The optimal inventory control of a system with random lead time where random supply interruptions affect the replenishment

This paper analyzes a continuous-review inventory system with random supply interruptions and stochastic lead time. In such a system, a monopolistic supplier alternates between random ON and OFF periods. The variable (r,q)-policy is used. With a constant demand rate, the leadtime may be interrupted by a random number of OFF periods of the supplier. Using the regenerative cycle analysis, a long-run average cost function is obtained and shown to have some important properties. Accordingly, an effective search algorithm is proposed to find the sub-optimal inventory policy. In the end, we also investigate the effects on the average cost of the uncertain order delay which attribute to both the supply interruptions and the random leadtime. Numerical examples are presented to demonstrate the effectiveness of the search algorithm.