This paper considers optimal infinite horizon stochastic production planning problems with capacity and demand to be finite state Markov chains. The existence of the optimal feedback control is shown with the aid of viscosity solutions to the dynamic programming equations. Turnpike set concepts...

A hierarchical approach to control a manufacturing system, subject to multiple machine states modeled by a Markov process with weak and strong interactions, is suggested. The idea is to aggregate strongly interacting or high transition probability states within a group of states and consider...

This paper considers an infinite horizon stochastic production planning problem with demand assumed to be a continuous-time Markov process. Problems with control (production) and state (inventory) constraints are treated. It is shown that a unique optimal feedback solution exists. This solution...

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...

This paper considers an infinite horizon stochastic production planning problem with demand assumed to be a continuous-time Markov chain. The problems with control (production) and state (inventory) constraints are treated. It is shown that a unique optimal feedback solution exists, after first...

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...

We deal with a single or parallel machine manufacturing system with convex cost of holding and backlogging and develop a new rigorous analysis to address the problem. We provide the results needed for the vanishing discount approach used for aour analysis. In particular, we show that one can go...

The paper is concerned with the reduction of a class of stochastic optimal control problems to simpler problems by using decomposition and aggregation. Decomposition is shown to provide a good approximation when the system dynamics involve nearly decomposable matrices or variables with strong...

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...