Models for 1-out-of Q systems with stochastic lead times and expedited ordering options for spares inventory

The purpose of this article is to develop two kinds of continuous-time cyclic inventory models with stochastic lead times and expedited ordering options. The order form under consideration is similar to that arising in the spare part inventory management. Especially, the control problem to determine the timing for the regular order is considered, and the optimal policy which minimizes the long-run average cost is analytically characterized. Finally, numerical examples are presented to evaluate the uncertainty of stochastic lead times, and the optimal inventory policy, which is composed of both the ordering time and the order quantity, is numerically calculated.