Multi-objective linear programming with interval coefficients

Purpose - The purpose of this paper is to extend a methodology for solving multi-objective linear programming (MOLP) problems, when the objective functions and constraints coefficients are stated as interval numbers.Design methodology approach - The approach proposed in this paper for the considered...

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Vydané v:Kybernetes Ročník 42; číslo 3; s. 482 - 496
Hlavní autori: Hossein Razavi Hajiagha, Seyed, Amoozad Mahdiraji, Hannan, Sadat Hashemi, Shide
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: London Emerald Group Publishing Limited 22.03.2013
Predmet:
Algorithms
Decision making
Linear programming
Operations research
Studies
Fuzzy logic
Pareto optimallity
Multi objective linear programming
Decision making
Linear programming
Order relations
Modelling
Interval numbers
Membership degree
Programming and algorithm theory
ISSN:0368-492X, 1758-7883
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Abstract Purpose - The purpose of this paper is to extend a methodology for solving multi-objective linear programming (MOLP) problems, when the objective functions and constraints coefficients are stated as interval numbers.Design methodology approach - The approach proposed in this paper for the considered problem is based on the maximization of the sum of membership degrees which are defined for each objective of multi objective problem. These membership degrees are constructed based on the deviation from optimal solutions of individual objectives. Then, the final model based on membership degrees is itself an interval linear programming which can be solved by current methods.Findings - The efficiency of the solutions obtained by the proposed method is proved. It is shown that the obtained solution by the proposed method for an interval multi objective problem is Pareto optimal.Research limitations implications - The proposed method can be used in modeling and analyzing of uncertain systems which are modeled in the context of multi objective problems and in which required information is ill defined.Originality value - The paper proposed a novel and well-defined algorithm to solve the considered problem.
AbstractList Purpose - The purpose of this paper is to extend a methodology for solving multi-objective linear programming (MOLP) problems, when the objective functions and constraints coefficients are stated as interval numbers. Design/methodology/approach - The approach proposed in this paper for the considered problem is based on the maximization of the sum of membership degrees which are defined for each objective of multi objective problem. These membership degrees are constructed based on the deviation from optimal solutions of individual objectives. Then, the final model based on membership degrees is itself an interval linear programming which can be solved by current methods. Findings - The efficiency of the solutions obtained by the proposed method is proved. It is shown that the obtained solution by the proposed method for an interval multi objective problem is Pareto optimal. Research limitations/implications - The proposed method can be used in modeling and analyzing of uncertain systems which are modeled in the context of multi objective problems and in which required information is ill defined. Originality/value - The paper proposed a novel and well-defined algorithm to solve the considered problem.
Author Hossein Razavi Hajiagha, Seyed
Amoozad Mahdiraji, Hannan
Sadat Hashemi, Shide
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  surname: Amoozad Mahdiraji
  fullname: Amoozad Mahdiraji, Hannan
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  givenname: Shide
  surname: Sadat Hashemi
  fullname: Sadat Hashemi, Shide
  organization: Department of Management, Kashan Branch, Islamic Azad University, Kashan, Iran
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Issue 3
Keywords Fuzzy logic
Pareto optimallity
Multi objective linear programming
Decision making
Linear programming
Order relations
Modelling
Interval numbers
Membership degree
Programming and algorithm theory
Language English
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SubjectTerms Algorithms
Decision making
Linear programming
Operations research
Studies
Title Multi-objective linear programming with interval coefficients
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