Scheduling with State-Dependent Machine Speed
We study a preemptive single machine scheduling problem where the machine speed is externally given and depends on the number unfinished jobs. The objective is to minimize the sum of weighted completion times. We develop a greedy algorithm that solves the problem to optimality when we work with either unit weights or unit processing times. If both weights and processing times are arbitrary, we show the problem is NP-hard by making a reduction from 3-partition.
We thank Urtzi Ayesta for helpful discussion after posing this open question during the Daghstuhl Seminar 13111 “Scheduling” in 2013. Furthermore, we thank the organizers of this seminar and Schloss Daghstuhl for providing the right atmosphere to facilitate research.
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