A. Soper, V. Strusevich

In this paper, for the problem of minimizing the makespan on two unrelated parallel machines we compare the quality of preemptive and non-preemptive schedules. It is known that there exists an optimal preemptive schedule with at most two preemptions. We show that the power of preemption, i.e., the ratio of the makespan computed for the best non-preemptive schedule to the makespan of the optimal preemptive schedule is at most 3/2. This result complements the only other known bound on the power of preemption for unrelated parallel machines which is 4 and tight in the limit of an infinite number of machines. We also show that the ratio of the makespan for the best schedule with at most one preemption to the makespan of the optimal preemptive schedule is at most 9/8. For both models, we present polynomial-time algorithms that find schedules of the required quality. These bounds match those previously
known for the less general problem with two uniform machines. We have found one point of difference between the two cases: if an optimal preemptive schedule has exactly one preemption then the power of preemption is 4/3 if the two machines are uniform and remains 3/2 if they are unrelated.

Keywords: Unrelated parallel machines, preemptive scheduling, power of preemption


TB1 Scheduling 1
June 10, 2021  11:15 AM
1 - GB Dantzig

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