Optimal control of a failure-prone machine under random demand

In this note, we consider a manufacturing system with random machine breakdowns, which is characterized by a fairly general probability distribution. The demand is not known during the finite planning horizon except the probability distribution of the cumulative demand at the end of the horizon. We propose a decomposition method that features a feedback control. Simulation is used to compare the average cost of the proposed method and that of the optimal solution. Our results of more than a hundred examples show that the difference between the two is less than 2.4%.