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

Abstract

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 (α, U). The service times are identically and independently distributed random variables having common phase type distribution with representation (β, V). The lead-time is zero. Costumers renege from the system at a constant rate γ. 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.