A Two-Time-Scale Approach for Production Planning in Discrete Time

Abstract

This work develops asymptotically optimal production planning strategies for a class of discrete-time manufacturing systems. To reflect uncertainty, finite-state Markov chains are used in the formulation. The state space of the underlying Markov chain is decomposed into a number of recurrent classes and a group of transient states. Using a hierarchical control approach, by aggregating the states in each recurrent class into a single state, a continuous-time limit control problem in which the resulting limit Markov chain has much smaller state space is derived. Using the optimal control of the limit problem, control policies for the original problem are constructed. Moreover, it is shown that the strategies so designed are nearly optimal.