AHP Youtube video example – matrix values and priority vectors

Here the detailed results of the example in my AHP video:

Buy an MP3 Player

Color Memory Delivery
1 2 3
1 1  1/3  1/2
2 3 1 1
3 2 1 1

Resulting weights: Color: 16.9%, Memory: 44.3%, Delivery: 38.7%, CR = 1.9%

Color:

pink blue green black red
1 2 3 4 5
1 1 2 3  1/2  1/4
2  1/2 1 3  1/4  1/3
3  1/3  1/3 1  1/7  1/7
4 2 4 7 1  1/3
5 4 3 7 3 1

Resulting weights: pink: 13.6%,  blue:  9.8%, green: 4.3%, black: 26.5%, red: 45.8%, CR = 4.9%

Memory:

8 MB 16 MB 32 MB 64 MB
1 2 3 4
1 1  1/5  1/7  1/8
2 5 1  1/7  1/8
3 7 7 1 1
4 8 8 1 1

Resulting weights: 8 MB: 4%, 16 MB: 9.5%, 32 MB: 41.7%, 64 MB: 44.8%, CR= 12.5%

Delivery

immediate one week 4 weeks
1 2 3
1 1 1 5
2 1 1 3
3  1/5  1/3 1

Resulting weights: Immediate: 48.1%, 1 week: 40.5%, 4 weeks: 11.4%, CR = 3%

Resulting Global Priorities

Welcome to BPMSG – Feb 2014

Concepts, Methods and Tools to manage Business Performance

Dear Friends, dear Visitors,

the development of my AHP online software is still continuing. Most of the recent changes were structural, and not so obvious to users, as I use the software on two different platforms and in two different designs. On the entry page you will now find a short introduction to the analytic hierarchy process, and links to further examples and documentation. From there you can go to the online priority calculator, or the AHP online solution to handle complete projects.

Overall the functionality is complete and the program is stable. Except for group inputs, the priority calculator includes all functions of my AHP excel template. With the AHP online system you can even define complete AHP hierarchies and evaluate alternatives. For both programs the results can now be exported as csv files for further processing in spreadsheet programs in two versions: using either dot or comma as decimal separator.

The next big step would be the implementation of group decision making. My idea is to implement web sessions for different users  on different computers, and an online consolidation of all judgments, to get the consolidated group result. This could be very useful when you are in a meeting and have group discussions, then all participant could do their judgment online, seeing the consolidated group result in real time.

It will still take some more time, so bookmark the page and revisit  from time to time to get the latest updates.

Now please enjoy your visit on the site and feel free to give me feedback – it is always appreciated.

Klaus D. Goepel,

Singapore, Feb 2014

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 give credit or a link to my site, if you use parts in your website or blog.

About the author

AHP Online System

As I was asked by many visitors, how to evaluate priorities and alternatives for a whole project in AHP, I have realized an online solution, where you can define a hierarchy, get the priorities for all categories and evaluate alternatives. The project is realized in PHP.

AHP OS Example

Links

AHP Online System – BPMSG
AHP-OS software Implementation (paper 2018)
Short description (pdf) for download.

Please rate the software at the end of this post!

Continue reading AHP Online System

Welcome to BPMSG – Dec 2013

Concepts, Methods and Tools to manage Business Performance

Dear Friends, dear Visitors,

Season Greetings from Singapore!

 Gong Xi Fa Cai!

Surprisingly the implementation of AHP as an online tool went smooth and faster than I expected. Now my AHP online calculator is live, and within a few weeks frequently used by many visitors. During its development I also found a way to show the “ideal” judgments in case of inconsistent inputs; so now it is easy to modify initial judgments in the right direction in order to improve consistency. A feature I also implemented in my last update of the AHP excel template.

In addition, I managed to come out with an AHP project tool, where you can define the hierarchy of your AHP projects, as well as do the calculation of global priorities and evaluation of alternatives. This was a bit tricky, as the hierarchy can vary widely from project to project, so I had to find a flexible way, how to input the hierarchy structure. It is done using plain text with a defined simple syntax for nodes and leafs of the hierarchy. Sounds more complicated as it is, so I published some examples, and I am sure you will find it easy to use.

I use the tool for my own projects, the latest one developing a decision tree for the evaluation of company internal IT projects. Using the hierarchy tool you can export your defined hierarchy structure as csv and use it in Excel for further calculations.

Now please enjoy your visit on the site and feel free to give me feedback – it is always appreciated.

Klaus D. Goepel,

Singapore, Dec 2013

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 give credit or a link to my site, if you use parts in your website or blog.

