Complexity Issues in Bilevel Linear Programming

1998 ◽  
pp. 149-164 ◽  
Author(s):  
Xiaotie Deng
Keyword(s):  
Linear Programming ◽  
Bilevel Linear Programming

A method for solving bilevel linear programming problems

2008 ◽  
Vol 29 (2) ◽  
pp. 335-338 ◽  
Author(s):  
C. O. Pieume ◽  
L. P. Fotso ◽  
P. Siarry
Keyword(s):  
Linear Programming ◽  
Bilevel Linear Programming ◽  
Linear Programming Problems

scholarly journals Solving the Fully Fuzzy Bilevel Linear Programming Problem through Deviation Degree Measures and a Ranking Function Method

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Aihong Ren
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Function Method ◽  
Optimal Solution ◽  
Ranking Function ◽  
Objective Functions ◽  
Bilevel Linear Programming ◽  
Fuzzy Optimal Solution ◽  
Deviation Degree

This paper is concerned with a class of fully fuzzy bilevel linear programming problems where all the coefficients and decision variables of both objective functions and the constraints are fuzzy numbers. A new approach based on deviation degree measures and a ranking function method is proposed to solve these problems. We first introduce concepts of the feasible region and the fuzzy optimal solution of a fully fuzzy bilevel linear programming problem. In order to obtain a fuzzy optimal solution of the problem, we apply deviation degree measures to deal with the fuzzy constraints and use a ranking function method of fuzzy numbers to rank the upper and lower level fuzzy objective functions. Then the fully fuzzy bilevel linear programming problem can be transformed into a deterministic bilevel programming problem. Considering the overall balance between improving objective function values and decreasing allowed deviation degrees, the computational procedure for finding a fuzzy optimal solution is proposed. Finally, a numerical example is provided to illustrate the proposed approach. The results indicate that the proposed approach gives a better optimal solution in comparison with the existing method.

Random fuzzy bilevel linear programming through possibility-based value at risk model

2012 ◽  
Vol 5 (2) ◽  
pp. 211-224 ◽  
Author(s):  
Hideki Katagiri ◽  
Takeshi Uno ◽  
Kosuke Kato ◽  
Hiroshi Tsuda ◽  
Hiroe Tsubaki
Keyword(s):  
At Risk ◽  
Linear Programming ◽  
Value At Risk ◽  
Risk Model ◽  
Bilevel Linear Programming
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