Optimal continuous review policies for spare part provisioning with random lead times

The purpose of this paper is to analyze two kinds of continuous review cyclic models with random lead times and an expedited order. The order form under consideration is similar to those arising in the spare part inventory management. The control problem to determine the best timing for the regular order is considered, and the optimal policies which minimize the expected costs during one cycle are analytically characterized. Numerical examples are presented to evaluate effects of random lead times, and to calculate the elements of the optimal inventory policies.