Updated AHP Excel Template Version 11.12.12 Due to feedback from several users, I revised the implementation of the power method for the calculation of the Eigenvector and Eigenvalue to improve the accuracy of my AHP excel template. The calculation sheet ‘8×8 in the workbook was completely reworked. My tests show a significant increase in accuracy. As an example see my updated post AHP template – numerical accuracy.

By default the number of iterations is now set to 12.  The check value in sheet ‘8×8 cell B33 shows the sum of all matrix elements solving the Eigenvalue equation (AI*λ) x = 0 with A the Decision matrix, λ = estimated principal Eigenvalue and x = estimated Eigenvector. The ideal check value is zero. With the example numbers given in the template the result is 5E-08.

Please let me know, if  you find any problems in the new version.

AHP template – numerical accuracy

Thanks to feedback from Mihail, here a few words about the numerical accuracy when using the AHP excel template.

AHP requires the calculation of the principal Eigenvalue, the weights are derived from the Eigenvector.  In my calculations I use the power method.  It is an iterative method, and  only one of several techniques that can be used to approximate the eigenvalues of a matrix.

Update 11.12.12

The whole calculation is shown in work sheet ’10×10′. I use 12 iterations; at the end of the sheet I do a check (the reverse calculation), using the Eigenvalue equation: (Aλ IX = 0,  with A the AHP matrix; λ the principal Eigenvalue, and X the estimated Eigenvector. The resulting check value in cell B33 shows the sum of all matrix element of the Eigenvalue equation using the iterated Eigenvector and Eigenvalue. Ideally it should be zero.

Update 9.5.14

From version 2014-05-09 onward the template shows the convergence of the power method, when calculating the eigenvalue. In the summary sheet a threshold (squared Euclidean distance d2) can be set, to show how many iterations it takes, until the change of the approximated eigenvector is below the given threshold. By default the value is set to Thresh: 1E-07. As the number of iterations in the template is fixed to 12, care should be taken if the value reaches 12.

Examples

Here a practical example comparing the results from the power method, as now implemented in my template, with  an example (7 criteria) given by Saaty in Int. J. Services Sciences, Vol. 1, No. 1, 2008 (p 86, table 2). The AHP matrix is:

 1 9 5 2 1 1 1/2 1/9 1 1/3 1/9 1/9 1/9 1/9 1/5 3 1 1/3 1/4 1/3 1/9 1/2 9 3 1 1/2 1 1/3 1 9 4 2 1 2 1/2 1 9 3 1 1/2 1 1/3 2 9 9 3 2 3 1

The result according Saaty is
(0.177,  0.019, 0.042, 0.116, 0.190, 0.129, 0.327) with consistency ratio of 0,022

The result from my AHP Excel template is
(0.1775, 0.0191, 0.0418, 0.1164, 0.1896, 0.1288, 0.3268) with CR 0f 0.022
exactly the same. The check value in sheet ‘8×8 is 4E-12.

More examples

Update AHP Excel Template Version 16.10.12

Thanks to the feedback from Pascal a bug is corrected, when you select the results of individual participants in the summary sheet. Selection/display  of results from participant 4 to 7 was not shown correctly.

AHP Consistency Ratio CR

Q: I read in some texts that a consistency ratio (actually inconsistency ratio) of less than 0.1 (10%) is good. I am not sure if your consistency ratio is a consistency ratio (i.e. the higher the percentage of the CR, the better and the more consistent the results are) vs inconsistency ratio (i.e. the consistency ratio percentage in your spreadsheet should be less in order to be more consistent).

Can you please let me know if a lower of higher percentage of the consistency ratio reflects a better more consistent response? Also, how important is the CR in the interpretation of results? If two consecutive rounds of solicited info yields very similar results, would that be acceptable even if the consistency ratio may not be good?

A: The CR in my spreadsheet is exactly the same you can find in the literature. A value less than 0.1 (10%) is good, but the threshold of 0.1 is a rule of thumb . Lower values are better than higher values, but values above 0.1 can be acceptable. It depends on the nature of your project. When you process the inputs from a group (several participants), it happens that individual CRs are above 10%, but the consolidated matrix CR is ok. Please read also my comment here.

How to use the AHP excel template in a project?

