Simple and objective determination of criteria weights for evaluating alternatives when using the Analytic Hierarchy Process
##plugins.themes.bootstrap3.article.main##
##plugins.themes.bootstrap3.article.sidebar##
Abstract
In both design and project management, it is usually necessary to make decisions based on criteria that, in many cases, are not completely objective. One of the most widely used methods to assist in multi-criteria decision making is the Analytic Hierarchy Process (AHP). The construction of the pairwise comparison matrix is the most critical element of the AHP method. Its construction usually requires a group of experts to make value judgments among the criteria for evaluating alternatives. This article presents a simple and objective method to construct the AHP pairwise comparison matrix, thereby reducing the degree of subjectivity. This contribution focuses on the step of assigning the scale values (1-9) to build the criteria matrix. The only step that requires human intervention is the ranking of the criteria. The rest of the steps can be programmed, e.g., in a spreadsheet, and performed automatically. Two options are presented to relate the criteria based on their positions in the ranking: option A by means of the ratios of the order of the criteria, and option B by means of the differences in the order of the criteria. The applicability of both options is evaluated using hypothetical cases compared to the rank-order centroid weight method, and an example taken from the literature. Both options of the method give good results, but option B seems to be more appropriate for problems with more than five criteria. Option A would be the most appropriate for problems with three to five criteria.
How to Cite
Downloads
##plugins.themes.bootstrap3.article.details##
AHP, criteria weights, pairwise comparison, MDCA, project management
Al-Harbi, K. M. A. S. (2001). Application of the AHP in project management. International Journal of Project Management, 19(1), 19–27. https://doi.org/10.1016/s0263-7863(99)00038-1
Alonso, J. A., & Lamata, M. T. (2006). Consistency in the Analytic Hierarchy Process: a New Approach. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 14(04), 445–459. https://doi.org/10.1142/S0218488506004114
Alvarez, P. A., Ishizaka, A., & Martínez, L. (2021). Multiple-criteria decision-making sorting methods: A survey. Expert Systems with Applications, 183, 115368. https://doi.org/10.1016/j.eswa.2021.115368
Andreolli, F., Bragolusi, P., D’Alpaos, C., Faleschini, F., & Zanini, M. A. (2022). An AHP model for multiple-criteria prioritization of seismic retrofit solutions in gravity-designed industrial buildings. Journal of Building Engineering, 45, 103493. https://doi.org/10.1016/j.jobe.2021.103493
Ardil, C. (2021a). A comparative analysis of multiple criteria decision making analysis methods for strategic, tactical, and operational decisions in military fighter aircraft selection. International Journal of Aerospace and Mechanical Engineering, 14(7), 275–288.
Ardil, C. (2021b). Scholar index for research performance evaluation using Multiple Criteria Decision Making Analysis. International Journal of Educational and Pedagogical Sciences, 13(2), 93–104.
Asadabadi, M. R., Chang, E., & Saberi, M. (2019). Are MCDM methods useful? A critical review of Analytic Hierarchy Process (AHP) and Analytic Network Process (ANP). Cogent Engineering, 6(1). https://doi.org/10.1080/23311916.2019.1623153
Bailey, R. W. (1982). Human performance engineering: A guide for system designers. Prentice Hall Professional Technical Reference.
Bana e Costa, C. A., & Vansnick, J.-C. (2008). A critical analysis of the eigenvalue method used to derive priorities in AHP. European Journal of Operational Research, 187(3), 1422–1428. https://doi.org/10.1016/j.ejor.2006.09.022
Barron, F. H., & Barrett, B. E. (1996). Decision quality using ranked attribute weights. Management Science, 42(11), 1515–1523. https://doi.org/10.1287/mnsc.42.11.1515
Bodziony, P., Patyk, M., & Kasztelewicz, Z. (2019). Multiple-criteria decision-making for the choice of equipment in mining using the AHP method. New Trends in Production Engineering, 2(1), 404–415. https://doi.org/10.2478/ntpe-2019-0043
Bruno, G., Esposito, E., Genovese, A., & Passaro, R. (2011). AHP based methodologies for suppliers selection: a critical review. International Symposium on the Analytic Hierarchy Process, 1–15.
Chen, T. (2021). A diversified AHP-tree approach for multiple-criteria supplier selection. Computational Management Science, 18(4), 431–453. https://doi.org/10.1007/s10287-021-00397-6
Cho, F. (2019). Analytic Hierarchy Process for Survey Data in R. https://cran.r-project.org/web/packages/ahpsurvey/vignettes/my-vignette.html.
