Implementation of an Online Software Tool for the Analytic Hierarchy Process (AHP-OS)



Published Dec 6, 2018
Klaus D Goepel


The Analytic Hierarchy Process (AHP) remains a popular multi-criteria decision method. The author has implemented a free, web-based AHP online system with noteworthy features, allowing for the detailed analysis of decision problems. Besides standard functions, like flexible decision hierarchies, support to improve inconsistent judgments, and alternative evaluation and sensitivity analysis, the software can handle group input, calculate group consensus based on Shannon ? and ?-entropy and estimate weight uncertainties based on randomized small variations of input judgments. In addition, different AHP judgment scales can be applied a posteriori and alternative evaluation can be done using the weighted sum (WSM) or weighted product model (WPM). This flexibility opens up opportunities to study decision projects under various parameters. The author’s intention was to provide a complete and free software tool for educational and research purposes where calculations and algorithms are well documented and all input data and results can be exported in an open format for further processing or presentation. The article describes the basic concept and structure of the software and the underlying mathematical algorithms and methods. Challenges and practical experiences during the implementation, validation and productive phase of the software are highlighted.

How to Cite

Goepel, K. D. (2018). Implementation of an Online Software Tool for the Analytic Hierarchy Process (AHP-OS). International Journal of the Analytic Hierarchy Process, 10(3).


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multi-criteria decision making, Analytic Hierarchy Process, AHP software, AHP online, AHP group decision making

Alonso, J. A., 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. Doi:

Bridgman, P.W. (1922). Dimensional Analysis. (Revised edition). New Haven, CT, U.S.A.: Yale University Press.

Goepel, K. D. (2013). Implementing the Analytic Hierarchy Process as a standard method for Multi-Criteria Decision Making in corporate enterprises – A new AHP Excel template with multiple inputs. Proceedings of the International Symposium on the Analytic Hierarchy Process for Multicriteria Decision Making, Kuala Lumpur, Malaysia.

Goepel, K. D. (2019). Comparison of judgment scales of the Analytical Hierarchy Process - A new approach. International Journal of Information Technology and Decision Making Vol.17(2019). DOI: 10.1142/S0219622019500044

Grošelj, P. Stirn, L. Z., Ayrilmis, N., Kuzman, M. K. (2015). Comparison of some aggregation techniques using group Analytic Hierarchy Process. Expert Systems with Applications, 42, 2198–2204. Doi:

Harker, P., Vargas, L. (1987). The theory of ratio scale estimation: Saaty's Analytic Hierarchy Process. Management Science, 33(11), 1383–1403. Doi:

Ishizaka,A., Labib, A. (2009). Analytic Hierarchy Process and Expert Choice: Benefits and limitations. OR Insight, 22(4), 201–220. Doi:

Ishizaka, A., Balkenborg, D., Kaplan, T. (2010). Influence of aggregation and measurement scale on ranking a compromise alternative in AHP. Journal of the Operational Research Society 62, 700–710. Doi:

Larsen, R. (2013). Elementary linear algebra. Boston, MA: Cengage Learning.

Lootsma, F. (2008). Conflict resolution via pairwise comparison of concessions. European Journal of Operational Research, 40,109–116. Doi:

Ma, D., & Zheng, X. (1991). 9/9–9/1 scale method of AHP. 2nd International Symposium on AHP, 1, 197–202.

Miller, D.W., Starr, M.K. (1960). Executive decisions and operations research. Englewood Cliffs, NJ, U.S.A.: Prentice-Hall Inc.

Ossadnik, W., Kaspar, R. (2013). Evaluation of AHP software from a management accounting perspective. Journal of Modelling in Management, 8(3), 305-319. Doi:

Saaty, T. L. (1980). The Analytic Hierarchy Process: Planning, priority setting, resource allocation. McGraw-Hill. Doi:

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

Salo, A., Hämäläinen, R. (1997). On the measurement of preferences in the Analytic Hierarchy Process. Journal of Multi-Criteria Decision Analysis, 6, 309–319. Doi:;2-2

Siraj, S., Mikhailov, L., Keane, J. A., (2015). An interactive decision support tool to estimate priorities from pairwise comparison judgments (PriEsT). International Transactions in Operational Research, 22(2), 217–235. Doi:

Triantaphyllou, E., Sánchez, A. (1997). Sensitivity analysis approach for some deterministic Multi-Criteria Decision Making Methods. Decision Sciences, 28(1), 151-194. Doi:

Wen-Hsiang Wu, Chang-tzu Chiang, Chin-tsai Lin (2008). Comparing the aggregation methods in the Analytic Hierarchy Process when uniform distribution. WSEAS Transactions On Business And Economics, 5(3), 82 – 87.
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