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Job shop scheduling with unit length tasks

Published online by Cambridge University Press:  21 December 2011

Meike Akveld  and
Raphael Bernhard
Meike Akveld
Affiliation:
Department of Mathematics, ETH Zürich, Zürich, Switzerland. akveld@math.ethz.ch
Raphael Bernhard
Affiliation:
Department of Information Technology and Electrical Engineering, ETH Zürich, Switzerland; beraphae@student.ethz.ch
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Abstract

In this paper, we consider a class of scheduling problems that are among the fundamental optimization problems in operations research. More specifically, we deal with a particular version called job shop scheduling with unit length tasks. Using the results of Hromkovič, Mömke, Steinhöfel, and Widmayer presented in their work Job Shop Scheduling with Unit Length Tasks: Bounds and Algorithms, we analyze the problem setting for 2 jobs with an unequal number of tasks. We contribute a deterministic algorithm which achieves a vanishing delay in certain cases and a randomized algorithm with a competitive ratio tending to 1. Furthermore, we investigate the problem with 3 jobs and we construct a randomized online algorithm which also has a competitive ratio tending to 1.

Keywords

Online algorithmscompetitive analysisjob shop scheduling
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 46 , Issue 3 , July 2012 , pp. 329 - 342
Copyright
© EDP Sciences 2011

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References

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