Thursday, October 22, 2015

Decision-Making Using Analytic Hierarchy Process (AHP)

This paper introduces how to use the Analytic Hierarchy Process (AHP), a famous method that is part of the Multi-Criteria Decision Making process (MCDM). AHP was created to solve issues when facing a mix of qualitative, quantitative, and conflicting factors in the MCDM process. AHP uses the judgements of decision makers to form a decomposition of problems into hierarchies. Each section is further broken down into different levels within the hierarchy which combine with the decision maker’s problem that needs to be solved. The hierarchy is used to derive ratio-scaled measures for alternatives, and the relative value that alternatives have against organizational goals and project risks. AHP contains 4 steps.

Step 1: Define the problem and state the goal or objective.
Step 2: Define the criteria or factors that influence the goal, and structure these factors into levels and sublevels.
Step 3: Use paired comparisons of each factor with respect to each other that forms a comparison matrix with calculated weights, ranked eigenvalues, and consistency measures. (See chart below for comparison matrix example).

Step 4: Synthesize the ranks of alternatives until the final choice is made.

The paper used a family upgrading smart phones to present an example how AHP was applied to make the best choice. 

Three smart phones were considered (1,2,3) and the four qualities that were evaluated were cost, display resolution, battery life and internal storage. 

The first step in the AHP process was to build a table illustrating the problem and comparing each phones attribute. 

The second step involves creating the “parent-child” relationship.

The third step is the most complex part of the process and involves assigning attributes from the matrix shown below step 3. The authors compared each criteria and device choice using a computer algorithm to determine the value of each selection in a measurable format. The graphic below shows the results of the calculations. Without explaining the math behind equations, each family member rated the criteria of what was important to them, and averaged the numbers from the matrix.

The results of the calculations above were further refined using mathematical equations. The chart below displays the results. The most important factor to consider is the Priority column which is the relative ranking of the criteria produced by dividing each element of the matrix with the sum of the column. 

Step 4 shows the final rankings of the AHP process based on the Priority and costs benefit ratio to come to a conclusion on the best smart phone to purchase.

The authors used SAS/IML statistical software to run the equations which I did not include due to the complexity of the problem. Nonetheless, I attempted to break down the AHP process by reducing as much technical information as possible, yet still highlight how the process works. When applying this process to intelligence analysis, one of the main problems that arises is assigning attributes to the criteria in a matrix. Because many of the issues analyst face are qualitative in nature, analysts may assign a high degree of varying importance to a piece of criteria. Nevertheless, this technique improves forecasting ability only when applied correctly, and can solve problems which have multiple scenarios.


  1. I thought this article was summed up very well. The graphics were helpful. You mentioned one of the difficulties that arises comes into play when assigning attributes to the criteria matrix. Do you think other SATs such as those in the idea generation category would help identify attributes effectively?

  2. Shadya, thank you for the comment. To answer your question, using other SATs may be helpful in streamlining the process of assigning attributes in the matrix, but may also confine an analyst’s viewpoint to a certain degree. Nonetheless, the issue of assigning attributes will likely come down to the facilitator, team leader or decision maker’s guidance or goal of the project.

  3. I found this article interesting and appreciated the easily digestible information and relatable example problem. I can see how step 3 can make the process more complex, but is necessary for easily comparable quantifiable data. Does the article address the difficulty in adding qualitative attributes to problems that are more non-quantitative? My only note is that the given example seems more straight forward in this process, though obviously this is for the sake of the reader grasping the subject matter.

  4. The authors used statistical data to process qualitative data which I excluded and vaguely understand myself. But to answer your question, the authors processed qualitative data by assigning attributes via the matrix, and using software to process the math. However, the issue is not the assigned attributes themselves, but the value assigned by each family member which was measured based upon their own significance. In this case, the authors did not provide any further literature or examples on how to ensure the values are meaningful, nor the implications.