Production inventory system with random supply interruptions statue and random lead times

This article analyzes a continuous-review inventory system with random supply interruptions and random lead time which may be interrupted by a random number of supplier's OFF periods. The inventory with constant demand rate is managed by a (r;q1,q2,…,qm) policy and supplies from an unreliable sole supplier. By renewal theory and matrix Geometric method, the long-run average cost function is obtained and some important properties of the function are proved. Furthermore, performance of the inventory is derived.