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Analytic Hierarchy Process and Expert Choice: Benefits and limitations

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Abstract

This article describes the original Analytic Hierarchy Process (AHP) as it is implemented in the software package Expert Choice. We demonstrate its application through a practical example. In particular, we discuss problem modelling, pairwise comparisons, judgement scales, derivation methods, consistency indices, synthesis of the weights and sensitivity analysis. Finally, the limitations of the original AHP along with the new proposed development are explained.

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References

  • Aguarón, J. and Moreno-Jiménez, J. (2000) Local stability intervals in the analytic hierarchy process. European Journal of Operational Research 125 (1): 113–132.

    Article  Google Scholar 

  • Aguarón, J. and Moreno-Jiménez, J. (2003) The geometric consistency index: Approximated thresholds. European Journal of Operational Research 147 (1): 137–145.

    Article  Google Scholar 

  • Alonso, J. and Lamata, T. (2006) Consistency in the analytic hierarchy process: A new approach. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 14 (4): 445–459.

    Article  Google Scholar 

  • Bajwa, G., Choo, E. and Wedley, W.C. (2008) Effectiveness analysis of deriving priority vectors from reciprocal pairwise comparison matrices. Asia-Pacific Journal of Operational Research 25 (3): 279–299.

    Article  Google Scholar 

  • Bana e Costa, C. and Vansnick, J. (2008) A critical analysis of the eigenvalue method used to derive priorities in AHP. European Journal of Operational Research 187 (3): 1422–1428.

    Article  Google Scholar 

  • Barzilai, J. (1997) Deriving weights from pairwise comparisons matrices. Journal of the Operational Research Society 48 (12): 1226–1232.

    Article  Google Scholar 

  • Barzilai, J. (2005) Measurement and preference function modelling. International Transactions in Operational Research 12 (2): 173–183.

    Article  Google Scholar 

  • Barzilai, J. and Lootsma, F. (1997) Power relation and group aggregation in the multiplicative AHP and SMART. Journal of Multi-Criteria Decision Analysis 6 (3): 155–165.

    Article  Google Scholar 

  • Belton, V. and Gear, A. (1983) On a shortcoming of Saaty's method of analytical hierarchies. OMEGA 11 (3): 228–230.

    Article  Google Scholar 

  • Belton, V. and Stewart, T.J. (2002) Multiple Criteria Decision Analysis: An Integrated Approach. Boston: Kluwer Academic Publishers.

    Book  Google Scholar 

  • Brugha, C. (2004) Structure of multi-criteria decision-making. Journal of the Operational Research Society 55 (1): 1156–1168.

    Article  Google Scholar 

  • Budescu, D. (1984) Scaling binary comparison matrices: A comment on Narasimhan's proposal and other methods. Fuzzy Sets and Systems 14 (2): 187–192.

    Article  Google Scholar 

  • Budescu, D., Zwick, R. and Rapoport, A. (1986) A comparison of the eigenvalue method and the geometric mean procedure for ratio scaling. Applied psychological measurement 10 (1): 69–78.

    Article  Google Scholar 

  • Cho, E. and Wedley, W. (2004) A common framework for deriving preference values from pairwise comparison matrices. Computers and Operations Research 31 (6): 893–908.

    Article  Google Scholar 

  • Crawford, G. and Williams, C. (1985) A note on the analysis of subjective judgement matrices. Journal of Mathematical Psychology 29 (4): 387–405.

    Article  Google Scholar 

  • Dodd, F. and Donegan, H. (1995) Comparison of priotization techniques using interhierarchy mappings. Journal of the Operational Research Society 46 (4): 492–498.

    Article  Google Scholar 

  • Donegan, H., Dodd, F. and Mc Master, T.B.M. (1992) A new approach to AHP decision-making. The Statician 41 (3): 295–302.

    Article  Google Scholar 

  • Dyer, J. (1990a) A clarification of ‘Remarks on the Analytic Hierarchy Process’. Management Science 36 (3): 274–275.

    Article  Google Scholar 

  • Dyer, J. (1990b) Remarks on the analytic hierarchy process. Management Science 36 (3): 249–258.

    Article  Google Scholar 

  • Escobar, M. and Moreno-Jiménez, J. (2000) Reciprocal distributions in the analytic hierarchy process. European Journal of Operational Research 123 (1): 154–174.

    Article  Google Scholar 

  • Fichtner, J. (1986) On deriving priority vectors from matrices of pairwise comparisons. Socio-Economic Planning Sciences 20 (6): 341–345.

    Article  Google Scholar 

  • Figueira, J., Greco, S. and Ehrgott, M. (2005) Multiple Criteria Decision Analysis: State of the Art Surveys. New York: Springer-Verlag.