Cinelli, M., Kadziński, M., Gonzalez, M., & Słowiński, R. (2020). How to support the application of multiple criteria decision analysis? Let us start with a comprehensive taxonomy. Omega, 96, 102261. https://doi.org/10.1016/j.omega.2020.102261
Cinelli, M., Kadziński, M., Miebs, G., Gonzalez, M., & Słowiński, R. (2022). Recommending multiple criteria decision analysis methods with a new taxonomy-based decision support system. European Journal of Operational Research, 302(2), 633–651. https://doi.org/10.1016/j.ejor.2022.01.011
Djamel, M. M., Hichem, A., & Mohyiddine, S. (2021). A Multiple Criteria Decision Making improvement strategy in complex manufacturing processes. International Journal of Operational Research, 1(1), 1. https://doi.org/10.1504/IJOR.2021.10030582
Edwards, W., & Barron, F. H. (1994). SMARTS and SMARTER: Improved simple methods for multiattribute utility measurement. Organizational Behavior and Human Decision Processes, 60(3), 306–325. https://doi.org/10.1006/obhd.1994.1087
Figueira, J., & Roy, B. (2002). Determining the weights of criteria in the ELECTRE type methods with a revised Simos’ procedure. European Journal of Operational Research, 139(2), 317–326. https://doi.org/10.1016/S0377-2217(01)00370-8
Forman, E. H., & Gass, S. I. (2001). The analytic hierarchy process - an exposition. Operations Research, 49(4), 469–486.
Franek, J., & Kresta, A. (2014). Judgment scales and consistency measure in AHP. Procedia Economics and Finance, 12, 164–173. https://doi.org/10.1016/S2212-5671(14)00332-3
Gunduz, M., & Alfar, M. (2019). Integration of innovation through analytical hierarchy process (AHP) in project management and planning. Technological and Economic Development of Economy, 25(2), 258–276. https://doi.org/10.3846/tede.2019.8063
Holder, R. D. (1990). Some comments on the Analytic Hierarchy Process. The Journal of the Operational Research Society, 41(11), 1073. https://doi.org/10.2307/2582904
Hutton Barron, F. (1992). Selecting a best multiattribute alternative with partial information about attribute weights. Acta Psychologica, 80(1–3), 91–103. https://doi.org/10.1016/0001-6918(92)90042-C
Ishizaka, A., & Labib, A. (2011). Review of the main developments in the analytic hierarchy process. Expert Systems with Application, 38(11), 14336–14345. https://doi.org/10.1016/j.eswa.2011.04.143
Karpak, B. (2022). Theory and applications of AHP/ANP at MCDM 2022. International Journal of the Analytic Hierarchy Process, 14(2), 1–8. https://doi.org/10.13033/ijahp.v14i2.1027
Kou, G., Yang, P., Peng, Y., Xiao, F., Chen, Y., & Alsaadi, F. E. (2020). Evaluation of feature selection methods for text classification with small datasets using multiple criteria decision-making methods. Applied Soft Computing, 86, 105836. https://doi.org/10.1016/j.asoc.2019.105836
Kumar, A., & Kumar, M. (2019). Implementation of analytic hierarchy process (AHP) as a decision-making tool for selection of materials for the robot arm. International Journal of Applied Engineering Research, 14(11), 2727–2733.
Kumar, R., Dubey, R., Singh, S., Singh, S., Prakash, C., Nirsanametla, Y., Królczyk, G., & Chudy, R. (2021). Multiple-Criteria Decision-Making and sensitivity analysis for selection of materials for knee implant Femoral Component. Materials, 14(8), 2084. https://doi.org/10.3390/ma14082084
Lootsma, F. A. (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. https://doi.org/10.1016/0377-2217(95)00129-8
Munier, N., & Hontoria, E. (2021). Uses and limitations of the AHP method. Springer International Publishing.
Noh, J., & Lee, K. M. (2003). Application of multiattribute decision-making methods for the determination of relative significance factor of impact categories. Environmental Management, 31(5), 633–641. https://doi.org/10.1007/s00267-002-2907-0
Olson, D. L., & Dorai, V. K. (1992). Implementation of the centroid method of Solymosi and Dombi. European Journal of Operational Research, 60(1), 117–129. https://doi.org/10.1016/0377-2217(92)90339-B
Ponsich, A., Domenech, B., Ferrer-Martí, L., Juanpera, M., & Pastor, R. (2022). A multi-objective optimization approach for the design of stand-alone electrification systems based on renewable energies. Expert Systems with Applications, 199, 116939. https://doi.org/10.1016/j.eswa.2022.116939
Roszkowska, E. (2013). Rank Ordering criteria weighting methods – a comparative overview. Optimum. Studia Ekonomiczne, 5(65), 14–33. https://doi.org/10.15290/ose.2013.05.65.02
Saaty, T. L. (1980). The Analytic Hierarchy Process. McGraw-Hill.
