A sensitivity analysis in MCDM problems: A statistical approach

Authors

  • Irik Mukhametzyanov Ufa State Petroleum Technological University, 1 Kosmonavtov st., 450062, Ufa, Russia
  • Dragan Pamucar University of defence in Belgrade, Military academy, Department of logistics, Belgrade, Serbia

DOI:

https://doi.org/10.31181/dmame1802050m

Keywords:

Multi-criteria Decision-making, SAW, MOORA, VIKOR, COPRAS, CODAS, TOPSIS, D’IDEAL, MABAC, PROMETHEE-I,II, ORESTE-II, Sensitivity Analysis

Abstract

This study provides a model for result consistency evaluation of multi-criteria decision-making (MDM) methods and selection of the optimal one. The study presents the results of an analysis of the sensitivity of decision-making based on the rank methods: SAW, MOORA, VIKOR, COPRAS, CODAS, TOPSIS, D’IDEAL, MABAC, PROMETHEE-I,II, ORESTE-II with variations in the elements in the decision matrix within a given error (imprecision). It is suggested to use multiple simulation of the elements estimations of the decision matrix within a given error for calculating the ranks of alternatives, which allows obtaining statistical estimates of ranks. Based on the statistics of simulations, decision-making can be carried out not only on the alternatives statistics having rank I but also on the statistics of alternatives having the largest total I and II rank or I, II and III ranks. This is especially true when the difference in rank values ​​is not large and is distributed evenly among the first three ranks. The calculations results for the task of selecting the adequate location of 8 objects by 11 criteria are presented here. The main result shows that the alternatives having I, II and III ranks for some ranking methods are not distinguishable within the selected error value of the elements in the decision matrix. A quantitative analysis can only narrow the number of effective alternatives for a final decision. A statistical analysis makes the number of options estimation possible in which an alternative has a priority. Additional criteria that take into account both aggregate priorities and the availability of possible priorities for other alternatives with small variations in the decision matrix provide additional important information for the decision-maker.

Downloads

Download data is not yet available.

References

Anojkumar, L., Ilangkumaran, M., & Sasirekha, V. (2014). Comparative analysis of MCDM methods for pipe material selection in sugar industry. Expert systems with applications, 41(6), 2964-2980.

Anupama, K. S. S., Gowri, S. S., Rao, B. P., & Rajesh, P. (2015). Application of madm algorithms to network selection. International Journal of Innovative Research in Electrical, Electronics, Instrumentation and Control Engineering, 3(6), 64-67.

Barron, H., & Schmidt, C. P. (1988). Sensitivity analysis of additive multi-attribute value models. Operations Research, 36(1), 122-127.

Brans, J., P., Vincke, P., Mareschal, B. (1986). How to select and how to rank projects: The ORESTE method. European Journal of Operational Research, 24, pp. 228–238.

Brauers, W. K. M. (2008). Multi-objective contractor’s ranking by applying the MOORA method. Journal of Business Economics and management, (4), 245-255.

Brauers, W. K. M., Zavadskas, E. K., Peldschus, F., & Turskis, Z. (2008). Multi-objective optimization of road design alternatives with an application of the MOORA method.

Brauers, W. K., & Zavadskas, E. K. (2006). The MOORA method and its application to privatization in a transition economy. Control and cybernetics, 35(2), 445-469.

Chang, C. H., Lin, J. J., Linc, J. H., Chiang, M. C. (2010). Domestic open-end equity mutual fund performance evaluation using extended TOPSIS method with different distance approaches. Expert Systems with Applications, 37(6), 4642-4649.

Corrente, S., Figueira, J. R., & Greco, S. (2014). The smaa-promethee method. European Journal of Operational Research, 239(2), 514-522.

Evans, J. R. (1984). Sensitivity analysis in decision theory. Decision Sciences, 1(15), 239-247.

Figueira, J., Greco, S., & Ehrgott, M. (2005). Multiple Criteria Decision Analysis: State of the Art Surveys. Springer Verlag.

