Multi-level linear programming problem involving some multi-choice parameters

Abstract

In a multi-level decision making problem the decision is taken jointly by several decision makers who are at different levels. In this paper, we consider a multi-level linear programming problem where some of the cost coefficients of the objective functions and some of the right hand side parameters of the constraints are multi-choice type. The aim of this paper is to establish a suitable solution procedure to solve the stated multi-level programming problem. To tackle the multi-choice parameters of the multi-level programming problem, we use some interpolating polynomials and transform the stated problem into a multi-level mixed integer non-linear programming problem. Then we apply fuzzy programming method to solve the transformed multi-level programming problem. One numerical example is included to illustrate the solution procedure of the multi-level linear programming problem which has some multi-choice parameters.