Approximate solution of a dynamic job shop model with several job classes

Abstract

A closed job shop system with a FIFO managed dispatch area is considered, under the assumption that the machine shop subsystem is constrained by an upper limit on the number of circulating jobs. An approach for the approximate solution of the nonproduct form queueing network model of the system is well established only for the case of a single class of jobs flowing through the system. In this paper we extend the previous approach to cover the case of multiple job classes. We combine hierarchical decomposition with the class aggregation technique, in order to obtain a practical approximate solution method. Class aggregation also enables to incorporate in our method the consolidated ‘exponentialization approach’. Hence the method also covers the case of machine centers having different and nonexponential service times per job class. The approximations developed are validated by simulation experiments.