An (s,Q)(s,Q) Markovian inventory system with lost sales and two demand classes

In this article a lost sales (s,Q)(s,Q) inventory system with two types of customers viz. ordinary and priority customers and exponentially distributed leadtimes is analyzed. Demands from each type of customer arrive according to two independent Poisson processes with different parameters. The expression for the long-run expected cost rate is derived. A computationally efficient algorithm for determining the optimal values for reorder level and reorder quantity is developed.