# Hierarchical Decision-making using a New Mathematical Model based on the Best-worst Method

• Mohammad Hashemi Tabatabaei Department of Industrial Management Faculty of Management and Accounting, Allameh Tabataba’i University, 14348-63111 Tehran, Iran
• Maghsoud Amiri Department of Industrial Management Faculty of Management and Accounting, Allameh Tabataba’i University, 14348-63111 Tehran, Iran
• Mohammad Ghahremanloo Department of Management Faculty of Industrial Engineering and Management, Shahrood University of Technology, 36199-95161 Shahrood, Iran , m.ghahremanloo@shahroodut.ac.ir
• Mehdi Keshavarz-Ghorabaee Department of Management Faculty of Humanities (Azadshahr Branch), Gonbad Kavous University, 49717-99151 Gonbad Kavous, Iran m.keshavarz@gonbad.ac.ir,
• Edmundas Kazimieras Zavadskas Vilnius Gediminas University
• Jurgita Antucheviciene Department of Construction Management and Real Estate Vilnius Gediminas Technical University, Sauletekio al. 11, LT-10223 Vilnius, Lithuania

### Abstract

Decision-making processes in different organizations often have a hierarchical and multilevel structure with various criteria and sub-criteria. The application of hierarchical decision-making has been increased in recent years in many different areas. Researchers have used different hierarchical decision-making methods through mathematical modeling. The best-worst method (BWM) is a multi-criteria evaluation methodology based on pairwise comparisons. In this paper, we introduce a new hierarchical BWM (HBWM) which consists of seven steps. In this new approach, the weights of the criteria and sub-criteria are obtained by using a novel integrated mathematical model. To analyze the proposed model, two numerical examples are provided. To show the performance of the introduced approach, a comparison is also made between the results of the HBWM and BWM methodologies. The analysis demonstrates that HBWM can effectively determine the weights of criteria and sub-criteria through an integrated model.

### References

[1] Aboutorab, H., Saberi, M., Asadabadi, M.R., Hussain, O.,Chang, E. (2018). ZBWM: The Z-number extension of Best Worst Method and its application for supplier development, Expert Systems with Applications, 107, 115-125, 2018.
https://doi.org/10.1016/j.eswa.2018.04.015

[2] Badi, I.; Ballem, M. (2018). Supplier selection using the rough BWM-MAIRCA model: A case study in pharmaceutical supplying in Libya, Decision Making: Applications in Management and Engineering, 1(2), 16-33, 2018.
https://doi.org/10.31181/dmame1802016b

[3] Baky, I.A. (2014). Interactive TOPSIS algorithms for solving multi-level non-linear multiobjective decision-making problems, Applied Mathematical Modelling, 38(4), 1417-1433, 2014.
https://doi.org/10.1016/j.apm.2013.08.016

[4] Ecer, F. (2018). Third-party logistics (3PLs) provider selection via Fuzzy AHP and EDAS integrated model, Technological and Economic Development of Economy, 24(2), 615-634, 2018.
https://doi.org/10.3846/20294913.2016.1213207

[5] Farias, L.M.S.; Santos, L.C.; Gohr, C.F.; Rocha, L.O. (2019). An ANP-based approach for lean and green performance assessment, Resources, Conservation and Recycling, 143, 77-89, 2019.
https://doi.org/10.1016/j.resconrec.2018.12.004

[6] Guo, S.; Zhao, H. (2017). Fuzzy best-worst multi-criteria decision-making method and its applications, Knowledge-Based Systems, 121, 23-31, 2017.
https://doi.org/10.1016/j.knosys.2017.01.010

[7] Gupta, H.; Barua, M.K. (2016). Identifying enablers of technological innovation for Indian MSMEs using best-worst multi criteria decision making method, Technological Forecasting and Social Change, 107, 69-79, 2016.
https://doi.org/10.1016/j.techfore.2016.03.028

[8] Gupta, H.; Barua, M.K. (2017). Supplier selection among SMEs on the basis of their green innovation ability using BWM and fuzzy TOPSIS, Journal of Cleaner Production, 152, 242- 258, 2017.
https://doi.org/10.1016/j.jclepro.2017.03.125

[9] Gupta, P.; Anand, S.; Gupta, H. (2017). Developing a roadmap to overcome barriers to energy efficiency in buildings using best worst method, Sustainable Cities and Society, 31, 244-259, 2017.
https://doi.org/10.1016/j.scs.2017.02.005

[10] Hafezalkotob, A.; Hafezalkotob, A. (2017). A novel approach for combination of individual and group decisions based on fuzzy best-worst method, Applied Soft Computing, 59, 316-325, 2017.
https://doi.org/10.1016/j.asoc.2017.05.036

[11] Ilieva, G.; Yankova, T.; Klisarova-Belcheva, S. (2018). Decision analysis with classic and fuzzy EDAS modifications, Computational and Applied Mathematics, 37(5), 5650-5680, 2017.
https://doi.org/10.1007/s40314-018-0652-0

