5 Hierarchical Controls under the Long-Run
Average Cost Criterion

In this section, the results on hierarchical controls with the long-run average cost criterion are reviewed. Hierarchical controls for stochastic manufacturing systems including single/parallel machine system, the flowshops, and the general jobshops are discussed. For each model, the corresponding limiting problem is given, and the optimal value of the original problem is shown to converge to the optimal value of the limiting problem. Also constructed are asymptotic optimal controls for the original problem by using a near-optimal control of the limiting problem. The rate of convergence and error bounds of the constructed controls are provided.