Insua, D. R. (1989). Sensitivity analysis in multi-objective decision making (Doctoral dissertation, University of Leeds).

Kaklauskas, A., Zavadskas, E. K., Raslanas, S., Ginevicius, R., Komka, A., & Malinauskas, P. (2006). Selection of low-e windows in retrofit of public buildings by applying multiple criteria method COPRAS: A Lithuanian case. Energy and buildings, 38(5), 454-462.

Kalibatas, D., & Turskis, Z. (2008). Multicriteria evaluation of inner climate by using MOORA method. Information technology and control, 37(1), 79-83.

Kannan, D., de Sousa Jabbour, A. B. L., & Jabbour, C. J. C. (2014). Selecting green suppliers based on GSCM practices: Using fuzzy TOPSIS applied to a Brazilian electronics company. European Journal of operational research, 233(2), 432-447.

Keshavarz Ghorabaee, M., Zavadskas, E. K., Turskis, Z., & Antucheviciene, J. (2016). A new combinative distance-based assessment (CODAS) method for multi-criteria decision-making. Economic Computation & Economic Cybernetics Studies & Research, 50(3).

Li, P., Qian, H., Wu, J., & Chen, J. (2013a). Sensitivity analysis of TOPSIS method in water quality assessment: I. Sensitivity to the parameter weights, Environmental Monitoring and Assessment 185, 2453–2461.

Li, P., Qian, H., Wu, J., & Chen, J. (2013b). Sensitivity analysis of TOPSIS method in water quality assessment II: Sensitivity to the index input data, Environmental Monitoring and Assessment 185, 2463–2474.

Liu, H. C., Wu, J., & Li, P. (2013). Assessment of health-care waste disposal methods using a VIKOR-based fuzzy multi-criteria decision making method. Waste management, 33(12), 2744-2751.

Mehrjerdi, Y. Z., & Nadizadeh, A. (2013). Using greedy clustering method to solve capacitated location-routing problem with fuzzy demands. European Journal of Operational Research, 229(1), 75-84.

Mukhametzyanov, I. (2018a). MCDM_tools. Mathworks File Exchange: https://www.mathworks.com/matlabcentral/fileexchange/65742-mcdm-tools. Accessed 6 Jun 2018.

Mukhametzyanov, I. (2018b). IZ-norm method. Mathworks File Exchange: https://www.mathworks.com/matlabcentral/fileexchange/67950-iz-norm-method. Accessed 5 July 2018.

Mukhametzyanov, I. (2018c). Norm_Analysis. Mathworks File Exchange: https://www.mathworks.com/matlabcentral/fileexchange/67705-norm-analysis. Accessed 12 Jun 2018.

Mukhametzyanov, I. (2018d). Sens_Analysis. Mathworks File Exchange: https://www.mathworks.com/matlabcentral/fileexchange/67803-mcdm-sens-analysis. Accessed 21 Jun 2018.

Mukhametzyanov, I., & Pamučar, D. (2017). MCDM METODS: Sensitivity of results in variation of estimations of alternatives by criteria. International Conference on Management, Engineering and Environment (ICMNEE). September 28-29, 2017. Beograde: RABEK and ECOR, pp. 2-24.

Opricovic, S., & Tzeng, G. H. (2004). Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. European journal of operational research, 156(2), 445-455.

Pamučar, D. S., Božanić, D., & Ranđelović, A. (2017). Multi-criteria decision making: An example of sensitivity analysis. Serbian journal of management, 12(1), 1-27.

Pamučar, D., & Ćirović, G. (2015). The selection of transport and handling resources in logistics centers using Multi-Attributive Border Approximation area Comparison (MABAC). Expert systems with applications, 42(6), 3016-3028.

Pavličić, D. M. (1997). Calibration or the ability to evaluate own judgments objectively. Psihologija, 30(4), 353-378.

Peng, Y., Kou, G., Wang, G., & Shi, Y. (2011). FAMCDM: A fusion approach of MCDM methods to rank multiclass classification algorithms. Omega, 39(6), 677-689.

