Optimal order limit policy under cost effectiveness criterion

The reorder point/reorder quantity policies referred as (r, Q) policies are widely used in industry and extensively studied in the literature. It should be noted, however, that the shortage often occurs in practical situations even if the optimal reorder point and reorder quantity maximizing or minimizing any optimality criteria are rationally determined. In this paper, we present a mathematical model to adjust the shortage period by the emergency order. The problem is to choice the timing for the expedited order. Applying the concept on repair limit policy in the context of reliability theory, the optimal order limit policy maximizing an optimality criterion called cost effectiveness is analytically derived in the framework of (r, Q) inventory system. Finally, some examples for stochastic lead times are given to explain the numerical procedure to obtain the optimal policy.