A Novel Multi-Criteria Decision Sorting Approach based on Chebyshev’s Theorem for Supplier Classification Problem

Mohammad Azadfallah

MCDM/ MADM; Classification; Sorting; Chebyshev’s Theorem; Supplier Selection Problem

One of the interesting features of Multi-Criteria Decision Making/ Multiple Attribute Decision Making (MCDM/ MADM) is that a number of techniques that can be used to solve the same problem. In general, three common categories of decision problems are choice problem, ranking problem, and sorting problem. While, the issue of choice and ranking problems is more emphasized in MCDM/ MADM, but the literature weakly consider sorting problems. Several solutions for the above problem are suggested (i.e., Flow sort, AHP-Sort, ELECTRE Tri, etc.). Theoretically, there is no reason to be limited to these techniques. Hence, in this paper we propose a novel multi-criteria sorting method that is based on Chebyshev’s theorem. More specifically, different from other studies on MCDM sorting problems, which put more emphasis on the extension of new models, this work attempts to present a general framework using the Chebyshev’s inequality, to transform the results of conventional MCDM models from ranking format to sort mode. Finally, the proposed approach is compared with three existed models. Compared results show that the proposed method is efficient and the results are stable.

[1] Amidan, B. G., Ferryman, T. A., and Cooley, S. K. (2005). Data outlier detection using the Chebyshev theorem. Conference paper in IEEE Aerospace conference proceedings. April 2005. doi: 10.1109/AERO.2005.1559688.Source: IEEE Explore, 1-6.
[2] Arabzad, S. M., Ghorbani, M., Razmi, J., and Shirouyehzad, H. (2014). Employing fuzzy TOPSIS and SWOT for supplier selection and order allocation problem. Int J Adv Manuf Technol, DOI: 10.1007/s00170-014-6288-3.
[3] Araz, C. and Ozkarahan, I. (2005). A multi-criteria sorting procedure for financial classification problems: the case of business failure risk assessment. Conference, intelligent data engineering and automated learning-IDEAL 2005, 6th international conference Brisbane, Australia, July 6-8, 2005, Proceedings, 563-570.
[4] Ayhan, M. B. (2013). A fuzzy AHP approach for supplier selection problem: A case study in a Gearmotor company. International Journal of Managing value and Supply Chains, 4(3), 1-11.
[5] Birnbaum, M. H. (1998). Measurement-judgment and decision-making. Academic Press, San Diego, USA.
[6] Belton, V. and Stewart, T. J. (2002). Multiple criteria decision analysis-An integrated approach. Springer Science+ Business Media Dordrecht.
[7] Bouyssou, D. and Merchant, T. (2007a). An axiomatic approach to noncompensatory sorting methods in MCDM I: the case of two categories. European Journal of operational research, 178(1), 217-245.
[8] Bouyssou, D. and Merchant, T. (2007b). An axiomatic approach to noncompensatory sorting methods in MCDM II: more than two categories. European Journal of operational research, 178(1), 246-276.
[9] Chen, Y. (2006). Multiple criteria decision analysis: classification problems and solutions. PhD thesis, Supervisor: K. W. Hipel and M. Kilgour, University of waterloo, Canada.
[10] Corrente, S., Greco, S., and Slowinski, R. (2016). Multiple criteria Hierarchy process for ELECTRE Tri methods. European Journal of operational research, 252(2016), 191-203.
[11] Damart, S., Dias, L. C., and Mousseau, V. (2007). Supporting groups in sorting decisions: methodology and use of a multi-criteria aggregation/ Disaggregation in DSS. Decision Support Systems, 43(4), 1464-1475.
[12] Dias, J., Figueira, J., and Roy, B. (2008). ELECTRE Tri-C: A multiple criteria sorting method based on central reference actions. 2008. hal-00281307V2. University Paris Dauphine, CAHIER DU LAMSADE, 274, 2008, 1-32.
[13] Dias, J. A., Figueira, J., and Roy, B. (2012). A multiple criteria sorting method where each category is characterized by several reference actions: the ELECTRE Tri-nC method. European Journal of operational research, 217(2012), 567-579.
