This paper considers the problem of sequencing n jobs in a three-machi
ne flow shop with the objective of minimizing the makespan, which is t
he completion time of the last job. An O(n 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 ra
tio of 2. An application to the general flow shop is also discussed.