HEURISTIC ALGORITHMS FOR SCHEDULING n JOBS IN A FLOWSHOP *

The classical problem of scheduling n jobs on M machines in a flowshop to minimize the throughput: time of all jobs is examined under the assumption that all jobs are processed on all machines in the same order. Based on the mathematical formulation of the job and machine slacks, a schedule evaluation algorithm is presented which consists of annotating the process time array. This proposed schedule evaluation algorithm identifies those jobs that are critical to the completion time of any job-thus yielding the critical path(s) and illus* This is a modified version of a paper presented at the 39th National Meeting of Operations Research Society of America, Dallas, Texas, May 5-7, 1971. 131 © 1973 The Operations Research Society of Japan 132 Jatinder N. D. Gupta and Albert R. Maykut trates the manner in which job and machine slacks propagate through the flowshop. By defining and exploiting the concept of a synthetic job to represent a partial sequence, the basic ideas of the schedule evaluation algorithm are generalized to the point where they can serve as heuristic approaches to flowshop scheduling problem. One such algorithm, based on Gupta's idle time rule, is described and its performance (regarding its computational efficiency and solution effectiveness) discussed.