[14] Dias, L. C. and Mousseau, V. (2003). IRIS: A DSS for multiple criteria sorting problems. Journal of Multi-Criteria decision Analysis, 12(2003), 285-298.
[15] Dizaji, L. Y. and Khanmohammadi, S. (2016). A new multi-criteria decision making based on fuzzy-TOPSIS theory. Journal of Advances in Computer Engineering and Technology, 2(4), 39-48.
[16] Doumpos, M. and Zopounidis, C. (2018). Disaggregation approaches for multi-criteria classification: An overview, 99. 77-78. in: preference Disaggregation in multi criteria decision analysis, Essay in honor of Yannis Siskos, Editor: N. Matsasinis & E. Grigorondis, Springer International Publishing AG, Part of Springer Nature 2018.
[17] Dunn, D. S. (2001). Statistics and data analysis for the behavioral sciences. McGraw-Hill companies, Inc., Newyork.
[18] Fallahpour, A. (2016). Development of multi-criteria decision-making model for supplier selection using Gene expression programming. PhD thesis, Supervisor: Dr. Ollugu and Dr. Sitinurmaya, Faculty of Engineering University of MALAYA, Kualalampur.
[19] Frej, E. A., Roselli, L. R. P., Almedia, J. A. D., and Almedia, A. T. D. (2017). A multi-criteria decision model for supplier selection in a food industry based on FITradeoff method. Mathematical Problems in Engineering, Vol. 2017, Article ID: 4541914, 1-9.
[20] Hwang, C. L. and Yoon, K. (1981). Multiple attribute decision making: methods and applications, Springer-verlag, Berlin.
[21] Ishizaka, A., Lolli, F., Gamberini, R., Rimini, B., and Balugani, E. (2017). AHP-K-GDSS: A new sorting method based on AHP for group decisions. Proceedings of the international conference on modeling and applied simulation 2017, ISBN 978-88-97999-91-1; Bruzzone, Defelice, Frjdman, Lougo, massei and Solis Eds., 1-5.
[22] Ishizaka, A. and Nemery, P. (2013). Multi-criteria decision analysis-methods and software. John Willy & Sons, Ltd.
[23] Ishizaka, A. and Nemery, PH. (2014). Assigning machines to incomparable maintenance strategies with ELECTRE Sort. Omega, 2014, Advance online Publications, 10.10161j.omega.2014.03.006.
[24] Ishizaka, A., Pearman, C., and Nemery, P. (2012). AHP Sort: An AHP based method for sorting problems. International Journal of Production Research, 50(17), 4767-4784.
[25] Kamal, M., Gupta, S., and Raina, A. A. (2018). Fuzzy multi-objective supplier selection problem in a supply chain. World Scientific News, 100(2018), An International Scientific Journal, 165-183.
[26] Karasakal, E. and Aker, P. (2017). A multi-criteria sorting approach based on data envelopment analysis for R&D project selection problem. Omega, 73(2), 79-92.
[27] Karsu, O. (2016). Approaches for inequity-averse sorting. Computer & Operations research, 66(2016), 67-80.
[28] Lourenco, R. P. and Costa, J. P. (2004). Using ELECTRE Tri outranking method to sort MOMILP nondominated solutions. European Journal of operational research, 153(2004), 271-289.
[29] Memmah, M. M., Turion, B. Q., and Rolland, A. (2014). Multi-criteria sorting methods to select virtual peach ideotypes. International Journal of Multi Criteria Decision Making, 4(4), 348-366.
[30] Mousseau, V. and Slowinski, R. (1998). Inferring ELECTRE Tri model from assignment examples. Journal of Global Optimization, 12(1998), 157-174.
[31] Pelissari, R., Amor, S. B., and Oliveira, M. C. (2019). A multi-criteria decision sorting model for pharmaceutical suppliers classification under multiple uncertainties. In book: Pharmaceutical supply chains-Medicines shortages, doi: 10.1007/978-3-030-15398-4¬_17.
