Group multiple criteria ABC inventory classification using TOPSIS approach extended by Gaussian interval type-2 fuzzy sets and optimization programs

Document Type : Article


1 Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran.

2 Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran.

3 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran


The traditional ABC inventory classification is one of such approaches in which items are classified into three classes: A, very important; B, moderately important; and C, relatively unimportant based on annual dollar usage. However, other qualitative or quantitative criteria in real world may affect grouping items in the ABC inventory classification. Hence, multiple criteria ABC inventory classification (MCABCIC) is applied to classify items, instead of using the traditional ABC inventory classification. Hence, it can be taken into account as a multiple-criteria decision making (MCDM) problem due to using different criteria. The aim of this paper is to the extent TOPSIS approach with Gaussian interval type-2 fuzzy sets (GIT2FSs) as an alternative to the traditional triangular membership functions (MFs) for the MCABCIC in which GIT2FSs are more suitable for stating curved MFs. For this purpose, a new limit distance is presented for prioritizing GIT2FSs which is based on alpha cuts. The proposed method determines the positive and negative ideal solutions as left and right reference limits and then calculates distances between assessments and these limits. In our approach, the weights of the quantitative and qualitative criteria are attained via two linear programming, respectively. The model is illustrated using a real case.


Main Subjects

1. Ramanathan, R. ABC inventory classi_cation with multiple-criteria using weighted linear optimization", Comput. Oper. Res., 33, pp. 695-700 (2006). 2. Bhattacharya, A., Sarkar, B., and Mukherjee, S.K. Distance-based consensus method for ABC analysis", Int. J. Prod. Res., 45, pp. 3405-3420 (2007). 3. Hwang, C.L. and Yoon, K., Multiple Attributes Decision Making Method and Application, Springer, Berlin (1981). 4. Zadeh, L. The concept of a linguistic variable and its application to approximate reasoning", Part 1, Inform. Sciences, 8, pp. 199-249 (1975). 5. Hameed, I.A. Using Gaussian membership functions for improving the reliability and robustness of stuA. dents' evaluation systems", Expert. Syst. Appl., 38, pp. 7135-7142 (2011). 6. Cherif, H. and Ladhari, T. A novel multi-criteria inventory classi_cation approach: arti_cial bee colony algorithm with VIKOR method", In: Czach_orski T., Gelenbe E., Grochla K., Lent R. (Eds.), Computer and Information Sciences, Communications in Computer and Information Science, 659, Springer, Cham (2016). 7. Isen, E. and Boran, S. A novel approach based on combining ANFIS, genetic algorithm and fuzzy cmeans methods for multiple criteria inventory classi_- cation", Arab. J. Sci. Eng., 43, pp. 3229-3239 (2018). 8. Lopez-Soto, D., Angel-Belloa, F., Yacoutb, S., and Alvarez, A. A multi-start algorithm to design a multi-class classi_er for a multi-criteria ABC inventory classi_cation problem", Expert. Syst. Appl., 81, pp. 12- 21 (2017). 9. Zhou, P. and Fan, L. A note on multi-criteria ABC inventory classi_cation using weighted linear optimization", Eur. J. Oper. Res., 182, pp. 1488-1491 (2007). 10. Ng, W.L. A simple classi_er for multiple criteria ABC analysis", Eur. J. Oper. Res., 177, pp. 344-353 (2007). 11. Hadi-Vencheh, A. An improvement to multiple criteria ABC inventory classi_cation", Eur. J. Oper. Res., 201, pp. 962-965 (2010). 12. Torabi, S.A., Hate_, S.M., and Saleck Pay, B. ABC inventory classi_cation in the presence of both quantitative and qualitative criteria", Comput. Ind. Eng., 63, pp. 530-537 (2012). 13. Hate_, S.M., Torabi, S.A., and Bagheri, P. Multicriteria ABC inventory classi_cation with mixed quantitative and qualitative criteria", Int. J. Prod. Econ., 52, pp. 776-786 (2014). 14. Kaabi, H. and Jabeur K. A new hybrid weighted optimization model for multi criteria ABC inventory classi_cation", In Proceedings of the Second International Afro-European Conference for Industrial Advancement, Springer, pp. 261-270 (2016). 15. Cohen, M.A. and Ernst, R. Multi-item classi_cation and generic inventory stock control policies", Prod. Inv. Manage. J., 29, pp. 6-8 (1988). 16. Lei, Q., Chen, J., and Zhou, Q. Multiple criteria inventory classi_cation based on principle components analysis and neural network", Adv. Neural. Network., 3498, pp. 1058-1063 (2005). 