Solving multi-level multi-objective linear programming problems through fuzzy goal programming approach

In this paper, two new algorithms are presented to solve multi-level multi-objective linear programming (ML-MOLP) problems through the fuzzy goal programming (FGP) approach. The membership functions for the defined fuzzy goals of all objective functions at all levels are developed in the model formu...

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Bibliographic Details
Published in:Applied mathematical modelling Vol. 34; no. 9; pp. 2377 - 2387
Main Author: Baky, Ibrahim A.
Format: Journal Article
Language:English
Published: Kidlington Elsevier Inc 01.09.2010
Elsevier
Subjects:
Algorithms
Applied sciences
Decision theory. Utility theory
Exact sciences and technology
Fuzzy
Fuzzy goal programming
Fuzzy logic
Fuzzy programming
Fuzzy set theory
Goal programming
Linear programming
Mathematical analysis
Mathematical models
Mathematical programming
Multi-level programming problems
Multi-objective linear programming
Operational research and scientific management
Operational research. Management science
Fuzzy goal programming
Fuzzy programming
Multi-level programming problems
Multi-objective linear programming
Goal programming
Membership function
Decision making
Multiobjective programming
Linear programming
Modeling
Fuzzy logic
Fuzzy decision
Objective function
ISSN:0307-904X
Online Access:Get full text
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Summary:In this paper, two new algorithms are presented to solve multi-level multi-objective linear programming (ML-MOLP) problems through the fuzzy goal programming (FGP) approach. The membership functions for the defined fuzzy goals of all objective functions at all levels are developed in the model formulation of the problem; so also are the membership functions for vectors of fuzzy goals of the decision variables, controlled by decision makers at the top levels. Then the fuzzy goal programming approach is used to achieve the highest degree of each of the membership goals by minimizing their deviational variables and thereby obtain the most satisfactory solution for all decision makers. The first suggested algorithm groups the membership functions for the defined fuzzy goals of the objective functions at all levels and the decision variables for each level except the lower level of the multi-level problem. The second proposed algorithm lexicographically solves MOLP problems of the ML-MOLP problem by taking into consideration the decisions of the MOLP problems for the upper levels. An illustrative numerical example is given to demonstrate the algorithms.
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ISSN:0307-904X
DOI:10.1016/j.apm.2009.11.004