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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Bibliographic Details
Published in:Computers & industrial engineering Vol. 128; pp. 170 - 179
Main Authors: Arana-Jiménez, Manuel, Blanco, Víctor
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.02.2019
Subjects:
Facility location
Fully fuzzy linear programming problem
Fuzzy numbers
Minimax optimization
Multiobjective optimization
Facility location
Minimax optimization
Fully fuzzy linear programming problem
Fuzzy numbers
Multiobjective optimization
ISSN:0360-8352, 1879-0550
Online Access:Get full text
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Summary:•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.
ISSN:0360-8352
1879-0550
DOI:10.1016/j.cie.2018.12.029