About the author

Updated AHP Excel template Version 2013-12-24

In this latest update of my AHP excel template, input sheets were modified to show the proposed ideal judgments for the three most inconsistent inputs, resulting in a lower consistency ratio CR.

Example

On the left side judgment A9, A7 and A6 are highlighted as inconsistent, CR is 32%. The consistent judgment is shown as A4, A9 and A3. After correction with the proposed intensities (right side) the consistency ratio decreases to 7% below the required threshold of 10%.

You might download the latest version from my AHP template download page.

AHP Online Calculator – Update 2013-12-20

In this latest version of the AHP online calculator I made some changes:

  • The three judgments with highest inconsistency will be highlighted with the last column showing the recommended judgment for lowest inconsistency
  • Selection of fundamental AHP or balanced Scale
  • Number of Criteria changed from 12 to 15 max.1)
  • Length of criteria names changed from 15 to max. 20 characters
  • Download of result (decision matrix, eigen vector, CR) as csv (comma separated values) instead of txt file

The .csv  file uses “,” as field separator and “.” as decimal symbol (unchanged). Depending on your operating system it will directly open in Excel.

1) Important Note: Though the maximum number of criteria is 15, you should always try to structure your decision problem in a way that the number of criteria is in the range Seven Plus or Minus Two.

AHP Online Calculator

The AHP online calculator is part of BPMSG’s free web-based AHP online system AHP-OS. If you need to handle a complete decision hierarchy, group inputs and alternative evaluation, use AHP-OS.

Calculate priorities from pairwise comparisons using the analytic hierarchy process (AHP) with eigen vector method. Input the number of criteria  between 2 and 20 1) and a name for each criterion. Next, do a pairwise comparison: Which of the criterion in each pair is more important, and how many times more, on a one to nine scale. With Check consistency you will then get the resulting priorities, their ranking, and a consistency ratio CR2) (ideally < 10%). Calculation is done using the fundamental 1 to 9 AHP ratio scale.

The three judgments with highest inconsistency will be highlighted, with the last column showing the recommended judgment for lowest consistency ratio. Slightly modify your comparisons, if you want to improve consistency, and recalculate the result, or download the result as a csv file.

Pairwise-comparison
Example of inconsistent pair-wise comparisons. The most inconsistent judgment no 2 is marked in red (Color or Delivery); the consistent judgment would be 3 (B) and is highlighted in light green. Decision makers can decide to adjust some of their original judgments to improve consistency.

Here the link: AHP priority calculator

Kindly rate the software from 1 star (poor) to 5 stars (excellent) at the bottom of this post.

Please make reference to the author and website, when you use the online calculator for your work. For terms of use please see our user agreement and privacy policy.

Format of the csv file

Fields are separated by tabs:

  • Line 1: Date (yyyy-mm-dd)  Time (hh:mm:ss) Title (text)
  • Line 2: Number of criteria n
  • Line 3: Criteria
  • Line 4 to 4+n: Decison matrix
  • Second last line:  Priority vector
  • Last line: eigenvalue and consistency ratio CR

References

1) Though the maximum number of criteria is 15, you should always try to structure your decision problem in a way that the number of criteria is in the range 5 to 9.

2) Alonso, Lamata, (2006). Consistency in the analytic hierarchy process: a new approach. International Journal of Uncertainty, Fuzziness and Knowledge based systems, Vol 14, No 4, 445-459.

Welcome to BPMSG – Oct 2013

Dear Friends, dear Visitors,

Nearly half a year has passed since my last update in May on this page, and the year 2013 is soon coming to an end. In June, I had the opportunity to present my practical experience with the Analytic Hierarchy Process (AHP) on the International Symposium ISAHP 2013 in Kuala Lumpur, Malaysia. You can download my paper here. It was interesting to meet the experts from around the world, dealing with decision making methods, and listening to some of their presentations. A short video shows my impressions of the meeting and the nice touristic spots in K.L.

I was invited to the panel discussion, and could discuss my newly introduced AHP consensus indicator for group decisions. It is based on the concept of diversity. Like AHP, diversity is a very interesting topic, as it can be applied in so many different areas. Originating from information theory (Shannon 1948), it became a well-established concept in ecology and economy. I used the principles to develop a key performance indicator (KPI), describing the diversification of businesses and the quality of growth. Feel free to watch my videos or read my posts on this blog.

What is coming next?

There will be one more video on my YouTube channel, showing the application of Shannon diversity to measure the quality of growth. Looking at diversity and growth over time we can display a growth trajectory of a company, giving a clear picture about the direction, where the company is heading.

