Let there be m parallel machines and n jobs to be scheduled non-preemptively. A job j scheduled on machine i takes p_{i,j} time units to complete, where 1 ≤ i ≤ m and 1 ≤ j ≤ n. For a given schedule, the makespan is the completion time of a machine that finishes last. The goal is to produce a schedule of all n jobs with minimum makespan. This is known as the makespan problem on unrelated parallel machines (UPMs), denoted as R||C_{max}. In this thesis, we focus on subclasses of R||C_{max}. Our research consists of two components. First, a survey of theoretic results for R||C_{max} with a focus on approximation algorithms is presented. Second, we present exact polynomial-time algorithms and approximation algorithms for some subclasses of R||C_{max}. For instance, we present k-approximation algorithms on par with or better than the best known for certain subclasses of R||C_{max}.
| Identifer | oai:union.ndltd.org:MANITOBA/oai:mspace.lib.umanitoba.ca:1993/23825 |
| Date | 19 August 2014 |
| Creators | Page, Daniel |
| Contributors | Li, Ben (Computer Science), Durocher, Stephane (Computer Science) Cameron, Helen (Computer Science) Gunderson, David (Mathematics) |
| Source Sets | University of Manitoba Canada |
| Detected Language | English |
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