## 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.

## New AHP Excel template with multiple inputs

The AHP Excel template works under Office Libre 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: 2022-07-08.

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. 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.

hOUje EZf Haw dn k q

## BPMSG – One Year On-line

After being on-line with the website for 1 year, it’s time to change the entry page!

Here, on BPMSG.com you will find a couple of interesting articles related to business performance management, from a more practical than theoretical point of view.

Topics covered range from

A new topic was introduced just recently: “Value-driven leadership”. I started with a general article, and added a personality profiling tool (NEO-select). If interested, you might participate and send back the completed questionnaire to get a full report.

In the section other stuff  I post other interesting information, not fitting to the main topic of the site. For example a nice video of the olive-backed sunbird, a review of the Sennheiser Bluetooth Headset etc.

BPMSG stands for Business Performance Management Singapore. As of now, it is a non-commercial website, and information is shared for educational purposes. Please see licensing conditions and terms of use.

Please also be so kind, if you use parts in your web-site or blog, to give credit and a link to my site. I hope you will find some useful information, let me know your feedback or contact me directly for any suggestions.

Klaus Goepel, Mar 2012

## My AHP Video got more than 10000 viewers

Thanks to all visitors and viewers of my AHP video. Views exceeded 10000, quite a lot for such a special topic. I hope, you all enjoyed and could take something usefull out of it.

Another practical application for ANP is in preparation: The Marketing Mix. Will still take some more time, as ANP is more complex than AHP.

### More interesting things to come!

Currently I am working on the leadership topic, still trying to get more people to try out the personal inventory.

You will receive a full report free of charge when sending the file back to me. (bpmsg at bpmsg dot com)

For those, interested in nature: have a look at my sunbird video, its in HD and some of the shots are really nice in quality.

## Analytic Hierarchy Process (AHP)

AHP stands for Analytic Hierarchy Process. It is a multi-criteria decision making method, originally developed by Prof. Thomas L. Saaty. AHP derives ratio scales from paired comparisons of criteria, and allows for some small inconsistencies in judgments.

Inputs can be actual measurements, but also subjective opinions. As a result, ratio scales (weightings) and a consistency index will be calculated. For decision making with multiple inputs from different stakeholders, the geometric mean of individual inputs is used.

Mathematically the method is based on the solution of an Eigen value problem. The results of the pair-wise comparisons are arranged in a matrix. The first normalized Eigenvector of the matrix gives the ratio scale (weighting), the largest Eigenvalue determines the consistency ratio.

An explanation of the method can be found in my video on Youtube.

AHP can be applied in many fields:

• Evaluation of product features,
• Cost-Benefit Analysis,
• Strategy development,
• Selection of Key Performance Indicators,
• Deriving weights for a combined performance index,
• Deriving a consolidated scale of importance from different inputs.

We used AHP for the evaluation of weights for the combined service index and  the hotline performance index. We also applied the method to evaluate the importance of different strategies, using multiple inputs from different colleagues, and to find the ranking of financial key performance indicators for the operational performance assessment of our companies.

## 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.

Feel free to comment and feedback here!

## AHP Excel Template

 NEW! BPMSG’s free AHP online software: For a quick evaluation of priorities use my AHP online calculator. If you need to handle a complete AHP hierarchy, try out my new AHP-OS System.