An evaluation of sequencing heuristics in flow shops with multiple processors

In this paper we investigate scheduling procedures which seek to minimize the makespan in the static flow shop with multiple processors (FSMP) scheduling environment. The FSMP (or flexible flow shop) problem is characterized as the scheduling of jobs in a flow shop environment that has, at any stage, multiple copies of a processor. A previous work is discussed in which all permutations of the job indices are used in developing a first stage queuing sequence—the remaining stages are queued in a FIFO manner. The previous study shows, on a set of 653 FSMP problems with known optimal solutions, that choosing the best initial sequence with a FIFO progression produces good, often near-optimal, makespans. While FIFO scheduling is efficient, searching through all permutations is not. This study tries to answer the question posed in that work which suggests a focus on the development of a “good” initial sequence. Four previously existing pure flow shop sequencing methods are now utilized for use in FSMP application. Herein, a pure flow shop concerns the environment where every stage has exactly one processor. An analysis of these methods using the same set of 653 problems is discussed. Since two of the methods obtain an optimal makespan in at least one-third of the cases and the other two obtain optimality in 29 and 20% of the cases, this study indicates that it is desirable to utilize the pure flow shop methods in the FSMP environment.