    Book  Google Scholar 

  • Forman, E. (1990) Random indices for incomplete pairwise comparison matrices. European Journal of Operational Research 48 (1): 153–155.

    Article  Google Scholar 

  • Forman, E. and Gass, S. (2001) The analytic hierarchy process – An exposition. Operations Research 49 (4): 469–486.

    Article  Google Scholar 

  • Golany, B. and Kress, M. (1993) A multicriteria evaluation of the methods for obtaining weights from ratio-scale matrices. European Journal of Operational Research 69 (2): 210–220.

    Article  Google Scholar 

  • Golden, B., Wasil, E. and Harker, P. (1989) The Analytic Hierarchy Process: Applications and Studies. Heidelberg, Germany: Springer-Verlag.

    Book  Google Scholar 

  • Harker, P. and Vargas, L. (1987) The theory of ratio scale estimation: Saaty's analytic hierarchy process. Management Science 33 (11): 1383–1403.

    Article  Google Scholar 

  • Harker, P. and Vargas, L. (1990) Reply to ‘Remarks on the Analytic Hierarchy Process’. Management Science 36 (3): 269–273.

    Article  Google Scholar 

  • Herman, M. and Koczkodaj, W. (1996) A Monte Carlo study of pairwise comparison. Information Processing Letters 57 (11): 25–29.

    Article  Google Scholar 

  • Ho, W. (2008) Integrated analytic hierarchy process and its applications – A literature review. European Journal of Operational Research 186 (1): 211–228.

    Article  Google Scholar 

  • Holder, R. (1990) Some comment on the analytic hierarchy process. Journal of the Operational Research Society 41 (11): 1073–1076.

    Article  Google Scholar 

  • Holder, R. (1991) Response to holder's comments on the analytic hierarchy process: Response to the response. Journal of the Operational Research Society 42 (10): 914–918.

    Article  Google Scholar 

  • Hovanov, N., Kolari, J. and Sokolov, M.V. (2008) Deriving weights from general pairwise comparisons matrices. Mathematical Social Sciences 55 (2): 205–220.

    Article  Google Scholar 

  • Ishizaka, A. (2004a) The advantages of clusters in AHP. 15th Mini-Euro Conference MUDSM, Coimbra.

  • Ishizaka, A. (2004b) Développement d’un Système Tutorial Intelligent pour Dériver des Priorités dans l’AHP, Berlin, http://www.dissertation.de.

  • Ishizaka, A., Balkenborg, D. and Kaplan, T. (2006) Influence of aggregation and preference scale on ranking a compromise alternative in AHP. Proceedings of the Multidisciplinary Workshop on Advances in Preference Handling, 28–29 August, Riva del Garda, pp. 51–57.

  • Ishizaka, A. and Lusti, M. (2004) An expert module to improve the consistency of AHP matrices. International Transactions in Operational Research 11 (1): 97–105.

    Article  Google Scholar 

  • Ishizaka, A. and Lusti, M. (2006) How to derive priorities in AHP: A comparative study. Central European Journal of Operations Research 14 (4): 387–400.

    Article  Google Scholar 

  • Ji, P. and Jiang, R. (2003) Scale transitivity in the AHP. Journal of the Operational Research Society 54 (8): 896–905.

    Article  Google Scholar 

  • Johnson, C., Beine, W. and Wang, T.Y. (1979) Right-left asymmetry in an eigenvector ranking procedure. Journal of Mathematical Psychology 19 (1): 61–64.

    Article  Google Scholar 

  • Jones, D. and Mardle, S. (2004) A distance-metric methodology for the derivation of weights from a pairwise comparison matrix. Journal of the Operational Research Society 55 (8): 869–875.

    Article  Google Scholar 

  • Kainulainen, T., Leskinen, P., Korhonen, P., Haara, A. and Hujala, T. (2009) A statistical approach to assessing interval scale preferences in discrete choice problems. Journal of the Operational Research Society 60 (2): 252–258.

    Article  Google Scholar 

  • Karapetrovic, S. and Rosenbloom, E. (1999) A quality control approach to consistency paradoxes in AHP. European Journal of Operational Research 119 (3): 704–718.

    Article  Google Scholar 

  • Kumar, S. and Vaidya, O. (2006) Analytic hierarchy process: An overview of applications. European Journal of Operational Research 169 (1): 1–29.

    Article  Google Scholar 

  • Kwiesielewicz, M. and van Uden, E. (2004) Inconsistent and contradictory judgements in pairwise comparison method in AHP. Computers and Operations Research 31 (5): 713–719.

