A multiple objective programming approach to linear bilevel multi-follower programming

Habibe Sadeghi; Fatemeh Moslemi; Habibe Sadeghi; Fatemeh Moslemi

doi:10.3934/math.2019.3.763

AIMS Mathematics

2019, Volume 4, Issue 3: 763-778. doi: 10.3934/math.2019.3.763

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Research article

A multiple objective programming approach to linear bilevel multi-follower programming

Habibe Sadeghi ^,,
Fatemeh Moslemi

Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran

Received: 24 January 2019 Accepted: 14 June 2019 Published: 01 July 2019
MSC : 90C29, 90C08

In this paper, we investigate the relationship between a certain class of linear bilevel multifollower programming problems and multiple objective programming. We introduce two multiple objective linear programming problems with different objective functions and the same constraint region. We show that the extreme points of the set of efficient solutions for both problems are the same as those of the set of feasible solutions to the linear bilevel multi-follower programming problem. Based on this relationship, a new algorithm to find an optimal solution for the linear bilevel multifollower programming problem is developed. Some numerical examples are presented to show the feasibility of the proposed algorithm.
- linear bilevel programming,
- multi-follower,
- multiple objective programming,
- efficient set
Citation: Habibe Sadeghi, Fatemeh Moslemi. A multiple objective programming approach to linear bilevel multi-follower programming[J]. AIMS Mathematics, 2019, 4(3): 763-778. doi: 10.3934/math.2019.3.763

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Abstract

In this paper, we investigate the relationship between a certain class of linear bilevel multifollower programming problems and multiple objective programming. We introduce two multiple objective linear programming problems with different objective functions and the same constraint region. We show that the extreme points of the set of efficient solutions for both problems are the same as those of the set of feasible solutions to the linear bilevel multi-follower programming problem. Based on this relationship, a new algorithm to find an optimal solution for the linear bilevel multifollower programming problem is developed. Some numerical examples are presented to show the feasibility of the proposed algorithm.

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