Technical Note—Improved Dominance Conditions for the Three-Machine Flowshop Scheduling Problem

Existing combinatorial (or elimination) approaches for solving the three-machine flowshop scheduling problem are not applicable for the situation where the jobs have their least processing time on the second machine. We present improved dominance conditions that extend the applicability of combinatorial approaches to this situation. To derive these conditions we use Johnson's two-machine results as well as the nature of unscheduled jobs.