Modeling Analytic Hierarchy Process

SpiceLogic offers Analytic Hierarchy Process or Ahp tools in Rational Will. Also, It is completely wizard-based, no worry about learning curve or annoyances with confusion about the UI. It is as simple as starting the application and following on-screen instructions.

If you are using Rational Will application, then from the dashboard, click the 'Decision Matrix' button to start modeling an Analytic Hierarchy Process.


Identifying Objectives (criteria)

Say, you want to buy a car and your objectives are

1. Maximize Safety.
2. Maximize Comfort
3. Minimize Cost

When you start the Decision Matrix, you are presented with the following screen.


Once you click the "Identify your Objectives" button, you will see the following wizard screen.


This screen is actually asking you to identify your first objective. You know that your first objective is to "Maximize safety". So, in the drop-down box, select "Maximize" and then in the text box, enter safety, as shown in the above screenshot. Then click the Proceed button.

Once you click to proceed, you will be asked what is the type of your objective. As we do not want to deal with numbers, rather we want to express the attributes subjectively using a pairwise comparison, click "Subjective". The analytic Hierarchy Process model can be used when your objective attributes are subjective type.


Once you click the Subjective button, you will be asked if you have any more objective.


Click Yes and follow the same process to add 2 more objectives

- Maximize Comfort
- Minimize Cost

Finally, when all of these 3 objectives are identified, you do not have any more objective to add. so click No button in the following wizard screen.


No worries if you want to add more objective or modify/delete an existing objective. You can do that later.

Deriving Priorities for the Criteria

Once you click No in the above-shown screen, you will be presented to perform a pairwise comparison among objectives. For this example where the pair comparison number is very low, let's uncheck the checkbox "Enforce Transitivity Rule" which is checked by default. We will explain more about this feature in the upcoming section. Suppose you prefer to Maximize Safety 3 times as much as Maximizing comfort. Then set the weight slider position as shown in the following screenshot.

pair-comparison- 1

Once you click the Next button on the toolbar for the next set of pair comparisons, do the pairwise comparison according to your preferences. Say, you prefer, to Minimize Cost 7 times as much as you prefer to Maximize Comfort and you prefer to Minimize Cost 3 times as much as to Maximize Safety.



Finally, when you are done all objectives pairwise comparison, click the 'Proceed' button in the wizard as shown below.


Consistency Ratio Metric

Suppose you like an apple twice as much as an orange and an orange 3 times as much as a banana. Logically, you should like an apple 6 times as much as a banana. If your preference between an 'apple' and a 'banana' does not reflect that proportion, then you are said to be inconsistent in your preferences. Consistency ratio measures that inconsistency. It is a measurement that indicates how much you violate the transitivity rule. Naturally, when the transitivity rule is enforced, or when you are 100% consistent in your preferences, the deviation will be 0. The higher is this number, the more inconsistent you are.

Notice the number shown as CR. This is the consistency ratio.


According to Thomas L. Saaty, the consistency ratio should be less or equal to 10%. Therefore, it is necessary to revise the judgments. If your Consistency ratio goes over 10%, the software will indicate that using a Red bold color, as you can see on this screen.


Enforce Transitivity Rule

It is possible using our software that you can enforce consistency in all pair comparisons. That means, instead of asking you to compare apple-orange, apple-banana, and orange-banana, the software will ask you just 2 comparisons to perform. Apple-orange and apple-banana. Then it will infer the comparison of orange-banana. In that way, you can reduce the number of comparisons from ½ * n * (n -1) to just (n -1). Think about it. It can be a huge time-saver for you as the number of comparison gets reduced dramatically. You can enforce the Transitivity rule by checking this checkbox. As soon as you do so, you will see the number of pair comparisons has been reduced significantly.


Also, you will notice that, when the transitivity rule is enforced, the Consistency ratio metric is always shown as 0%.

Identifying Options

Once you click the 'Proceed' button in the wizard after completing all objectives pairwise comparisons, you will be presented to a screen where you will be asked to identify your options. Say, you have identified that you have the following 2 options.

1. Car 1
2. Car 2

Enter these options in the wizard screen.


Deriving Local Priorities (Preferences) for the Options.

Click 'Proceed'. Now, you will be asked to judge the 2 cars against one of your Criteria "Safety". You can consult statistical data, research online forums, or based on your experience/beliefs, you can set a weight. Suppose your belief is that Car 2 is 9 times safer than Car 1. Set the comparison as shown below:


Then click the 'Next' button. You will be asked to judge the options based on Cost. Suppose, you found that, the 'Car 2' price is 7 times as much as the 'Car 1'. You can set that comparison as shown here.


Click the 'Next' button and finally, you are asked to judge the options based on "Comfort". Say, Car 2 is 5 times as much comfortable as Car 1. Set the preference as shown below.


Finally, click the 'Finish' button. You will see the AHP model is calculated and presented as shown below. The Result panel is showing the Recommendation as "Car 1". Because the "Car 1" has the overall priority number "63.03%". And the "Car 2" has the overall priority number "36.97%"


Now, if you want to change any comparison, simply click on the Scale button and the pair comparison dialog will appear.


If you want to modify the Objective comparison weights, you can select the "View" tab in the Ribbon and click the "Objectives" button. Once the 'Objectives' button is clicked, the Objectives page is shown. As you can see, you can reprioritize any of the objectives over another from this page.


Radar Chart

Notice that, in the Result panel carousel, a Radar chart is also available for getting a perspective.


Sensitivity Analysis

It is very important to perform a 'What-if' analysis to get an idea of how the calculation results would have changed if the weights of the criteria would have been different. No final decision should be made without performing sensitivity analysis, as sensitivity analysis allows us to understand how robust is our decision. Rational Will can perform a one-way sensitivity analysis and display a chart showing a variable's value change affects the Value of options.

For example, we see that the Options preference based on 'Cost' Criteria has a sensitivity index of 79.59%. The more is the index, the more is the sensitivity. If the index is 0, the variable is insensitivity in that decision context. Notice the following chart. See that, if the left side weight value is changed 20% of its total possible value, the Overall value of Car 1 gets dropped below Car 2. That's how the Sensitivity index is calculated. It is calculated as Sensitivity Index = 100 - X%, where X% is the distance the variable needs to be changed to affect the decision.


Expand the Sensitivity Analysis tab and you will see the variables are arranged based on the Higher to Lower Sensitivity index.


Last updated on Apr 29, 2020