Title: A bi-level multi-choice programming problem

Authors: Avik Pradhan; M.P. Biswal

Addresses: Department of Mathematics, Indian Institute of Technology, Kharagpur – 721 302, India ' Department of Mathematics, Indian Institute of Technology, Kharagpur – 721 302, India

Abstract: A bi-level linear programming problem is treated as a multi-objective optimisation problem where the decision is taken by two different decision makers who are at two different levels. In this paper we consider a bi-level linear programming problem where some of the cost coefficient of the objectives, and some of the right hand side parameters of the constraints are multi-choice parameters. The aim of this paper is to establish a suitable solution procedure to solve the stated bi-level programming problem. To tackle the multi-choice parameters of the bi-level programming problem, we use some interpolating polynomials. Multi-choice parameters are replaced with interpolating polynomials. Then we use fuzzy programming method to solve the transformed bi-level programming problem. We present a numerical example to illustrate the solution procedure of the bi-level linear programming problem involving some multi-choice parameters.

Keywords: bi-level programming; interpolating polynomials; fuzzy programming; multi-choice programming; MSP; multi-objective optimisation.

DOI: 10.1504/IJMOR.2015.065945

International Journal of Mathematics in Operational Research, 2015 Vol.7 No.1, pp.1 - 18

Available online: 08 Nov 2014 *

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