An Asymptotic Analysis of Hierarchical Control of Manufacturing Systems Under Uncertainty

This paper presents an asymptotic analysis of a hierarchical manufacturing system with machines subject to breakdown and repair. The rate of change in machine states is much larger than the rate of fluctuation in demand and the rate of discounting of costs, and this gives rise to a limiting problem in which the stochastic machine availability is replaced by the equilibrium mean availability. The value function for the original problem converges to the value function of the limiting problem. Moreover, the control for the original problem can be constructed from the optimal controls of the limiting problem in a way which guarantees asymptotic optimality of the value function. The limiting problem is computationally more tractable and sometimes has a closed form solution.