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.
International Journal of Mathematics in Operational Research, 2015 Vol.7 No.1, pp.1 - 18
Available online: 08 Nov 2014 *Full-text access for editors Access for subscribers Purchase this article Comment on this article