On a fully fuzzy framework for minimax mixed integer linear programming
•A crisp multiobjective MILP formulation is proposed to solve the problem.•We extend the notion of maximum to fuzzy numbers by means of the minimal upper bound.•We provide equivalent formulations for fully fuzzy minimax mixed integer programs.•The methodology is applied to Center Capacitated Facilit...
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| Vydáno v: | Computers & industrial engineering Ročník 128; s. 170 - 179 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier Ltd
01.02.2019
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| ISSN: | 0360-8352, 1879-0550 |
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| Abstract | •A crisp multiobjective MILP formulation is proposed to solve the problem.•We extend the notion of maximum to fuzzy numbers by means of the minimal upper bound.•We provide equivalent formulations for fully fuzzy minimax mixed integer programs.•The methodology is applied to Center Capacitated Facility Location Problem.
In this work, we present a modeling framework for minimax mixed 0–1 fuzzy linear problems. It is based on extending the usual rewriting of crisp minimax problems via auxiliary variables to model the maximum of a finite set of fuzzy linear functions. We prove that the considered problem can be equivalently formulated as a (crips) multiple objective mixed integer programming problem. The framework is applied to a fully fuzzy version of the capacitated center facility location problem. |
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| AbstractList | •A crisp multiobjective MILP formulation is proposed to solve the problem.•We extend the notion of maximum to fuzzy numbers by means of the minimal upper bound.•We provide equivalent formulations for fully fuzzy minimax mixed integer programs.•The methodology is applied to Center Capacitated Facility Location Problem.
In this work, we present a modeling framework for minimax mixed 0–1 fuzzy linear problems. It is based on extending the usual rewriting of crisp minimax problems via auxiliary variables to model the maximum of a finite set of fuzzy linear functions. We prove that the considered problem can be equivalently formulated as a (crips) multiple objective mixed integer programming problem. The framework is applied to a fully fuzzy version of the capacitated center facility location problem. |
| Author | Blanco, Víctor Arana-Jiménez, Manuel |
| Author_xml | – sequence: 1 givenname: Manuel surname: Arana-Jiménez fullname: Arana-Jiménez, Manuel email: manuel.arana@uca.es organization: Dept. Statistics and Operational Research, Universidad de Cádiz, Spain – sequence: 2 givenname: Víctor surname: Blanco fullname: Blanco, Víctor email: vblanco@ugr.es organization: IEMath-GR, Universidad de Granada, Spain |
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| CitedBy_id | crossref_primary_10_1016_j_asoc_2021_107757 crossref_primary_10_1016_j_eswa_2024_123201 crossref_primary_10_1007_s00500_020_05228_5 crossref_primary_10_1016_j_ejor_2019_11_036 crossref_primary_10_3233_JIFS_202398 crossref_primary_10_1016_j_eswa_2020_113906 |
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| Keywords | Facility location Minimax optimization Fully fuzzy linear programming problem Fuzzy numbers Multiobjective optimization |
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