Developed by Thomas L. Saaty in the 1970s, the **analytic hierarchy process** (AHP) is a structured technique for organizing and analyzing complex decisions. The foundation of AHP is mathematics and psychology. SpiceLogic Analytic Hierarchy Process software (Ahp software) is a wizard-based software for modeling Analytic hierarchy process. It is completely wizard-based, no worry about learning curve or annoyances with confusion about the User interface.

In order to get started with AHP Software, we will present an example of choosing a car based on 3 objectives. Also, we will assume that we have identified 2 options. We will show how to model this decision problem using the software and in that way, all of the features of this software will be explored and explained.

The following topics will be introduced in this tutorial.

### 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 AHP Software, you are presented with the following screen.

Click the button labeled "Identify your Objectives", you will see the following screen. In the drop-down, notice that you can specify your objective with goal identifier as "Maximize" and "Minimize". For our first objective, select "Maximize" and then enter "Safety", as shown below. Then click the button labeled "Proceed".

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

Click Yes. Then you will be taken to the initial screen where you specified your first objective "Maximize Safety". So, in the same way, add 2 more objectives

- Maximize Comfort

- Minimize Cost

Once all of the 3 objectives are modeled, you do not have any more objectives, therefore, 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

After you have clicked the "No" button, you will be taken to a screen where you will be able to perform pairwise comparisons between the objectives you have identified. 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.

Once you click the Next button on the toolbar for next set of pair comparison, 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

The consistency ratio is a metric that indicates the consistency between pairwise comparisons. 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. When you are presented to compare Apple and banana and if you do not like apple 6 times as much as a banana, then obviously there is an inconsistency in your preference. 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%. So, if your consistency ratio is not less or equal to 10%, then it is necessary to revise your 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

Transitivity rule is a rule that basically means that the consistency ratio must be 0. When you prefer an apple twice as much as an orange and an orange three times as much as a banana, then according to the transitivity rule, you must prefer an apple 6 times as much as a banana. If you do not do so, then you violate the 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. When you enforce the transitivity rule. the number of pairwise comparisons will reduce from **½ * n * (n -1)** to just **(n -1)**. Think about it. It can be a huge time saver.

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 for the Options.

Click the button labeled '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.

#### Radar Chart

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

### Sensitivity Analysis

Sensitivity analysis is a crucial part of any robust decision analysis. By sensitivity analysis, you can understand which variables are affecting your decision significantly and which variables are merely affecting the decision. The analytic Hierarchy Process software 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.

### Editing Objectives

Anytime, you want to change the objectives that you have defined, you can open the View tab in the ribbon and you will find a button "Objectives".

Once you click that button, you will be taken to the Objectives page. From this page, you can reprioritize any of the objectives using the pairwise comparisons.

You can also right click on an objective item to see it's context menu, and from that context menu, you will find the Edit, disable and Delete option.

Once the editor shows up, you will see the following window for your objective.