The scheduling of a flow shop with multiple processors at one or more stages is a generalized case of the basic flow shop problem. It involves the sequencing of n jobs in a flow shop where more than one identical machine at a machine stage is allowable. The constrained flow shop with multiple processors problem is a special case of the flow shop with multiple processors problem, in which the total number of jobs that can concurrently exist in the system is limited to a pre-specified number. The purpose of this study is to evaluate the performance of six priority rules under different congestion levels in the system for two measures of performance, namely, mean tardiness and number of tardy jobs. A dynamic simulation model of the constrained flow shop with multiple processors has been developed. The priority rules considered in the study are localized procedures. However, the queueing priorities for sequencing the jobs in the simulation model are established dynamically at each processing stage. The results of the study provide conclusive evidence of the superiority of the first-in-first-out priority rule for the mean tardiness criterion. However, for the number of tardy jobs criterion, clear superiority of a particular priority rule is not established. It is found that different priority rules yield good performances for different congestion levels in the system. Thus, the study provides general guidelines for using a particular priority rule for the number of tardy jobs criterion depending upon the system parameters.
