Academic Journal
The role of mathematical formulation in solving the unbalanced assignment problem.
| Τίτλος: | The role of mathematical formulation in solving the unbalanced assignment problem. |
|---|---|
| Συγγραφείς: | Vasko, Francis J.1 vasko@emeriti.kutztown.eu, Lu, Yun1, Song, Myung Soon1 |
| Πηγή: | International Journal of Industrial Optimization. Feb2026, Vol. 7 Issue 1, p39-43. 5p. |
| Θεματικοί όροι: | *Mathematical optimization, *Mathematical models, *Algorithms, Assignment problems (Programming), Cost functions |
| Περίληψη: | In a 2019 paper, the authors claim to have developed a modified Hungarian method that performs better than a number of other solution methods for the unbalanced assignment problem (UAP) based on the solution of one UAP instance that has been discussed in the literature. The purpose of this short paper is to demonstrate that the math formulation used in the 2019 paper was not as restrictive as the standard one commonly used in the literature and therefore the comparison is not valid. The commonly used UAP math formulation not only tries to minimize cost, but also tries to level load the jobs onto the machines. The formulation from the 2019 paper allows many jobs to be assigned to a low-cost machine. Hence solutions (not even optimums) to the 2019 formulation can be better than the optimal solution using the standard UAP math formulation. Additionally, it will be shown that the Modified Hungarian method proposed in the 2019 paper does not generate guaranteed optimums to the math formulation used in that paper (let alone the standard UAP formulation). An 8-job and 5-machine assignment problem that appeared in the literature will be used to illustrate the points mentioned above. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Industrial Optimization is the property of International Journal of Industrial Optimization 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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| Items | – Name: Title Label: Title Group: Ti Data: The role of mathematical formulation in solving the unbalanced assignment problem. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Vasko%2C+Francis+J%2E%22">Vasko, Francis J.</searchLink><relatesTo>1</relatesTo><i> vasko@emeriti.kutztown.eu</i><br /><searchLink fieldCode="AR" term="%22Lu%2C+Yun%22">Lu, Yun</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Song%2C+Myung+Soon%22">Song, Myung Soon</searchLink><relatesTo>1</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Industrial+Optimization%22">International Journal of Industrial Optimization</searchLink>. Feb2026, Vol. 7 Issue 1, p39-43. 5p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br />*<searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink><br />*<searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Assignment+problems+%28Programming%29%22">Assignment problems (Programming)</searchLink><br /><searchLink fieldCode="DE" term="%22Cost+functions%22">Cost functions</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In a 2019 paper, the authors claim to have developed a modified Hungarian method that performs better than a number of other solution methods for the unbalanced assignment problem (UAP) based on the solution of one UAP instance that has been discussed in the literature. The purpose of this short paper is to demonstrate that the math formulation used in the 2019 paper was not as restrictive as the standard one commonly used in the literature and therefore the comparison is not valid. The commonly used UAP math formulation not only tries to minimize cost, but also tries to level load the jobs onto the machines. The formulation from the 2019 paper allows many jobs to be assigned to a low-cost machine. Hence solutions (not even optimums) to the 2019 formulation can be better than the optimal solution using the standard UAP math formulation. Additionally, it will be shown that the Modified Hungarian method proposed in the 2019 paper does not generate guaranteed optimums to the math formulation used in that paper (let alone the standard UAP formulation). An 8-job and 5-machine assignment problem that appeared in the literature will be used to illustrate the points mentioned above. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal of Industrial Optimization is the property of International Journal of Industrial Optimization 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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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.12928/ijio.v7i1.12987x Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 5 StartPage: 39 Subjects: – SubjectFull: Mathematical optimization Type: general – SubjectFull: Mathematical models Type: general – SubjectFull: Algorithms Type: general – SubjectFull: Assignment problems (Programming) Type: general – SubjectFull: Cost functions Type: general Titles: – TitleFull: The role of mathematical formulation in solving the unbalanced assignment problem. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Vasko, Francis J. – PersonEntity: Name: NameFull: Lu, Yun – PersonEntity: Name: NameFull: Song, Myung Soon IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 02 Text: Feb2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 27146006 Numbering: – Type: volume Value: 7 – Type: issue Value: 1 Titles: – TitleFull: International Journal of Industrial Optimization Type: main |
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