A fuzzy decomposition method for multistation production systems subject to blocking

Abstract

This study presents a new methodology to adjust the value of the proportionality constant (step length parameter) used in the general decomposition method for multistation heterogeneous production systems proposed in an earlier study for specially unbalanced production systems by using fuzzy logic control. The decomposition method is based on successive approximations. Namely, input rate to each subsystem is adjusted proportional to the difference in production rates of adjacent stations. This process continues until all the subsystems have the same production rate. Fuzzy logic control uses basic observations described in linguistic variables of how production rate changes as a function of input rate. Consequently, the proportionality constant in the successive approximation method is adjusted. These observations are not model specific. Thus, the fuzzy decomposition method can be applied to a wide variety of production systems. The same methodology can also be used in other applications where adjusting the step length parameter to attain the highest convergence rate is not trivial. For example, step length parameter used in subgradient optimization and other search methodologies can also be adjusted by using the fuzzy logic control methodology presented in this study. Numerical experience shows that this method yields a substantial improvement in the convergence rate of the decomposition method for highly unbalanced production system.