Multiple Objective Linear Programming with Parametric Criteria Coefficients

In this paper we study the multiple objective linear programming problem with parametric criteria coefficients. This problem is of interest since in many situations the coefficients of the objective functions of a multiple objective linear program either represent estimates of the true data or are s...

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Published in:Management science Vol. 31; no. 4; pp. 461 - 474
Main Author: Benson, Harold P
Format: Journal Article
Language:English
Published: Linthicum, MD INFORMS 01.04.1985
Institute of Management Sciences
Institute for Operations Research and the Management Sciences
Series:Management Science
Subjects:
Algorithms
Applied sciences
Candidates
Capital budgeting
Criteria
Decomposition methods
Estimates
Exact sciences and technology
Goal programming
Linear programming
Management science
Mathematical models
Mathematical programming
Mathematische Optimierung
Matrices
Multiple criteria decision making
Objective functions
Objectives
Operational research and scientific management
Operational research. Management science
Optimal solutions
Planning
programming: multicriteria
Public sector
Tableaux
Uncertainty
Water resources
Zero
Linear programming
Multicriteria analysis
Multiobjective programming
Parametric programming
Mathematical programming
ISSN:0025-1909, 1526-5501
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Abstract In this paper we study the multiple objective linear programming problem with parametric criteria coefficients. This problem is of interest since in many situations the coefficients of the objective functions of a multiple objective linear program either represent estimates of the true data or are subject to systematic variations. Properties of this problem are developed, and an algorithm for generating the set of all weakly-efficient extreme points of this problem is described. To implement this algorithm, a nonconvex subproblem must be solved for each candidate extreme point encountered. This is accomplished by applying the Generalized Benders Decomposition method. Computational results concerning the solution of these subproblems are presented.
AbstractList In this paper we study the multiple objective linear programming problem with parametric criteria coefficients. This problem is of interest since in many situations the coefficients of the objective functions of a multiple objective linear program either represent estimates of the true data or are subject to systematic variations. Properties of this problem are developed, and an algorithm for generating the set of all weakly-efficient extreme points of this problem is described. To implement this algorithm, a nonconvex subproblem must be solved for each candidate extreme point encountered. This is accomplished by applying the Generalized Benders Decomposition method. Computational results concerning the solution of these subproblems are presented.
The multiple objective linear programming problem with parametric criteria coefficients is examined. This problem is of interest since in many cases, the objective function coefficients of a multiple objective linear program may be subject to systematic variations or represent estimates of the true data, thus increasing the complexity and uncertainty of the problem. Attributes of this problem are described, followed by the development of an algorithm, based on Geoffrion's (1972) Generalized Benders Decomposition method, for generating the set of all extreme points of the problem that are weakly efficient. Implementation of this algorithm requires solving a nonconvex subproblem for each extreme point candidate. Computational results using this technique indicate that the algorithm is remarkably insensitive to increases in parameter values.
Author Benson, Harold P
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1985 INIST-CNRS
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Multicriteria analysis
Multiobjective programming
Parametric programming
Mathematical programming
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Snippet In this paper we study the multiple objective linear programming problem with parametric criteria coefficients. This problem is of interest since in many...
The multiple objective linear programming problem with parametric criteria coefficients is examined. This problem is of interest since in many cases, the...
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SubjectTerms Algorithms
Applied sciences
Candidates
Capital budgeting
Criteria
Decomposition methods
Estimates
Exact sciences and technology
Goal programming
Linear programming
Management science
Mathematical models
Mathematical programming
Mathematische Optimierung
Matrices
Multiple criteria decision making
Objective functions
Objectives
Operational research and scientific management
Operational research. Management science
Optimal solutions
Planning
programming: multicriteria
Public sector
Tableaux
Uncertainty
Water resources
Zero
Title Multiple Objective Linear Programming with Parametric Criteria Coefficients
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