[12] Jiang, W.; Huang, C. (2018). A multi-criteria decision-making model for evaluating suppliers in green SCM, International Journal of Computers Communications & Control, 13(3), 337- 352, 2018.
https://doi.org/10.15837/ijccc.2018.3.3283

[13] Khan, M.S.A. (2019). The Pythagorean fuzzy Einstein Choquet integral operators and their application in group decision making, Computational and Applied Mathematics, 38(3), 128, 2019.
https://doi.org/10.1007/s40314-019-0871-z

[14] Khanmohammadi, E.; Zandieh, M. (2018). Drawing a Strategy Canvas Using the Fuzzy Best-Worst Method, Global Journal of Flexible Systems Management, 20(1), 57-75, 2018.
https://doi.org/10.1007/s40171-018-0202-z

[15] Lei, L.; Zhang, W.F. (2013). Extended VIKOR method for multi-level hybrid multi-attribute group decision making, 25th Chinese Control & Decision Conference(CCDC), 1718-1722, 2013.
https://doi.org/10.1109/CCDC.2013.6561209

[16] Lu, J.; Han, J.; Hu, Y.; Zhang, G. (2016). Multilevel decision-making: A survey, Information Sciences, 346, 463-487, 2016.
https://doi.org/10.1016/j.ins.2016.01.084

[17] Maghsoodi, A.I.; Mosavat, M.; Hafezalkotob, A.; Hafezalkotob, A. (2019). Hybrid hierarchical fuzzy group decision-making based on information axioms and BWM: Prototype design selection, Computers & Industrial Engineering, 127, 788-804, 2019.
https://doi.org/10.1016/j.cie.2018.11.018

[18] Mardani, A.; Jusoh, A.; Nor, K.; Khalifah, Z.; Zakwan, N.; Valipour, A. (2015). Multiple criteria decision-making techniques and their applications-a review of the literature from 2000 to 2014., Economic Research-Ekonomska IstraLživanja, 28(1), 516-571, 2015.
https://doi.org/10.1080/1331677X.2015.1075139

[19] Mardani, A.; Jusoh, A.; Zavadskas, E.K. (2015). Fuzzy multiple criteria decision-making techniques and applications-Two decades review from 1994 to 2014, Expert Systems with Applications, 42(8), 4126-4148, 2015.
https://doi.org/10.1016/j.eswa.2015.01.003

[20] Mou, Q.; Xu, Z.; Liao, H. (2016). An intuitionistic fuzzy multiplicative best-worst method for multi-criteria group decision making, Information Sciences, 374, 224-239, 2016.
https://doi.org/10.1016/j.ins.2016.08.074

[21] Naz, S.; Akram, M. (2019). Novel decision-making approach based on hesitant fuzzy sets and graph theory, Computational and Applied Mathematics, 38(1), 7, 2019.
https://doi.org/10.1007/s40314-019-0773-0

[22] Pamucar, D.; Chatterjee, K.; Zavadskas, E.K. (2019). Assessment of third-party logistics provider using multi-criteria decision-making approach based on interval rough numbers, Computers & Industrial Engineering, 127, 383-407, 2019.
https://doi.org/10.1016/j.cie.2018.10.023

[23] Patriarca, R.; Di Gravio, G.; Costantino, F.; Falegnami, A.; Bilotta, F. (2018). An Analytic Framework to Assess Organizational Resilience, Safety and Health at Work, 9(3), 265-276, 2018.
https://doi.org/10.1016/j.shaw.2017.10.005

[24] Ren, H.; Liu, M.; Zhou, H. (2019). Extended TODIM method for MADM problem under trapezoidal intuitionistic fuzzy environment, International Journal of Computers Communications & Control, 14(2), 220-232, 2019.
https://doi.org/10.15837/ijccc.2019.2.3428

[25] Ren, J.; Liang, H.; Chan, F.T.S. (2017). Urban sewage sludge, sustainability, and transition for Eco-City: Multi-criteria sustainability assessment of technologies based on best-worst method, Technological Forecasting and Social Change, 116, 29-39, 2017.
https://doi.org/10.1016/j.techfore.2016.10.070

[26] Rezaei, J. (2015). Best-worst multi-criteria decision-making method, Omega, 53, 49-57, 2015.
https://doi.org/10.1016/j.omega.2014.11.009

[27] Rezaei, J. (2016). Best-worst multi-criteria decision-making method: Some properties and a linear model, Omega, 64, 126-130, 2016.
https://doi.org/10.1016/j.omega.2015.12.001

[28] Rezaei, J.; Wang, J.; Tavasszy, L. (2015). Linking supplier development to supplier segmentation using Best-Worst Method, Expert Systems with Applications, 42(23), 9152-9164, 2015.
https://doi.org/10.1016/j.eswa.2015.07.073

[29] Saaty, T.L. (1977). A scaling method for priorities in hierarchical structure, Journal of Mathematical Psychology, 15(3), 234-281, 1997.
https://doi.org/10.1016/0022-2496(77)90033-5