Rahmaniani, R., Saidi-Mehrabad, M., & Ashouri, H. (2013). Robust capacitated facility location problem optimization model and solution algorithms. Journal of Uncertain Systems, 7(1), 22–35.

Rodrigues F. L. J., Osiro, L., & Carpinetti L. C. R. (2014). A comparation between Fuzzy AHP and Fuzzy TOPSIS methods to supplier selection Applied Soft Computing, 21, 194–209.

Roubens, M. (1978). Agrégation des préférences en présence de préordres totaux sur l'ensemble des actions et d'une relation de préférence du type (IPQ) sur les points de vue. MCDM Work shop, Aix-en-Provence, France.

Samson, D. (1988). Managerial decision analysis. Chicago, IL: Irwin.

Shanian, A., & Savadogo, O. (2006). TOPSIS multiple-criteria decision support analysis for material selection of metallic bipolar plates for polymer electrolyte fuel cell. Journal of Power Sources, 159(2), 1095-1104.

Stevens-Navarro, E., Martinez-Morales, J. D., & Pineda-Rico, U. (2012). Evaluation of vertical handoff decision algorightms based on madm methods for heterogeneous wireless networks. Journal of applied research and technology, 10(4), 534-548.

Sun, M. (2012). A tabu search heuristic procedure for the capacitated facility location problem. Journal of Heuristics, 18(1), 91–118.

Triantaphyllou E. (2011). Multi-criteria Decision-making Methods: A Comparative Study. Springer, doi: 10.1007/978-1-4757-3157-6.

Triantaphyllou, E. & Lin, C. T. (1996). Development and evaluation of five fuzzy multi-attribute decision-making methods. Approximate Reasoning, 14(4), 281-310.

Triantaphyllou, E. (1992). A sensitivity analysis of a (Ti, Si) inventory policy with increasing demand. Operations Research Letters, 11(3), 167-172.

Triantaphyllou, E., & Mann, S. H. (1989). An examination of the effectiveness of multi-dimensional decision-making methods: A decision-making paradox. Decision Support Systems, 5, 303-312.

Tzeng, G. H. & Huang, J. J. (2011). Multiple Attribute Decision-making: Methods and Applications, Chapman and Hall/CRC.

Ustinovichius, L., Zavadskas, E. K., & Podvezko, V. (2007). Application of a quantitative multiple criteria decision making (MCDM-1) approach to the analysis of investments in construction. Control and cybernetics, 36(1), 251-268.

Viteikiene, M., & Zavadskas, E. K. (2007). Evaluating the sustainability of Vilnius city residential areas. Journal of civil engineering and management, 13(2), 149-155.

Von Winterfeldt, D., & Edwards, W. (1986). Decision analysis and behavioral research. Cambridge: Cambridge University Press.

Wang, Y. L., & Tzeng, G. H. (2012). Brand marketing for creating brand value based on a MCDM model combining DEMATEL with ANP and VIKOR methods. Expert systems with applications, 39(5), 5600-5615.

Watson, S., & Buede, D. (1987). Decision synthesis. Cambridge: Cambridge University Press.

Yang, J. L., Chiu, H. N., Tzeng, G. H., & Yeh, R. H. (2008). Vendor selection by integrated fuzzy MCDM techniques with independent and interdependent relationships. Information Sciences, 178(21), 4166-4183.

Yu, O. Y., Guikema, S. D., Briaud, J. L., & Burnett, D. (2012). Sensitivity analysis for multi‐attribute system selection problems in onshore Environmentally Friendly Drilling (EFD). Systems engineering, 15(2), 153-171.

Downloads

Published

2018-10-15

How to Cite

Mukhametzyanov, I., & Pamucar, D. (2018). A sensitivity analysis in MCDM problems: A statistical approach. Decision Making: Applications in Management and Engineering, 1(2), 51–80. https://doi.org/10.31181/dmame1802050m

Issue

Vol. 1 No. 2 (2018): Decision Making: Applications in Management and Engineering

Section

Regular articles

License

Copyright (c) 2018 Decision Making: Applications in Management and Engineering

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.