Tag: AHP

Welcome to BPMSG – July 2019

Concepts, Methods and Tools to manage Business Performance

Dear Friends, dear Visitors,

We released a major update of my free AHP online software. It is now running under PHP 7 and should be noticeable faster than before. Beside some under-the-hood improvement a few new features were added. For more details read my post here.

As a new tool on my website I added a collection of my literature about multi-criteria decision making and AHP. It is available for everyone under the menu point Tools -> Literature. I am using the open source software package Wikindx5. You can browse or search for articles, authors, journals etc. Over time I will fill it up with more article and other research contributions. You can also register as a user and add your own literature to share with others.

Wikindx allows to include citations into a blog. As an example, the following reference is taken from Wikindx:

Many thanks to all donors, supporting this website. Unfortunately, over the last months I didn’t receive many donations. The annual invoice from my hosting provider is expected to come soon, therefore, please continue to support my effort with a small donation, especially when you use my free template or online software.

For now, please enjoy your visit on the site and feel free to leave a comment – it is always appreciated. And keep in mind: Better to be approximately right than precisely wrong.

Klaus

Klaus D. Goepel, Singapore, July 2019

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.

About the author

AHP Alternative Evaluation – Weighted Sum or Weighted Product Model?

In AHP the preference Pi of alternative Ai is usually calculated using the weigthed sum model (WSM), i.e. calculation of global priorities for alternatives results from the additive aggregation of local preferences and criteria weights.

In my online software AHP-OS users can also select the weighted product model (WPM), where alternatives are aggregated using the product instead of the sum (Goepel 2018). We call this – in contrast to the classical (additive) AHP – multiplicative AHP or MAHP.

AHP-OS Group Result Menu: tick the wpm box and refresh to get the MAHP results.

Ishizaka, Balkenborg and Kaplan (2011) have shown that the additive AHP will overrate alternatives with extreme ratings and penalize balanced ones. Bafahm and Sun (2019) examine in their paper some abnormal results of AHP, contradictory to common expectations and basis decision-making logic in very simple cases. These conflicting results can be easily avoided using WPM.

Krejci and Stoklasa (2018) clearly show in their paper the superiority of using the weighted product model over the weighted sum model for the purpose of deriving global priorities of alternatives.

Aggregation of local priorities of alternatives into global priorities in AHP should not be done using the weighted sum model (WSM). Instead, the Weighted Product Method (WSM) should be used.

Literature

Bafahm A., Sun M. (2019). Some Conflicting Results in the Analytic Hierarchy Process, International Journal of Information Technology & Decision Making Volume 18, Issue 02 (March 2019) Pages:419–443 https://doi.org/10.1142/S0219622018500517

Goepel, K.D. (2018). Implementation of an Online Software Tool for the Analytic Hierarchy Process (AHP-OS). International Journal of the Analytic Hierarchy Process, Vol. 10 Issue 3 2018, pp 469-487 https://doi.org/10.13033/ijahp.v10i3.590

Ishizaka A., Balkenborg D., Kaplan T. (2011). Influence of aggregation and measurement scale on ranking a compromise alternative in AHP. Journal of the Operational Research Society (2011) 62: 700. https://doi.org/10.1057/jors.2010.23

Krejci J., Stoklasa J. (2018). Aggregation in the analytic hierarchy process: Why weighted geometric mean should be used instead of weighted arithmetic mean. Expert Systems with Applications Volume 114, 30 December 2018, Pages 97-106 https://doi.org/10.1016/j.eswa.2018.06.060

AHP-OS and AHP Judgment Scales – Published Articles

My latest articles related to AHP:

AHP-OS:

Goepel, K.D. (2018). Implementation of an Online Software Tool for the Analytic Hierarchy Process (AHP-OS). International Journal of the Analytic Hierarchy Process, Vol. 10 Issue 3 2018, pp 469-487

https://doi.org/10.13033/ijahp.v10i3.590

https://www.ijahp.org/index.php/IJAHP/article/view/590/652

AHP Judgment scales:

Goepel, K.D. (2018). Comparison of Judgment Scales of the Analytical Hierarchy Process — A New Approach. International Journal of Information Technology & Decision Making, published Dec 11, 2018

https://doi.org/10.1142/S0219622019500044

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AHP Excel Template Update Version 2018-09-15

A new version of of the AHP Excel template with some major updates is now available for download. Based on the work of Tomashevskii (2014, 2015), errors for the resulting priorities/weights are shown.

Calculated weights with error indication

In addition the overall dissonance (ordinal inconsistency) according to Sajid Siraj (2011) is indicated. The zip file for download also contains the updated manual, showing the calculations and references.

Continue reading AHP Excel Template Update Version 2018-09-15

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AHP Excel Template Update Version 2018-08-22

In this latest version of the template, the balanced scale was replaced by the generalized balanced scale (balanced-n), and the adaptive scale was added. The maximum number of iterations for the power method was increased from 12 to 20.