17. Ghorabaee, M.K., Zavadskas, E.K., and Zenonas Turskis, L.O. Multi-criteria inventory classi_cation using a new method of evaluation based on distance from average solution (EDAS)", Informatica., 26, pp. 435-451 (2015). 18. Raja, A.M.L., Ai, J., and Astanti, R.D. A clustering classi_cation of spare parts for improving inventory policies", IOP Conf. Series: Materials Science and Engineering, 114, Kuala Lumpur, Malaysia (2016). 19. Chen,Y., Li, K.W., Kilgour, D.M., and Hipel, K.W. A case-based distance model for multiple criteria ABC analysis", Comput. Oper. Res., 35, pp. 776-796 (2008). 20. Ma, L.C. A two-phase case-based distance approach for multiple-group classi_cation problems", Comput. Ind. Eng., 63, pp. 89-97 (2012). 21. Jiang, H. A multi-attribute classi_cation method on fresh agricultural products", J. Comput., 9, pp. 2443- 2448 (2014). 22. Arikan, F. and Citak, S. Multiple criteria inventory classi_cation in an electronics _rm", Int. J. Info. Tech. Dec. Mak., 16, pp. 315-331 (2017). 23. Dhar, A.R. and Sarkar, B. Application of the MOORA method for multi-criteria inventory classi_cation", Conference: 1st Frontiers in Optimization: Theory and Applications, Heritage Institute of Technology Kolkata (2017). 24. Douissa, M.R. and Jabeur, K. A new model for multicriteria ABC inventory classi_cation: PROAFTN method", Procedia. Comput. Sci., 96, pp. 550-559 (2016). 25. Lajili, I., Ladhari, T., and Babai, Z. Adaptive machine learning classi_ers for the class imbalance problem in ABC inventory classi_cation", 6th International Conference on Information Systems, Logistics and Supply Chain. ILS Conference, Bordeaux, France (2016). 26. Hu, Q., Chakhar, S., Siraj, S., and Labib, A. Spare parts classi_cation in industrial manufacturing using the dominance-based rough set approach", Eur. J. Oper. Res., 262, pp. 1136-1163 (2017). 27. Lolli, F., Ishizaka, A., Gamberini, R., Balugani, E., and Rimini, B. Decision trees for supervised multicriteria inventory classi_cation", Procedia. Manuf., 11, pp. 1871-1881 (2017). 28. Hadi-Vencheh, A. and Mohamadghasemi, A. A fuzzy AHP-DEA approach for multiple criteria ABC inventory classi_cation", Expert. Syst. Appl., 38, pp. 3346- 3352 (2011). 29. Kabir, G. and Sumi, R.S. Integrating fuzzy Delphi with fuzzy analytic hierarchy process for multiple criteria inventory classi_cation", J. Eng. Proj. Prod. Manag., 3, pp. 22-34 (2013). 30. Kabir, G. and Hasin, M.A.A. Multi-criteria inventory classi_cation through integration of fuzzy analytic hierarchy process and arti_cial neural network", Int. J. Ind. Syst. Eng., 14, pp. 74-103 (2013). 31. Lolli, F., Ishizaka, A., and Gamberini, R. New AHPbased approaches for multi-criteria inventory classi_- cation", Int. J. Prod. Econ., 156, pp. 62-74 (2014). 32. Douissa, M.R. and Jabeur, K. A new multi-criteria ABC inventory classi_cation model based on a simpli _ed electre III method and the continuous variable 3006 A. Mohamadghasemi et al./Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 2988{3006 neighborhood search", 6th International Conference on Information Systems, Logistics and Supply Chain, Bordeaux, France (2016). 33. Mendel, J.M., John, R.I., and Feilong, L. Interval type-2 fuzzy logic systems made simple", IEEE Trans. Fuzzy. Syst., 14, pp. 808-821 (2006). 34. Mendel, J.M., Uncertain Rule-based Fuzzy Logic Systems: Introduction and New Directions, Prentice Hall, Upper Saddle River, NJ (2001). 35. Chen, T.Y. An integrated approach for assessing criterion importance with interval type-2 fuzzy sets and signed distances", J. Chinese. Inst. Indus. Eng., 28, pp. 553-572 (2011). 36. Chen, T.Y. Multiple criteria group decision-making with generalized interval-valued fuzzy numbers based on signed distances and incomplete weights", Appl. Math. Modell., 36, pp. 3029-3052 (2012). 37. Tahayori, H., Tettamanzi, A., and Antoni, G.D. Approximated type-2 fuzzy set operations", In Proceedings of FUZZ-IEEE 2006, Vancouver, Canada, pp. 9042-9049 (2006). 38. Moore, R.E. Methods and applications of interval analysis", Philadelphia, SIAM (1979). 39. Buckley, J.J. Ranking alternatives using fuzzy numbers", Fuzzy. Set. Syst., 15, pp. 21-31 (1985). 40. Rashid, T., Beg, I., and Husnine, S.M. Robot selection by using generalized interval-valued fuzzy numbers with TOPSS", Appl. Soft. Comput., 21, pp. 462-468 (2014). 41. Shipley, M.F., Korvin, D.K., and Obit, R. A decision making model for multi-attribute problems incorporating uncertainty and bias measures", Comp. Oper. Res., 18, pp. 335-342 (1991).