    Article  Google Scholar 

  • Lane, E. and Verdini, W. (1989) A consistency test for AHP decision makers. Decision Sciences 20 (3): 575–590.

    Article  Google Scholar 

  • Leskinen, P. and Kangas, J. (2005) Rank reversal in multi-criteria decision analysis with statistical modelling of ratio-scale pairwise comparisons. Journal of the Operational Research Society 56 (7): 855–861.

    Article  Google Scholar 

  • Liberatore, M. and Nydick, R. (2008) The analytic hierarchy process in medical and health care decision making: A literature review. European Journal of Operational Research 189 (1): 194–207.

    Article  Google Scholar 

  • Lin, C. (2007) A revised framework for deriving preference values from pairwise comparison matrices. European Journal of Operational Research 176 (2): 1145–1150.

    Article  Google Scholar 

  • Lootsma, F. (1989) Conflict resolution via pairwise comparison of concessions. European Journal of Operational Research 40 (1): 109–116.

    Article  Google Scholar 

  • Lootsma, F. (1993) Scale sensitivity in the multiplicative AHP and SMART. Journal of Multi-Criteria Decision Analysis 2 (2): 87–110.

    Article  Google Scholar 

  • Lootsma, F. (1996) A model for the relative importance of the criteria in the multiplicative AHP and SMART. European Journal of Operational Research 94 (3): 467–476.

    Article  Google Scholar 

  • Ma, D. and Zheng, X. (1991) 9/9–9/1 Scale method of AHP. 2nd International Symposium on AHP, Pittsburgh, Vol. 1; pp. 197–202.

  • Millet, I. and Saaty, T. (2000) On the relativity of relative measures-accommodating both rank preservation and rank reversals in the AHP. European Journal of Operational Research 121 (1): 205–212.

    Article  Google Scholar 

  • Millet, I. and Schoner, B. (2005) Incorporating negative values into the analytic hierarchy process. Computers and Operations Research 32 (12): 3163–3173.

    Article  Google Scholar 

  • Omkarprasad, V. and Sushil, K. (2006) Analytic hierarchy process: An overview of applications. European Journal of Operational Research 169 (1): 1–29.

    Article  Google Scholar 

  • Peláez, P. and Lamata, M. (2003) A new measure of consistency for positive reciprocal matrices. Computers & Mathematics with Applications 46 (12): 1839–1845.

    Article  Google Scholar 

  • Pérez, J. (1995) Some comments on Saaty's AHP. Management Science 41 (6): 1091–1095.

    Article  Google Scholar 

  • Pöyhönen, M., Hämäläinen, R. and Salo, A.A. (1997) An experiment on the numerical modelling of verbal ratio statements. Journal of Multi-Criteria Decision Analysis 6 (1): 1–10.

    Article  Google Scholar 

  • Roy, B. (1996) Multicriteria Methodology for Decision Analysis. Dordrecht, the Netherlands: Kluwer Academic Publishers.

    Book  Google Scholar 

  • Saaty, T. (1972) An Eigenvalue Allocation Model for Prioritization and Planning. Energy Management and Policy Center, University of Pennsylvania. Working Paper.

  • Saaty, T. (1977) A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology 15 (3): 234–281.

    Article  Google Scholar 

  • Saaty, T. (1980) The Analytic Hierarchy Process. New York: McGraw-Hill.

    Google Scholar 

  • Saaty, T. (1986) Axiomatic foundation of the analytic hierarchy process. Management Science 32 (7): 841–855.

    Article  Google Scholar 

  • Saaty, T. (1990) An exposition of the AHP in reply to the paper ‘Remarks on the Analytic Hierarchy Process’. Management Science 36 (3): 259–268.

    Article  Google Scholar 

  • Saaty, T. (1991) Response to holder's comments on the analytic hierarchy process. journal of the Operational Research Society 42 (10): 909–929.

    Article  Google Scholar 

  • Saaty, T. (1994) Highlights and critical points in the theory and application of the analytic hierarchy process. European Journal of Operational Research 74 (3): 426–447.

    Article  Google Scholar 

  • Saaty, T. (2003) Decision-making with the AHP: Why is the principal eigenvector necessary? European Journal of Operational Research 145 (1): 85–91.

    Article  Google Scholar 

  • Saaty, T. (2006) Rank from comparisons and from ratings in the analytic hierarchy/network processes. European Journal of Operational Research 168 (2): 557–570.

    Article  Google Scholar 

  • Saaty, T. and Forman, E. (1992) The Hierarchon: A Dictionary of Hierarchies. Pittsburgh, PA: RWS Publications.

