An asymptotic analysis of hierarchical control of manufacturing systems

An asymptotic analysis of a hierarchical manufacturing system with machines subject to breakdown and repair is presented. The machine fluctuations are much faster than the accumulation and 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. The limiting problem is computationally tractable and sometimes has a closed-form solution