A State Aggregation Approach to Manufacturing Systems Having Machine States with Weak and Strong Interactions

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.