The larger project will be the implementation of my AHP template as an AHP online tool. The idea is that you can input your criteria and do the pair-wise comparison online, to get as a result the calculated priorities. So at the moment I am busy to practice some web scripting and become more familiar with php. A first small exercise was my online diversity calculator.

Now please enjoy your visit on the site and feel free to give me feedback – it is always appreciated.

Klaus D. Goepel,

Singapore, Oct 2013

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 give credit or a link to my site, if you use parts in your website or blog.

About the author

What is AHP?

AHP stands for analytic hierarchy process, and belongs to the multi-criteria decision making methods (MCDM). In AHP, values like price, weight, or area, or even subjective opinions such as feelings, preferences, or satisfaction, can be translated into measurable numeric relations. The core of AHP is the comparison of pairs instead of sorting (ranking), voting (e.g. assigning points) or the free assignment of priorities.

Read my simple write-up about AHP for people, who have not heared about the method. You might download it as pdf document.

Principia Mathematica Decernendi

or “Mathematical Principles of Decision Making” is the title of a book by Prof. Thomas L. Saaty, in which he describes his method for the mathematical treatment of decision problems, which he developed in the 70s. Called AHP, it is now used around the world in many different fields. AHP stands for analytic hierarchy process, and belongs to the multi-criteria decision making methods (MCDM) group.

In AHP, values like price, weight, or area, or even subjective opinions such as feelings, preferences, or satisfaction, can be translated into measurable numeric relations.

Mathematically, the method is based on the solution of an “eigenvalue problem” – but this is mentioned here only tangentially and is not meant to dissuade anyone.

Analytic hierarchy process

The basic steps in the solution of a decision problem using AHP are quite simple:

  1. Define the goal of the decision – what do I want to decide, for what purpose, and what are my alternatives?
  2. Structure the decision problem in a hierarchy – what are the categories and criteria that figure into my decision?
  3. Pair comparison of criteria in each category – e.g. blue or green? Which do I prefer, and by how much do I prefer one or the other color?
  4. Calculate the priorities and a consistency index – were my comparisons logical and consistent?
  5. Evaluate alternatives according to the priorities identified – what alternative optimum solution is there to the decision problem?

Sometimes alternatives are already implicitly defined by the problem and it is sufficient merely to define the priorities.

The core of AHP is the comparison of pairs instead of sorting (ranking), voting (e.g. assigning points) or the free assignment of priorities. Validation of the method in practical testing shows surprisingly good agreement with actual measured values.

One of the most interesting fields and a very current application of AHP is the identification of suspects by witnesses in criminal cases, where the candidates for identification are not shown all together or sequentially, but in pairs. AHP is then used to evaluate the results. Initial studies show that this increases the reliability of identification from 55 % to 83 % and reduces the false identification rate from 20 % to 17 %, and that the consistency index is a good measure of the reliability of statements by witnesses.

Example

To demonstrate how the method works, let us take a simple example. I want to buy an MP3 player. I have the choice of colors (pink, blue, green, black, red), storage (8, 16, 32, 64 Gbyte), and availability (immediate, 1 week, 1 month). The available models are:

  • Model A – pink, 32 Gbyte, immediate availability, USD 120
  • Model B – blue , 16 Gbyte, immediate availability, USD 120
  • Model C – black , 32 Gbyte, 1 week wait, USD 150
  • Model D – red, 64 Gbyte, 1 month wait, USD 150

We can structure the problem hierarchically as shown in Fig. 1.  In the solution process itself each element is compared by pairs in each category and sub-category, and the criteria are weighted.


Fig. 1 AHP hierarchy for solving a decision problem

Complex decision problems and networks

For complex decision problems a two-layer model can be introduced, in which hierarchies are examined separately by the criteria Benefits (B), Opportunities (O), Costs (C) and Risks (R). This is known as the BOCR model. The problem is then evaluated using the simple formula (B*O)/(C*R) (multiplicative) or (B+O)-(C-R) (additive).

The analytical network process (ANP) is a further development of AHP. In it, the decision problem is modeled not as a hierarchy, but as a network. However, its practical application and mathematical treatment are much more involved.

Applications

AHP has been used successfully in many institutions and companies. Although the method is so universal, it is still simple enough to execute in Excel. One of AHP’s great advantages is the ability to use it for group decisions, in which all participants evaluate pairs and the group result is determined as the mathematically optimum consensus. In practice the solutions arrived at by the method are well accepted, since the results are objective and free of political influence.

Examples of projects in a business context are the weighting of key performance indicators (KPI) or the identification of key strategies for sustained growth.

Klaus D. Goepel – Singapore Aug 2013. 

Calculate priorities using my AHP online calculator or handle a complete AHP project using my AHP online software AHP-OS.

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