The benefit of preemption for single machine scheduling so as to minimize total weighted completion time

Abstract

We study the preemptive and non-preemptive problems of scheduling weighted jobs on a single machine so as to minimize the total weighted completion time. We analyze the relation between non-preemptive and preemptive schedules for the problem, and find the worst-case ratio between their costs, also called the benefit of preemption. We show that this value is equal to ee−1≈1.581.