Optimal policy of inventory system with random supply interruptions and random lead times depends on the supplier's production information

This paper analyzes an inventory system with random supply interruptions, random lead time and constant demand. The downside inventory is managed by (r(i) q(i)) policy (i=1,2...m; and i is the state of supplier's production). To reveal the dependence of the optimal policy on the information of the supply production state, the supplier's ON period with PH-distribution is structured by a Continuous Time Markov Chain(CTMC). When the supplier is in the state i of his production and the inventory level drops to the reorder level r(i), an order is placed and the inventory level is r(i)+q(i) when the delivery arrives after lead time which is interrupted by the supplier's OFF. If the supplier is OFF and the state of the supplier's recovery is i, the ordering is held on until the supplier recoveries. By law of the regenerative cycle, a long-run average cost function is obtained. According to the important properties of the long-run average cost, an algorithm of the sub-optimal ordering policy is formulated.