Optimality of Zero-Inventory Policies for an Unreliable Manufacturing System Producing Two Part Types

This paper is concerned with optimal production rates for a failure-prone machine that produces two distinct part types. We consider the problem of controlling production rates so as to minimize the expected long-run average cost of product surpluses over time. We assume constant per unit holding and shortage costs and constant demand rates for the par types. We provide an expression for the potentila function and prove the optimality of a zero-inventory policy, when the average capacity is sufficiently large