On the solution of Large Scale Bi-Level Linear Vector Optimization Problems through TOPSIS

Abstract

In this paper, we extend TOPSIS (Technique for Order Preference by Similarity Ideal Solution) for solving Large Scale Bi-level Linear Vector Optimization  Problems (LS-BL-LVOP). In order to obtain a compromise ( satisfactory) solution to the LS-BL-LVOP problems using the proposed TOPSIS approach, a modified formulas for the distance function from the positive ideal solution (PIS ) and the distance function from the negative ideal solution (NIS) are proposed and modeled to include all the objective functions of both the first and the second levels. An  interactive decision  making algorithm for generating a compromise ( satisfactory) solution through TOPSIS approach is provided where the first level decision maker (FLDM) is asked to specify the relative importance of  the objectives. Finally, a numerical example is given to clarify the main results developed in the paper.