[32] Rao, R. V. (2007). Decision making in the manufacturing environment, using graph theory and fuzzy multiple attribute decision-making methods. Springer-Verlag, London.
[33] Ravindran, A. (2008). Operations Research and Management science Handbook. Taylor & Francis group, LLC.
[34] Rocha, C. and Dias, L. C. (2008). An algorithm for ordinal sorting based on ELECTRE with categories defined by examples. J Glob Optim, 42(2008), 255-277.
[35] Roostaee, R., Izadikhah, M., Lotfi, F. H., and Malkhalifeh, M. R. (2012). A multi-criteria intuitionistic fuzzy group decision making method for supplier selection with VIKOR method. International journal of Fuzzy System Applications, 2(1), 1-17.
[36] Roszkowska, E. (2011). Multi-criteria decision-making models by applying the TOPSIS method to crisp and interval data. Multiple Criteria Decision Making/ University of Economics in Katowice 6, 200-230, 2011.
[37] Roszkowska, E. (2013). Rank ordering criteria weighting methods – A comparative overview. Optimum, Studia Ekonomiczne, NR 5(65), 14-33.
[38] Roy, B. (1996). Multicriteria methodology for decision aiding. Translator: M. R. McCord, Springer Science+Business Media Dordrecht.
[39] Saaty, T L. and Daj, E. (2015). When is a decision making evaluation multi-criteria decision making methods. International Journal of Information Technology & Decision Making, IJITDM-D-15-000031R1, 1-18.
[40] Sabokbar, H. F., Hosseini, A., Banaitis, A., and Banaitiene, N. (2016). A novel sorting method TOPSIS-Sort: An application for Tehran environmental quality evaluation. Business administration and Management, 2(XIX), 87-.
[41] Seifbarghy, M., Gilklayeh, A. P., & Alidoost, M. (2011). A comprehensive fuzzy multiobjective supplier selection model under price brakes and using interval comparison matrices. Journal of Industrial and Systems Engineering, 4(4), 224-244.
[42] Shih, H. S., Shyur, H. J., and Lee, E. S. (2007). An extension of TOPSIS for group decision making. Mathematical and Computer Modelling, 45(2007), 801-813.
[43] Sobrie, O. (2016). Learning preferences with multi-criteria models. Universite Paris-Saclay; Universite de Mous, 2016, English, NNT: 2016 SACLC057.Supervisor: prof. M. Pirlot.
[44] Tabar, A. A. and Charkhgard, H. (2012). Supplier selection in supply chain management by using ANP and fuzzy TOPSIS. International Journal of Applied Physics and Mathematics. 2(6), 458-461.
[45] Tayeb, S., Ahcene, B., Omar, P. J. S., and Mouloud, B. K. (2007) ‘Equipment selection by numerical resolution of the Hessian matrix and Topsis algorithm’, Asian Journal of Information Technology, Vol. 6, No. 1, pp.81-88.
[46] Tervonen, T., Figueira, J., Lahdelma, R., Dias, J. A. and Salminen, P. (2009). A stochastic method for robustness analysis in sorting problems. European Journal of operational research, 192(2009), 236-242.
[47] Walpole, R. E., Myers, R. H., Myers, S. L., and Ye, K. (2016). Probability & statistics for engineers & Scientists. Prentice Hall, PEARSON.
[48] Wang X. (2007). study of ranking irregularities when evaluating alternatives by using some ELECTRE methods and proposed new MCDM method based on Regret and Rejoicing. MSc. Thesis, supervisor: E. Triantaphyllou, Louisiana State University, USA.
[49] Xu, Z. (2015). Uncertain multi attribute decision-making methods and applications. Springer-Verlag, Berlin Heidelberg.
[50] Yue, Z. (2013a). Group decision making with multi-attribute interval data. Information Fusion, 14(2013), 551-561.
[51] Yue, Z. (2013b). An avoiding information loss approach to group decision making. Applied Mathematical Modelling, 37(2013), 112-126.
[52] Zopounidis, C. and Doumpos, M. (2002). Multi-Criteria classification and sorting method: A literature review. European Journal of operational research, 138(2002), 229-246.