Minimax regret solution to multiobjective linear programming problems with interval objective functions coefficients

The current paper focuses on a multiobjective linear programming problem with interval objective functions coefficients. Taking into account the minimax regret criterion, an attempt is being made to propose a new solution i.e. minimax regret solution. With respect to its properties, a minimax regret...

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Bibliographic Details
Published in:Central European journal of operations research 2013-09, Vol.21 (3), p.625-649
Main Authors: Rivaz, S., Yaghoobi, M. A.
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Business and Management
Computer programming
Criteria
Decision making
Interval arithmetic
Intervals
Linear programming
Mathematical analysis
Mathematical models
Methods
Minimax technique
Multiple criteria decision making
Operations research
Operations Research/Decision Theory
Original Paper
Random variables
Studies
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Summary:The current paper focuses on a multiobjective linear programming problem with interval objective functions coefficients. Taking into account the minimax regret criterion, an attempt is being made to propose a new solution i.e. minimax regret solution. With respect to its properties, a minimax regret solution is necessarily ideal when a necessarily ideal solution exists; otherwise it is still considered a possibly weak efficient solution. In order to obtain a minimax regret solution, an algorithm based on a relaxation procedure is suggested. A numerical example demonstrates the validity and strengths of the proposed algorithm. Finally, two special cases are investigated: the minimax regret solution for fixed objective functions coefficients as well as the minimax regret solution with a reference point. Some of the characteristic features of both cases are highlighted thereafter.
ISSN:1435-246X
1613-9178
DOI:10.1007/s10100-012-0252-9