Saaty, T. L. (2008). Decision making with the analytic hierarchy process. International Journal of Services Sciences, 1(1), 83–98.
Sangiorgio, V., Di Pierro, B., Roccotelli, M., & Silvestri, B. (2021). Card game analysis for fast multi-criteria decision making. RAIRO - Operations Research, 55(3), 1213–1229. https://doi.org/10.1051/ro/2021059
Santos, M. dos, Costa, I. P. de A., & Gomes, C. F. S. (2021). Multicriteria decision-making in the selection of warships: a new approach to the AHP method. International Journal of the Analytic Hierarchy Process, 13(1), 147–169. https://doi.org/10.13033/ijahp.v13i1.833
Siekelova, A., Podhorska, I., & Imppola, J. J. (2021). Analytic Hierarchy Process in Multiple–Criteria Decision–Making: A model example. SHS Web of Conferences, 90, 01019. https://doi.org/10.1051/shsconf/20219001019
Sisto, R., Fernández-Portillo, L. A., Yazdani, M., Estepa-Mohedano, L., & Torkayesh, A. E. (2022). Strategic planning of rural areas: Integrating participatory backcasting and multiple criteria decision analysis tools. Socio-Economic Planning Sciences, 82, 101248. https://doi.org/10.1016/j.seps.2022.101248
Solymosi, T., & Dombi, J. (1986). A method for determining the weights of criteria: The centralized weights. European Journal of Operational Research, 26(1), 35–41. https://doi.org/10.1016/0377-2217(86)90157-8
Stillwell, W. G., Seaver, D. A., & Edwards, W. (1981). A comparison of weight approximation techniques in multiattribute utility decision making. Organizational Behavior and Human Performance, 28(1), 62–77. https://doi.org/10.1016/0030-5073(81)90015-5
Taylor, F. A., Ketcham, A. F., & Hoffman, D. (1998). Personnel evaluation with AHP. Management Decision, 36(10), 679–685. https://doi.org/10.1108/00251749810245336
Tiganis, A., Grigoroudis, E., & Chrysochou, P. (2023). Customer satisfaction in short food supply chains: A multiple criteria decision analysis approach. Food Quality and Preference, 104, 104750. https://doi.org/10.1016/j.foodqual.2022.104750
Vargas, L. G. (1990). An overview of the analytic hierarchy process and its applications. European Journal of Operational Research, 48(1), 2–8.
Zhu, X., Meng, X., & Zhang, M. (2021). Application of multiple criteria decision making methods in construction: A systematic literature review. Journal of Civil Engineering and Management, 27(6), 372–403. https://doi.org/10.3846/jcem.2021.15260
Copyright of all articles published in IJAHP is transferred to Creative Decisions Foundation (CDF). However, the author(s) reserve the following:
- All proprietary rights other than copyright, such as patent rights.
- The right to grant or refuse permission to third parties to republish all or part of the article or translations thereof. In case of whole articles, such third parties must obtain permission from CDF as well. However, CDF may grant rights with respect to journal issues as a whole.
- The right to use all or parts of this article in future works of their own, such as lectures, press releases, reviews, textbooks, or reprint books.
- The authors affirm that the article has been neither copyrighted nor published, that it is not being submitted for publication elsewhere, and that if the work is officially sponsored, it has been released for open publication.
The only exception to the statements in the paragraph above is the following: If an article published in IJAHP contains copyrighted material, such as a teaching case, as an appendix, then the copyright (and all commercial rights) of such material remains with the original copyright holder.
CDF will receive permission for publication of copyrighted material in IJAHP. This permission is not transferable to third parties. Permission to make electronic and paper copies of part or all of the articles, including all computer files that are linked to the articles, for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage.
This permission does not apply to previously copyrighted material, such as teaching cases. In paper copies of the article, the copyright notice and the title of the publication and its date should be visible. To copy otherwise is permitted provided that a per-copy fee is paid.
To republish, to post on servers, or redistribute to lists requires that you post a link to the IJAHP article, which is available in open access delivery mode. Do not upload the article itself.
Authors are permitted to present a talk, based on a paper submitted to or accepted by IJAHP, at a conference where the paper would not be published in a copyrighted publication either before or after the conference and where the author did not assign copyright to the conference or related publisher.