TOPSIS APPROACH TO CHANCE CONSTRAINED MULTI - OBJECTIVE MULTILEVEL QUADRATIC PROGRAMMING PROBLEM

Abstract

This paper presents TOPSIS approach to solve chance constrained multi – objective multi – level quadratic programming problem. The proposed approach actually combines TOPSIS and fuzzy goal programming. In the TOPSIS approach, most appropriate alternative is to be finding out among all possible alternatives based on both the shortest distance from positive ideal solution (PIS) and furthest distance from the negative ideal solution (NIS). PIS and NIS for all objective functions of each level have been determined in the solution process. Distance functions which measure distances from PIS and NIS have been formulated for each level. The membership functions of the distance functions have been constructed and linearized in order to approximate nonlinear membership functions into equivalent linear membership functions. Stanojevic’s normalization technique for normalization has been employed in the proposed approach. For avoiding decision deadlock, each level decision maker provides relaxation on the upper and lower bounds of the decision variables. Two FGP models have been developed in the proposed approach. Euclidean distance function has been utilized to identify the optimal compromise solution. An illustrative example has been solved to demonstrate the proposed approach.