Control policies for inventory with service time

This article introduces an additional control policy-the N -policy-into ( s, S ) inventory system with positive service time. Under specified interarrival and service time distributions, which are independent of each other, we obtain the necessary and sufficient condition for the system to be stable. We also obtain the optimal values of the control variables s, S , and N ; it is seen that the cost function attains the minimum value at s = 0. It is also shown that the cost function is separately convex in the variables S and N . Numerical illustrations are provided. Several measures of performance of the system are evaluated.