This paper presents an extension of earlier research on heirarchical control of stochastic manufacturing systems with linear production costs. A new method is introduced to construct asymptotically optimal open-loop and feedback controls for manufacturing systems in which the rates of machine...

Most manufacturing systems are large and complex and operate in an uncertain environment. One approach to managing such systems is that of hierarchical decomposition. This paper reviews the research devoted to proving that a hierarchy based on the frequencies of occurrence of different types of...

We present an approach of hierarchical decision making in production planning and capacity expansion problems under uncertainty. We show that under reasonable assumptions, the strategic level management can base the capacity decision on aggregated information from the shopfloor, and the...

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...

This review is an introduction to asymptotic methods for portfolio choice problems with small transaction costs. We outline how to derive the corresponding dynamic programming equations and how to simplify them in the small-cost limit. This allows one to obtain explicit solutions in a wide range...

We present a sufficient condition for a feedback Stackelberg equilibrium of a stochastic differential game on an infinite horizon. This condition gives rise to a system of elliptic partial differential equations involving a static Stackelberg game at the level of Lagrangian. As an example, we...