Maximising the total weight of on-time jobs on parallel machines subject to a conflict graph

The paper considers scheduling on parallel machines under the constraint that some pairs of jobs cannot be processed concurrently. Each job has an associated weight, and all jobs have the same deadline. The objective is to maximise the total weight of on-time jobs. The problem is known to be strongl...

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Published in:arXiv.org
Main Authors: Zinder, Yakov, Berlińska, Joanna, Peter, Charlie
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 04.03.2021
Subjects:
Integer programming
Linear programming
Polynomials
Scheduling
Search algorithms
Weight
ISSN:2331-8422
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Abstract The paper considers scheduling on parallel machines under the constraint that some pairs of jobs cannot be processed concurrently. Each job has an associated weight, and all jobs have the same deadline. The objective is to maximise the total weight of on-time jobs. The problem is known to be strongly NP-hard in general. A polynomial-time algorithm for scheduling unit execution time jobs on two machines is proposed. The performance of a broad family of approximation algorithms for scheduling unit execution time jobs on more than two machines is analysed. For the case of arbitrary job processing times, two integer linear programming formulations are proposed and compared with two formulations known from the earlier literature. An iterated variable neighborhood search algorithm is also proposed and evaluated by means of computational experiments.
AbstractList The paper considers scheduling on parallel machines under the constraint that some pairs of jobs cannot be processed concurrently. Each job has an associated weight, and all jobs have the same deadline. The objective is to maximise the total weight of on-time jobs. The problem is known to be strongly NP-hard in general. A polynomial-time algorithm for scheduling unit execution time jobs on two machines is proposed. The performance of a broad family of approximation algorithms for scheduling unit execution time jobs on more than two machines is analysed. For the case of arbitrary job processing times, two integer linear programming formulations are proposed and compared with two formulations known from the earlier literature. An iterated variable neighborhood search algorithm is also proposed and evaluated by means of computational experiments.
Author Zinder, Yakov
Peter, Charlie
Berlińska, Joanna
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Linear programming
Polynomials
Scheduling
Search algorithms
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Title Maximising the total weight of on-time jobs on parallel machines subject to a conflict graph
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