Production and inventory rationing in a make-to-stock system with a failure-prone machine and lost sales

We consider production and inventory rationing of a product to fulfill multiple demand classes in a make-to-stock production system with a failure-prone machine. Demand that cannot be satisfied immediately is lost and incurs a lost sales cost, which differs from class to class. We find that the optimal control policies under both the expected total discounted cost criterion and the average cost criterion have similar structural properties. Specifically, the optimal production policy is the base-stock policy and the optimal inventory allocation policy is the threshold control policy with machine-state-dependent threshold levels. Finally, we provide numerical examples to show the importance of taking machine failures into consideration and the effectiveness of the optimal control policy.