Optimal production control in a discrete manufacturing system with unreliable machines and random demands

We consider a production control problem in a manufacturing system with a f ailure-prone machine and a stochastic demand. The objective is to minimize a discounted inventory holding and backlog cost over an infinite planning h orizon. The optimal production control of continuous, stochastic manufactur ing systems with a failure-prone machine and a constant demand has been con sidered in Akella and Kumar [1], However, the problem of optimal production control for discrete stochastic manufacturing systems with uncertain deman ds remains open. In this paper, we investigate a case where the exogenous d emand forms a homogeneous Poisson flow. Primarily, we show that the optimal production control for such a system is of the threshold control type. In addition, the explicit form of production control policy and the objective functions are provided. Numerical examples are included to demonstrate the results obtained in the paper and to compare with the one in Akella and Kum ar.