Asymptotic Optimal Controls in Stochastic Manufacturing Systems With Machine Failures Dependent on Production Rates

This paper is concerned with hierarchical control of stochastic manufacturing systems with machines whose capacity states are governed by a Markov process dependent on the rates of production. The objective is to choose production rates that minimize the total inventory/shortage and production costs over the infinite horizon. The problem is formulated as a control problem of piecewise-deterministic processes. When the rates of machine breakdown and repair are much larger than the rate of fluctuation in demand and rate of discounting of costs, we show that the original problem can be approximated by a limiting problem obtained by replacing the stochastic machine capacity by its averaged machine capacity and by appropriately modifying the cost function. Asymptotically optimal controls for the original problem are constructed by using optimal controls of the limiting problem