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Scheduling two agents on uniform parallel machines with makespan and cost functions.

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Title: Scheduling two agents on uniform parallel machines with makespan and cost functions.
Authors: Elvikis, Donatas1 elvikis@mathematik.uni-kl.de, Hamacher, Horst1 hamacher@mathematik.uni-kl.de, T'kindt, Vincent2 vincent.tkindt@univ-tours.fr
Source: Journal of Scheduling. Oct2011, Vol. 14 Issue 5, p471-481. 11p.
Subjects: Sequential scheduling, Parallel processing, Pareto optimum, Parallel computers, Industrial costs
Abstract: We consider the problem of scheduling two jobs A and B on a set of m uniform parallel machines. Each job is assumed to be independent from the other: job A and job B are made up of n and n operations, respectively. Each operation is defined by its processing time and possibly additional data such as a due date, a weight, etc., and must be processed on a single machine. All machines are uniform, i.e. each machine has its own processing speed. Notice that we consider the special case of equal-size operations, i.e. all operations have the same processing time. The scheduling of operations of job A must be achieved to minimize a general cost function F, whereas it is the makespan that must be minimized when scheduling the operations of job B. These kind of problems are called multiple agent scheduling problems. As we are dealing with two conflicting criteria, we focus on the calculation of strict Pareto optima for F and $C_{\mathrm{max}}^{B}$ criteria. In this paper we consider different min-max and min-sum versions of function F and provide special properties as well as polynomial time algorithms. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Scheduling is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: We consider the problem of scheduling two jobs A and B on a set of m uniform parallel machines. Each job is assumed to be independent from the other: job A and job B are made up of n and n operations, respectively. Each operation is defined by its processing time and possibly additional data such as a due date, a weight, etc., and must be processed on a single machine. All machines are uniform, i.e. each machine has its own processing speed. Notice that we consider the special case of equal-size operations, i.e. all operations have the same processing time. The scheduling of operations of job A must be achieved to minimize a general cost function F, whereas it is the makespan that must be minimized when scheduling the operations of job B. These kind of problems are called multiple agent scheduling problems. As we are dealing with two conflicting criteria, we focus on the calculation of strict Pareto optima for F and $C_{\mathrm{max}}^{B}$ criteria. In this paper we consider different min-max and min-sum versions of function F and provide special properties as well as polynomial time algorithms. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Scheduling is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – SubjectFull: Pareto optimum
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              Text: Oct2011
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