Scheduling on (Un-)Related Machines with Setup Times
Klaus Jansen, Marten Maack, Alexander M\"acker

TL;DR
This paper studies scheduling jobs on machines with setup times when switching between job classes, providing approximation algorithms for related and unrelated machines, including a polynomial-time scheme for related machines.
Contribution
It introduces approximation algorithms for scheduling with setup times on related and unrelated machines, including a PTAS for related machines and an optimal approximation for unrelated machines.
Findings
Polynomial-time approximation scheme for uniformly related machines.
O(log n + log m)-approximation for unrelated machines, proven optimal.
Two special cases with constant factor approximations.
Abstract
We consider a natural generalization of scheduling jobs on parallel machines so as to minimize the makespan. In our extension the set of jobs is partitioned into several classes and a machine requires a setup whenever it switches from processing jobs of one class to jobs of a different class. During such a setup, a machine cannot process jobs and the duration of a setup may depend on the machine as well as the class of the job to be processed next. For this problem, we study approximation algorithms for non-identical machines. We develop a polynomial-time approximation scheme for uniformly related machines. For unrelated machines we obtain an -approximation, which we show to be optimal (up to constant factors) unless . We also identify two special cases that admit constant factor approximations.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
