging of customers and finite shortage of items. We assume that arrivals occur according to a phase type renewal process. The associated phase type distribution has representation ( , ) U α . The service times are identically and independently distributed random variables having common phase type distribution with representation ( , ) V β . The lead-time is zero. Costumers renege from the system at a constant rateγ . Shortage is permitted and hence shortage cost is finite. We perform the steady state analysis of the inventory model using Matrix analytic method. A suitable cost function is defined and analyzed numerically. The optimal shortage level is numerically evaluated. Some measures of the system performance in the steady state are also derived.