A Compromise Decision-Making Model Based on TOPSIS and VIKOR for Multi-Objective Large- Scale Nonlinear Programming Problems with A Block Angular Structure under Fuzzy Environment

Subject Areas : Statistics

B. Vahdani ¹ , M. Salimi ² , T. Allahviranloo ³

1 - Assistant professor, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
2 - Msc, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
3 - Professor, Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

Received: 2016-04-24 Accepted : 2016-09-01 Published : 2016-06-21

Keywords: برنامه ریزی چند هدفه غیرخطی, مسائل مقیاس بزرگ, ساختار بلوکی زاویه دار VIKOR, TOPSIS,

Abstract :

This paper proposes a compromise model, based on a new method, to solve the multiobjectivelarge scale linear programming (MOLSLP) problems with block angular structureinvolving fuzzy parameters. The problem involves fuzzy parameters in the objectivefunctions and constraints. In this compromise programming method, two concepts areconsidered simultaneously. First of them is that the optimal alternative is closer to fuzzypositive ideal solution (FPIS) and farther from fuzzy negative ideal solution (FNIS). Secondof them is that the proposed method provides a maximum ‘‘group utility’’ for the‘‘majority’’ and a minimum of an individual regret for the ‘‘opponent’’. In proposedmethod, the decomposition algorithm is utilized to reduce the large-dimensional objectivespace. A multi objective identical crisp linear programming derived from the fuzzy linearmodel for solving the problem. Then, a compromise solution method is applied to solve eachsub problem based on TOPSIS and VIKOR simultaneously. Finally, to illustrate theproposed method, an illustrative example is provided.