    Google Scholar 

  • Saaty, T. and Hu, G. (1998) Ranking by eigenvector versus other methods in the analytic hierarchy process. Applied Mathematics Letters 11 (4): 121–125.

    Article  Google Scholar 

  • Saaty, T. and Ozdemir, M. (2003) Negative priorities in the analytic hierarchy process. Mathematical and Computer Modelling 37 (9–10): 1063–1075.

    Article  Google Scholar 

  • Saaty, T. and Takizawa, M. (1986) Dependence and independence: From linear hierarchies to nonlinear networks. European Journal of Operational Research 26 (2): 229–237.

    Article  Google Scholar 

  • Saaty, T. and Vargas, L. (1984a) Comparison of eigenvalue, logarithmic least squares and least squares methods in estimating ratios. Mathematical Modeling 5 (5): 309–324.

    Article  Google Scholar 

  • Saaty, T. and Vargas, L. (1984b) Inconsistency and rank preservation. Journal of Mathematical Psychology 28 (2): 205–214.

    Article  Google Scholar 

  • Salo, A. and Hämäläinen, R. (1997) On the measurement of preference in the analytic hierarchy process. Journal of Multi-Criteria Decision Analysis 6 (6): 309–319.

    Article  Google Scholar 

  • Shim, J. (1989) Bibliography research on the analytic hierarchy process (AHP). Socio-Economic Planning Sciences 23 (3): 161–167.

    Article  Google Scholar 

  • Stam, A. and Duarte Silva, P. (2003) On multiplicative priority rating methods for AHP. European Journal of Operational Research 145 (1): 92–108.

    Article  Google Scholar 

  • Stein, W. and Mizzi, P. (2007) The harmonic consistency index for the analytic hierarchy process. European Journal of Operational Research 177 (1): 488–497.

    Article  Google Scholar 

  • Stillwell, W., von Winterfeldt, D. and John, R.S. (1987) Comparing hierarchical and non-hierarchical weighting methods for eliciting multiattribute value models. Management Science 33 (4): 442–450.

    Article  Google Scholar 

  • Temiz, N. and Tecim, V. (2009) The use of GIS and multi-criteria decision-making as a decision tool in forestry. ORInsight 22 (2): 105–123.

    Google Scholar 

  • Triantaphyllou, E. (2001) Two new cases of rank reversals when the AHP and some of its additive variants are used that do not occur with the multiplicative AHP. Journal of Multi-Criteria Decision Analysis 10 (1): 11–25.

    Article  Google Scholar 

  • Troutt, M. (1988) Rank reversal and the dependence of priorities on the underlying MAV function. Omega 16 (4): 365–367.

    Article  Google Scholar 

  • Tummala, V. and Wan, Y. (1994) On the mean random inconsistency index of the analytic hierarchy process (AHP). Computers & Industrial Engineering 27 (1–4): 401–404.

    Article  Google Scholar 

  • Vargas, L. (1990) An overview of the analytic hierarchy process and its applications. European Journal of Operational Research 48 (1): 2–8.

    Article  Google Scholar 

  • Vargas, L. (1997) Comments on Barzilai and Lootsma why the multiplicative AHP is invalid: A practical counterexample. Journal of Multi-Criteria Decision Analysis 6 (4): 169–170.

    Article  Google Scholar 

  • Wang, Y., Chin, K.-S. and Luo, Y. (2009) Aggregation of direct and indirect judgements in pairwise comparison matrices with a re-examination of the criticisms by Bana e Costa and Vansnick. Information Sciences 179 (3): 329–337.

    Article  Google Scholar 

  • Wang, Y. and Luo, Y. (2009) On rank reversal in decision analysis. Mathematical and Computer Modelling 49 (5–6): 1221–1229.

    Article  Google Scholar 

  • Webber, S., Apostolou, B. and Hassell, J.M. (1996) The sensitivity of the analytic hierarchy process to alternative scale and cue presentations. European Journal of Operational Research 96 (2): 351–362.

    Article  Google Scholar 

  • Weber, M., Eisenführ, F. and Von Winterfeldt, D. (1988) The effects of spitting attributes on weights in multiattribute utility measurement. Management Science 34 (4): 431–445.

    Article  Google Scholar 

  • Zahedi, F. (1986) The analytic hierarchy process: A survey of the method and its applications. Interface 16 (4): 96–108.

    Article  Google Scholar 

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The authors thank the anonymous reviewer for the valuable feedback and constructive criticism.

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Ishizaka, A., Labib, A. Analytic Hierarchy Process and Expert Choice: Benefits and limitations. OR Insight 22, 201–220 (2009). https://doi.org/10.1057/ori.2009.10

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