A State Aggregation Approach to Manufacturing Systems Having Machine States with Weak and Strong Interactions
Operations Research · 1991 · Volume 39 · Issue 6
Abstract
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 only the transition between these groups for the analysis of the system in the long run. We show that such an aggregation results in a problem of reduced size, whose solution can be modified in a simple way to obtain an asymptotically optimal feedback solution to the original problem. Also, an example is solved to illustrate the results developed in the paper.
Keywords
dynamic programming, optimal control: stochastic, continuous time, probability, Markov processes: hierarchical control of Markov process driven systems, production/scheduling, hierarchical planning: manufacturing with unreliable machines
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