A Control Problem of Failure Prone Systems Considering Extra Capacity

The failure prone systems with the fixed maximum production rate, however uncertain demand levels, are examined. Each demand level may be larger or smaller than the maximum production rate of the systems. An optimal double hedging point (level) policy is proposed: a positive hedging point (inventory target) and a negative hedging point (backlog level below which extra capacity should be purchased). The analytical expressions of the positive and negative hedging points are obtained by a decomposition method. Meanwhile, a more straightforward necessary condition and a necessary and sufficient condition for the optimality of the just-in-time (JIT) control policy are presented respectively. A simple numerical comparison testifies and specifies our method