Q: I’m very new to AHP and I want to use it to identify which country is the best location to offshore a certain function of a company for my MBA project. I need to find relative importance of different factors for such decision and the relative ranking of different ountries from those factors.

How do I use this excel for such purpose? Do I run it multiple times; first for finding the priority of the factors, and then for the comparison of the countries one by one for each of the factors? And lastly multiply the priorities of the factors by each country’s priority? Is there an easier way via your template to do it?

A: There is no easier way. My template only calculates the priorities of factors in one single category of a hierarchy. If you have different categories, you have to run it multiple times (once in each category/ sub-category); then calculate the final weighting factors and make the evaluation of alternatives in your own sheet. NEW since Dec 2013: You might also use my online tool BMPSG AHP hierarchy.

I cannot generalize my template, as the hierarchy could be very different from one to another project.

News from BPMSG

I’m really getting lazy …
No update of my web site since May 2012; page rank down from 3 to 2. What is going on?

It seems less questions coming up regarding my AHP excel template, though the number of downloads is quite stable. I am still curious to know about your applications; so please kindly feedback, if you are using the template for your study or work.

In between I upgraded my video equipment, using a Canon XA10 video camera and Adobe Premier Elements for editing. I produced a couple of videos for work and on holidays. Very satisfied with the results, brilliant quality in HD. Hopefully I will find some time to share my experience here or on  my Youtube channel,  so just stay connected.

Thanks so far!

Klaus

September 2012

P.S. Update Nov 8th, 2012 – Now having  problems with my XA-10 Camcorder

Update AHP Excel Template Version 9.5.12

This update corrects a bug in the calculation of the consistency ratio CR. In the 8×8 sheet the correct random index is now selected from the table depending on the actual number of criteria.

New AHP Excel template with multiple inputs

The AHP Excel template works under Windows OS and Excel version MS Excel 2013. The workbook consists of 20 input worksheets for pair-wise comparisons, a sheet for the consolidation of all judgments, a summary sheet to display the result, a sheet with reference tables (random index, limits for geometric consistency index GCI, judgment scales) and a sheet for solving the eigenvalue problem when using the eigenvector method (EVM). Latest version: 2018-09-15.

Alternative for complex AHP projects: AHP free online software.

Excel Template

• Within the input worksheets (questionnaires) priorities are calculated using the row geometric mean method (RGMM).
• Three consistency indices (the consistency ratio CR, the geometric consistency index GCI and overall dissonance Psi) are calculated. The level of consistency needed (α) is implemented as a variable input field in the summary sheet, and can be set between zero and one.
• If CR exceeds α, the top 3 inconsistent pair-wise comparisons on the input sheets are highlighted, to allow the participants an adjustment of their judgments. The judgment resulting in lower inconsistency is proposed.
• Final priorities are shown in a summary sheet; their calculation is based on the eigen vector method (EVM). For the solution of the eigenvalue problem the power method algorithm is applied with a fixed number of 20 iterations.
• Different judgment scales are implemented.
• Errors of the EVM and RGMM are show beside the calculated priorities.
• Either individual participants, or an aggregation of individual judgments (AIJ) based on the weighted geometric mean of all participants’ judgments can be selected.

Limitations

• The template does not include the hierarchy of the decision problem and the final aggregation of weights, i.e. it is only suitable for finding the weights in each category or sub-category. For the definition of a hierarchy and evaluation of alternatives see here.
• Sensitivity analysis of the final result is not included.

Reference

When you use the template for your research, please make a reference to the author’s paper.

Klaus D. Goepel, (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, Kuala Lumpur 2013. DOI: https://doi.org/10.13033/isahp.y2013.047

Please consider a donation, it will help me to maintain the website and program. At least rate the template from 1 star (poor) to 5 stars (excellent) below. An explanation of AHP (Analytic Hierarchy Process) is given in my video here. For terms of use please see our user agreement and privacy policy.

AHP-ANP practical Application with Pros and Cons The analytic hierarchy (AHP) and analytic network process (ANP) are two multi-criteria decision methods (MCDM), originally developed by Prof. Thomas L. Saaty.

ANP is a more general approach, based on the description of the problem by means of a network instead of a hierarchy as in AHP. On the other hand, ANP is also more complex in its application.

In my latest video presentation, pros and cons for both methods are shown, and a few tips for the practical application of AHP,  and setting up a network for ANP are listed.