[30] Saaty, T.L. (1990). How to make a decision: the analytic hierarchy process, European Journal of Operational Research, 48(1), 9-26, 1990.
https://doi.org/10.1016/0377-2217(90)90057-I

[31] Saaty, T.L.; Takizawa, M. (1986). Dependence and independence: From linear hierarchies to nonlinear networks, European Journal of Operational Research, 26(2), 229-237, 1986.
https://doi.org/10.1016/0377-2217(86)90184-0

[32] Safarzadeh, S.; Khansefid, S.; Rasti-barzoki, M. (2018). A group multi-criteria decisionmaking based on best-worst method, Computers & Industrial Engineering, 126, 111-121, 2018.
https://doi.org/10.1016/j.cie.2018.09.011

[33] Salimi, N., Rezaei, J. (2016). Measuring efficiency of university-industry Ph. D. projects using best worst method, Scientometrics, 109(3), 1-28, 2016.
https://doi.org/10.1007/s11192-016-2121-0

[34] Serrai, W.; Abdelli, A.; Mokdad, L.; Hammal, Y. (2017). Towards an efficient and a more accurate web service selection using MCDM methods, Journal of Computational Science, 22, 253-267, 2017.
https://doi.org/10.1016/j.jocs.2017.05.024

[35] Sharaf, I.M. (2018). TOPSIS with similarity measure for MADM applied to network selection, Computational and Applied Mathematics, 37(4), 4104-4121, 2018.
https://doi.org/10.1007/s40314-017-0556-4

[36] Sitorus, F.; Cilliers, J.J.; Brito-Parada, P.R. (2018). Multi-Criteria Decision Making for the Choice Problem in Mining and Mineral Processing: Applications and Trends, Expert Systems with Applications, 121, 393-417, 2018.
https://doi.org/10.1016/j.eswa.2018.12.001

[37] Tabatabaei, M.H.; Amiri, M.; Khatami Firouzabadi, S.M.A.; Ghahremanloo, M.; Keshavarz-Ghorabaee, M.; Saparauskas, J. (2019). A new group decision-making model based on bwm and its application to managerial problems, Transformations in Business and Economics, 18(2), 197-214, 2019.

[38] Triantaphyllou, E.; Mann, S.H. (1995). Using the Analytic Hierarchy Process for Decision Making in Engineering Applications: Some Challenges, International Journal of Industrial Engineering: Applications and Practic, 2(1), 35-44, 1995.

[39] Van De Kaa, G.; Scholten, D.; Rezaei, J.; Milchram, C. (2017). The battle between battery and fuel cell powered electric vehicles: A BWM approach, Energies, 10(11), 1707, 2017.
https://doi.org/10.3390/en10111707

[40] Wei, G.; Wang, J. (2017). A comparative study of robust efficiency analysis and Data Envelopment Analysis with imprecise data, Expert Systems with Applications, 81, 28-38, 2017.
https://doi.org/10.1016/j.eswa.2017.03.043

[41] Xu, G.; Wang, S.; Yang, T.; Jiang, W. (2018). A neutrosophic approach based on TOPSIS method to image segmentation, International Journal of Computers Communications & Control, 13(6), 1047-1061, 2018.
https://doi.org/10.15837/ijccc.2018.6.3268

[42] You, P.; Guo, S.; Zhao, H.; Zhao, H. (2017). Operation performance evaluation of power grid enterprise using a hybrid BWM-TOPSIS method, Sustainability, 9(12), 2329, 2017.
https://doi.org/10.3390/su9122329

[43] Zak, J.; Kruszynski, M. (2015). Application of AHP and ELECTRE III/IV methods to multiple level, multiple criteria evaluation of urban transportation projects, Transportation Research Procedia, 10, 820-830, 2015.
https://doi.org/10.1016/j.trpro.2015.09.035

[44] Zhao, H.; Guo, S.; Zhao, H. (2018). Comprehensive performance assessment on various battery energy storage systems, Energies, 11(10), 2841, 2018.
https://doi.org/10.3390/en11102841

[45] Zhao, H.; Zhao, H.; Guo, S. (2018). Comprehensive Performance Evaluation of Electricity Grid Corporations Employing a Novel MCDM Model, Sustainability, 10(7), 2130, 2018.
https://doi.org/10.3390/su10072130
Published
2020-02-02
How to Cite
TABATABAEI, Mohammad Hashemi et al. Hierarchical Decision-making using a New Mathematical Model based on the Best-worst Method. INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL, [S.l.], v. 14, n. 6, p. 710-725, feb. 2020. ISSN 1841-9844. Available at: <http://univagora.ro/jour/index.php/ijccc/article/view/3675>. Date accessed: 01 dec. 2021.
Citation Formats
Section
Articles

### Keywords

decision model, MCDM, best-worst method, hierarchical decisionmaking, pairwise comparison