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A cutting plane method for bilevel linear programming with interval coefficients

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Abstract

This article considers the bilevel linear programming problem with interval coefficients in both objective functions. We propose a cutting plane method to solve such a problem. In order to obtain the best and worst optimal solutions, two types of cutting plane methods are developed based on the fact that the best and worst optimal solutions of this kind of problem occur at extreme points of its constraint region. The main idea of the proposed methods is to solve a sequence of linear programming problems with cutting planes that are successively introduced until the best and worst optimal solutions are found. Finally, we extend the two algorithms proposed to compute the best and worst optimal solutions of the general bilevel linear programming problem with interval coefficients in the objective functions as well as in the constraints.

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Acknowledgments

This work was supported by National Natural Science Foundation of China (No. 61272119, No. 61203372) and Fundamental Research Funds for the Central Universities (K5051303009).

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Authors and Affiliations

  1. Department of Mathematics, Baoji University of Arts and Sciences, Baoji, 721013, China

    Aihong Ren

  2. School of Computer Science and Technology, Xidian University, Xi’an, 710071, China

    Aihong Ren & Yuping Wang

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  1. Aihong Ren
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  2. Yuping Wang
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Correspondence to Aihong Ren.

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Ren, A., Wang, Y. A cutting plane method for bilevel linear programming with interval coefficients. Ann Oper Res 223, 355–378 (2014). https://doi.org/10.1007/s10479-014-1624-4

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