On solving multi-level multi objective linear programming problems through fuzzy goal programming approach

In this paper, we propose an alternate technique based on fuzzy goal programming approach for solving multi-level multi objective linear programming problem (ML-MOLPP) which is simpler and requires less computational works than that of proposed algorithm by Baky, I. A. (Applied Mathematical Modellin...

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Bibliographic Details
Published in:Opsearch Vol. 51; no. 4; pp. 624 - 637
Main Author: Lachhwani, Kailash
Format: Journal Article
Language:English
Published: India Springer India 01.12.2014
Springer Nature B.V
Subjects:
Algorithms
Business and Management
Control theory
Decision making
Goal programming
Linear programming
Literature reviews
Management
Mathematical models
Mathematical programming
Mathematics
Operations research
Operations Research/Decision Theory
Problem solving
Studies
Technical Note
Variables
Compromise optimal solution
Fuzzy goal programming
Membership function
Multi-level multi objective linear programming problem
ISSN:0030-3887, 0975-0320
Online Access:Get full text
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Summary:In this paper, we propose an alternate technique based on fuzzy goal programming approach for solving multi-level multi objective linear programming problem (ML-MOLPP) which is simpler and requires less computational works than that of proposed algorithm by Baky, I. A. (Applied Mathematical Modelling, 34(2010), 2377–2387). In formulation of FGP model each objective functions at each level are transformed into fuzzy goals. Suitable membership function for every fuzzily described transformed objective functions at each level as well as the control vectors of each level decision makers are defined by determining individual optimal solution of each objective function at each of the decision making level. Then FGP approach is used for achieving highest degree of each of these membership goals by minimizing the sum of negative deviational variables. To avoid decision deadlock, solution preferences by the decision makers at each level are not taken into account of proposed FGP technique. The aim of this paper is to present simple technique to obtain compromise optimal solution of ML-MOLP problems. A comparative analysis based on numerical examples is also carried out to show similarity between two solution methodologies.
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ISSN:0030-3887
0975-0320
DOI:10.1007/s12597-013-0157-y