A New Heuristic for Three-Machine Flow Shop Scheduling

This paper considers the problem of sequencing n jobs in a three-machine flow shop with the objective of minimizing the makespan, which is the completion time of the last job. An On log n time heuristic that is based on Johnson's algorithm is presented. It is shown to generate a schedule with length at most 5/3 times that of an optimal schedule, thereby reducing the previous best available worst-case performance ratio of 2. An application to the general flow shop is also discussed.