Various approaches to multiobjective linear programming problems with interval costs and interval weights

Optimization problems are often subject to various kinds of inexactness or inaccuracy of input data. Here, we consider multiobjective linear programming problems, in which two kinds of input entries have the form of interval data. First, we suppose that the objectives entries are interval values, an...

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Published in:Central European journal of operations research Vol. 31; no. 3; pp. 713 - 731
Main Author: Hladík, Milan
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2023
Springer
Springer Nature B.V
Subjects:
Analysis
Business and Management
Efficiency
Linear programming
Management research
Management science
Multiple objective analysis
Operations research
Operations Research/Decision Theory
Optimization
Simplex method
Vector spaces
Czech Republic
Interval analysis
Robust optimization
Multiobjective linear programming
Weighted scalarization
ISSN:1435-246X, 1613-9178
Online Access:Get full text
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Abstract Optimization problems are often subject to various kinds of inexactness or inaccuracy of input data. Here, we consider multiobjective linear programming problems, in which two kinds of input entries have the form of interval data. First, we suppose that the objectives entries are interval values, and, second, we suppose that we have an interval estimation of weights of the particular criteria. These two types of interval data naturally lead to various definitions of efficient solutions. We discuss six meaningful concepts of efficient solutions and compare them to each other. For each of them, we attempt to characterize the corresponding kind efficiency and investigate computational complexity of deciding whether a given solution is efficient.
AbstractList Optimization problems are often subject to various kinds of inexactness or inaccuracy of input data. Here, we consider multiobjective linear programming problems, in which two kinds of input entries have the form of interval data. First, we suppose that the objectives entries are interval values, and, second, we suppose that we have an interval estimation of weights of the particular criteria. These two types of interval data naturally lead to various definitions of efficient solutions. We discuss six meaningful concepts of efficient solutions and compare them to each other. For each of them, we attempt to characterize the corresponding kind efficiency and investigate computational complexity of deciding whether a given solution is efficient.
Audience Academic
Author Hladík, Milan
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  givenname: Milan
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  surname: Hladík
  fullname: Hladík, Milan
  email: hladik@kam.mff.cuni.cz
  organization: Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University
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Copyright The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022
COPYRIGHT 2023 Springer
The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022.
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Issue 3
Keywords Interval analysis
Robust optimization
Multiobjective linear programming
Weighted scalarization
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Snippet Optimization problems are often subject to various kinds of inexactness or inaccuracy of input data. Here, we consider multiobjective linear programming...
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SubjectTerms Analysis
Business and Management
Efficiency
Linear programming
Management research
Management science
Multiple objective analysis
Operations research
Operations Research/Decision Theory
Optimization
Simplex method
Vector spaces
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Title Various approaches to multiobjective linear programming problems with interval costs and interval weights
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