A bi-level multi-choice programming problem

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.