Optimal threshold control in discrete failure-prone manufacturing systems

Bielecki and Kumar show that the threshold or hedging-point production policies are optimal in a continuous manufacturing system, even if production ability is uncertain. Their analysis assumes constant demand and processing time. In this note, we consider a discrete manufacturing system in which production capacity, demand, and processing time are all nondeterministic. We formulate the problem into a discrete Markovian production model, and explore the most cost-effective control policy for such a system. With two more sources of uncertainty, we find that the threshold control policies are optimal among all feasible policies when the long-run average cost is to be minimized. This extends Bielecki and Kumar's result which shows that the threshold policies are optimal among a subset of feasible policies.