Extension of VIKOR Method to Find an Optimal Layout for Fixture's Supporting Points in Order to Reduce Work Piece Deformation

Document Type : Research Paper


Department of Industrial Engineering, Islamic Azad University, Arak Branch, Arak, Iran


In automotive industry fixtures have a direct effect on product manufacturing quality, productivity and cost, as a result fixtures, particularly welding fixture, play a crucial role in the auto industry. The fixture is a special tool for holding a work piece in proper position during manufacturing operation, so in the phase of the fixture design process positioning pins and surfaces are used to make sure that  the work piece is positioned correctly and remain in the same position throughout the operation. The less positioning surfaces leads to  the less work piece deformation. The aim of this paper is to find optimal number of positioning surfaces using VIKOR method with Shanon entropy concept to extract and utilize objective weights. VIKOR, means multi-criteria optimization and compromise solution, is a modern approach that has preference over other MCDM methods. An empirical example is presented to demonstrate an application of mentioned method. 


[1] Automotive Industry, 2014, Encyclopedia Britannica, Retrieved 25.
[2] Automobile Industry Analysis Essay , 2017.
[3] Silk Road, 2005, China's Automotive Industry.
[4] Morris D., Donnelly T., Donnelly T., 2004, Supplier parks in the automotive industry, Supply Chain Management: An International Journal 9(2): 129-133.
[5] Henriksen Erik K. ,1973, Jig and Fixture Design Manual, Industrial Press Inc, New York.
[6] Colvin Fred H., Haas Lucian L., 1938, Jigs and Fixtures: A Reference Book, McGraw-Hill Book Company, New York and London.
[7] Prabhaharan G., Padmanaban K. P., Krishnakumar R., 2007, Machining fixture layout optimization using FEM and evolutionary techniques, International Journal of Advanced Manufacturing Technology 32: 1090-1103.
[8] Zeshan A., 2013, Fixture layout optimization for large metal sheets using genetic algorithm, World Academy of Science, Engineering and Technology 7: 994-999.
[9] Krishnikumar K., 2000, Machining fixture layout optimization using the genetic algorithm, International Journal of Machine Tools & Manufacture 40: 579-598.
[10] Selvakumar S. , Arulshri K. P. , Padmanaban K. P. , Sasikumar K. S. K. , 2013, Design and optimization of machining fixture layout using ANN and DOE, The International Journal of Advanced Manufacturing Technology 65( 9-12): 1573-1586.
[11] Yang B. , Wang Z., Yang Y., Kang Y., Li Ch., 2017, Optimization of fixture locating layout for sheet metal part by cuckoo search algorithm combined with finite element analysis, Advances in Mechanical Engineering 9(6): 1-10.
[12] Zhang X., Yang W., Li M., 2010, An uncertainty approach for fixture layout optimization using monte carlo method, International Conference on Intelligent Robotics and Applications ICIRA, Intelligent Robotics and Applications.
[13] Bai X., Hu F., He G., Ding B., 2014, A memetic algorithm for multi-objective fixture layout optimization, SAGE Journals 229: 3047-3058.
[14] Wang Z. Q., Yang Y., Kang Y. G., Chang Z. P., 2014, A location optimization method for aircraft weakly-rigid structures, International Journal for Simulation and Multidisciplinary Design Optimization 5: A18-A21.
[15] Lu C., 2015, Fixture layout optimization for deformable sheet metal work piece, The International Journal of Advanced Manufacturing Technology 78: 85-98.
[16] Tao Z.J., Kumar A.S., Nee A.Y.C., 1999, A computational geometry approach to optimum clamping synthesis of machining fixtures, International Journal of Production Research 37(15): 3495-3517.
[17] Liao Y.J., Hu S.J., 2000, Flexible multibody dynamics based fixture–work piece analysis model for fixturing stability, International Journal of Machine Tools and Manufacture 40: 343-362.
[18] Li B., Melkote S.N., 2001, Optimal fixture design accounting for the effect of work piece dynamics, International Journal of Advanced Manufacturing Technology 18: 701-707.
[19] Li B., Shiu B. W., Lau K. J., 2002, Fixture configuration design for sheet metal assembly with laser welding: A case study, The International Journal of Advanced Manufacturing Technology 19: 501-509.
[20] Ma J., Wang M.Y., 2011, Compliant fixture layout design using topology optimization method, 2011 IEEE International Conference on Robotics and Automation, Shanghai, China.
[21] Jindo T., Hirasago K., Nagamachi M., 1995, Development of a design support system for office chairs using 3-D graphics, International Journal of Industrial Ergonomic 15: 49-62.
[22] Chen M. F., Tzeng G. H., Ding C. G., 2003, Fuzzy MCDM approach to select service provider, In IEEE International Conference on Fuzzy Systems.
[23] Wang T. C., Lee H. D., 2009, Developing a fuzzy TOPSIS approach based on subjective weights and objective weights, Expert Systems with Applications 36: 8980-8985.
[24] Deng H., Yeh C. H., Willis R. J., 2000, Inter-company comparison using modified TOPSIS with objective weights, Computers and Operations Research 27: 963-973.
[25] Opricovic S., 1998, Multicriteria optimization of civil engineering systems, Faculty of Civil Engineering 2: 5-21.
[26] Sayadi M. K., Heydari M., Shahanaghi K., 2009, Extension of VIKOR method for decision making problem with interval numbers, Applied Mathematical Modelling 33(5): 2257-2262.
[27] Yu P.L., 1973, A class of solutions for group decision problems, Management Science 19(8): 936-946.
[28] Zeleny M., 1982, Multiple Criteria Decision Making, McGraw Hill, New York.
[29] Zhang N., Wei G., 2013, Extension of VIKOR method for decision making problem based on hesitant fuzzy set, Mathematical Modelling 37: 4938-4947.