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

• Published in: Operations research Vol. 39; no. 6; pp. 970 - 978
• Main Authors: Jiang, J, Sethi, S. P
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01.11.1991; Operations Research Society of America; Institute for Operations Research and the Management Sciences
• Subjects: Aggregation; Applications; Applied sciences; continuous time; Control theory; Cost functions; dynamic programming; Exact sciences and technology; hierarchical planning: manufacturing with unreliable machines; Machinery; Manufacturing processes; Markov analysis; Markov processes; Markov processes: hierarchical control of Markov process driven systems; Mathematical models; Mathematics; Operational research and scientific management; Operational research. Management science; Operations research; Optimal control; optimal control: stochastic; Probability; Production controls; production/scheduling; Reliability theory. Replacement problems; Studies; Theory; Viscosity; Working conditions; Aggregation; Markov process; Production system; Weak interaction; Optimal control; Strong interaction; Reliability; Repair; Failures; Modeling
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.39.6.970

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.