If you need inputs for more than 20 participants, please contact the author. A version for up to 225 participants is available.

Go to download page.

For more information about AHP scales, please read my paper Comparison of Judgment Scales.

AHP Judgment Scales

A revised version of my paper can now be downloaded:

Goepel, K.D., Comparison of Judgment Scales
of the Analytical Hierarchy Process - A New Approach, Preprint of an article submitted for consideration in International Journal of Information Technology and Decision Making © 2017 World Scientific Publishing Company http://www.worldscientific.com/worldscinet/ijitdm (2017)

Welcome to BPMSG – Jan 2018

Concepts, Methods and Tools to manage Business Performance

Dear Friends, dear Visitors,

I wish all of you a Happy and Prosperous New Year 2018!

From July 13th to 15th the International Symposium on the Analytic Hierarchy Process (ISAHP) for Decision Making takes place in Hong Kong. Poster submission is possible from Nov 1st, 2017 to Mar 15th, 2018 and individual paper submission from Nov 1st, 2017 to Mar 6th. Early registration deadline May 15th, 2018. More Information about the ISAHP 2018 can be found on their website.

After my last participation in 2013, I plan to attend the conference in July. If you want to meet me personally, feel free to contact me. I submitted an individual paper about the implementation of my AHP-OS software; it is a short version of my detailed working paper. In additon I will probably submit a short version of my paper Comparison of Judgment Scales of the Analytical Hierarchy Process – A New Approach. This paper was submitted to the International Journal of Information Technology and Decision Making in June 2017, and is under review since then. All attempts to contact the editors and to find out, why the review process takes so long, were unsuccessful.

My AHP-OS software has now reached nearly 6000 registrations since its implementation in 2014. It should be quite stable and without major bugs. Unfortunately, there is still a minor sporadic problem with the storage of pairwise comparisons. It appears in 1 out of 1000 projects that a set pairwise comparisons just disappears. I am still trying to find the reason, kindly contact me, when this happens to you, and let me know the circumstances (It seems to have something to do with the browser and stored session data).

Please continue to support my effort, either with a donation, or at least give a 1 (poor) to 5 (excellent) rating to my web posts, which will help me to get some feedback on my work.

For now, please enjoy your visit on the site and feel free to leave a comment – it is always appreciated.

Klaus

Klaus D. Goepel,

Singapore, Jan 2018

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.

 

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AHP Consensus Indicator

The AHP consensus indicator, based on Shannon beta entropy (e.q. 1.1) for n criteria and k decision makers, was introduced in [1].

(1.1) Shannon beta entropy:

(1.2) Shannon alpha entropy:

(1.3) Shannon gamma entropy:

with

The similarity measure S (eq. 1.4) depends on the number of criteria, and we used a linear transformation to map it to a range from 0 to 1 (eq. 1.5)

(1.4)

(1.5) Consensus (0% to 100%):

In general Dα min = 1 and Dγ max = n. In the analytic hierarchy process (AHP) Dα min is a function of the maximum scale value M (M = 9 for the fundamental AHP scale) and the number of criteria n (eq. 1.6). The calculation of Dγ max was based on the assumption that respondents compare one distinct criterion M‑times more important than all others (eq. 1.7).

(1.6)

(1.7)

This assumption is actually an unnecessary constrain, because even when the number of decision makers is less than the number of criteria, both  can prioritize a complementing set of criteria as most important and as a result all consolidated criteria weights are equal. Therefore eq. 1.7 can be simplified to:

 (1.8)

As a result we get the AHP consensus indicator with:

(1.9)

(1.10) AHP Consensus: Equation (1.10) is used in the latest updated of the AHP excel template and the AHP-OS online software.

Reference

[1] 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

AHP-OS Quick Reference Guide

As I know from my own experience, manuals are seldomly read. On the other hand, a short guideline to complex software can be helpful, to use it effectively. I summarised the main menus of AHP-OS in a four page quick reference guide. The full manual is still available from the AHP-OS entry page (needs update …), and all details regarding methods and calculations are shown in my working paper about the AHP-OS software implemetation.

 

AHP-OS Hierarchy Evaluation with Partial Inputs from Participants

With the latest update of my AHP online software it is now possible to save judgments (pairwise comparisons) without completing the whole hierarchy evaluation. There are two scenarios, where this could be useful:

  1. You have a complex hierarchy with many nodes to be evaluated. Now participants can start a partial evaluation, save the judgments and complete the remaining nodes at a later time.
  2. As a participant you are only expert for a subset of nodes in the decision hierarchy. As a chair you can now ask participants to give their inputs for a few nodes of their expertise only.

Pairwise comparison input is started as usually: either using the link provided on the project session page, or using the link AHP Group Session on the AHP-OS main entry page. After providong session code and name, in case the participant hasn’t given any input, a message Ok. Group has x participants. Click “Go” to continue will be displayed. Nodes without judgment show the AHP button with red outline.

Continue reading AHP-OS Hierarchy Evaluation with Partial Inputs from Participants

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