Hierarchical feedback controls in two-machine flowshops

Abstract

In Chapters 6 and 7, asymptotic optimal open-loop controls are constructed for stochastic dynamic flowshops and jobshops. While asymptotically optimal, these open-loop controls are not expected to perform well unless the transition rates among machine states are unrealistically large (i.e., εis very small). What is required, therefore, is a construction of asymptotic optimal feedback controls. Thus far, such constructions are available only for single or parallel machine systems (see Chapter 5), in which no state constraints are present. In such systems, either the Lipschitz property of optimal control for the corresponding deterministic systems or the monotonicity property of optimal control with respect to the state variables makes the proof of asymptotic optimality go through. Unfortunately, these properties are no longer available in the case of flowshops or jobshops.