AHP as a Decision Making Tool in Projects, Programs and Portfolios

Revision as of 19:43, 26 September 2016

Analytical hierarchy process, AHP, is one of many multi-criteria decision making tool. It can be used both project, program and portfolio management as many decisions has to be made. AHP is a structured way of organizing complex decision. It’s based on math and psychology and it uses a scoring system. AHP differentiates from other multi-criteria decision making tools by rating the scores to make sure that no biased decision can be made. To use AHP the decision has to be formulated into a hierarchy with a goal, certain criteria and some alternatives to choose from. A hierarchy is the basic human way of dealing with decisions which makes the model highly intuitive, even when complex decisions has to be made.

For a project, program or portfolio manager who has to make many decisions AHP can be a help for standardizing and automating many of these decisions by providing the same framework for every decision made. This also goes for larger project organizations, where the tools can be used as a way of directing all the decisions made within the organization.

In this article the reader will first be introduced to the history of AHP. After this the relevance of the tool in project, program and portfolio management will be shortly discussed. Then the application of the tool will be introduced to the reader in a step by step manner with an example. Lastly a few examples of the use of AHP in project management, the criticism and an annotated library will be presented.

History

While directing research projects for United States Arms Control and Disarmament Agency in 1960’s Thomas L. Saaty worked with some of the world leading lawyers, economists and game theorists advising on which weapon to procure, keep and scrap. Even though working with some of the world leading academics Thomas L. Saaty wasn’t satisfied with the results gained throughout the different projects. He found that the models where to abstract to give a particular answer. They also had problems addressing the diverse concerns of the scientists.

Years later Thomas L. Saaty was still trouble by these issues. In an article from 1986 ^[1] he came up with the axioms for the AHP as a solution to his problem. AHP is a mathematical well-defined structure consisting of matrices and their associated right-eigenvector’s ability to generate true or approximate weights. The methodology compares criteria, or alternatives in a pairwise mode with the use of a fundamental scale.

Relevance for Project, Program and Portfolio Management

Both in projects, programs and portfolios decisions has to made on a daily basis. These decisions are often multi criteria decisions, which has to be made on an objective manor. AHP is ideal for this by its structure, simplicity and ease of use. What makes AHP even more relevant how it eliminates subjective and biased input with the eigenvectors.

The Analytic Hierarchy Process

The AHP methodology is based on three primary functions: Structuring complexity, measurements and synthesis. The basic human way of structuring complexity is by hierarchy, so to make the methodology simple this is how problems are structured. Hierarchical-based methodology has to use ratio-scale priorities for measurements. The reason for this is that the priority of an element at any level of the hierarchy is determined by multiplying the priorities of the elements in that level by the priorities of the parent element^[2]. When a multi criteria decision is made it often synthesizes over more dimensions than what the human intuition can handle. Therefor the last function of the AHP methodology is to synthesizes all the dimensions of the decision.

According to DSS Resources these three primary functions leads to the following definition:

From this definition 6 steps can be derived for the AHP methodology:

1. Define objective
2. Structure the multiple choice criteria into a hierarchy
3. Make a pair wise comparison of elements in each group
4. Socring and consistency ratio
5. Evaluate alternatives according to weighting
6. Get ranking

Application

To apply the AHP methodology the 6 steps has to be used in order. The first times AHP is used it will take a lot of time, but when it has been used several times it’s really easy to apply and use.

Step 1: Define objective

Here the goal for the multi criteria decision should be set. An example of an objective for a project could be the selection of a new computer supplier for a company.

Step 2: Hierarchy

The simplest way of structuring a decision problem is by a hierarchy. The goal of the decision being the top level. The criteria of the decision being the second. The third level are the different alternatives. This way of structuring the decision problem is illustrated in figure 1^[3]:

Figure 1:The hierarchical structure of a decision

The goal is what you want to obtain from the decision. In the example from before the goal is to choose a new computer supplier. Then the criteria are the different demands you have to the given supplier, it could be battery time, processing power and durability. The alternatives would then be the different suppliers like Lenovo, HP and Apple.

Step 3: Pair wise comparison

For the pair wise comparison of the scoring system the fundamental scale is used. This scale rank the criteria’s level of importance compared to the other criteria on a scale from 1-9. Where 1 is equally importance and 9 is that the criteria looked at is extremely important. The scale is given below ^[3]:

The scoring is done in a matrix. To illustrate the pairwise comparison an example is used. The goal is the purchase of a new computer. 3 alternatives are found: A Lenovo, a HP and a Mac. The budget for the purchase is fixed so the criteria for ranking the alternatives will be: Battery time, processing power and durability. The scoring of the 3 alternatives are now done in a matrix:

This is process is then done for the processing power and durability. This is the pairwise comparison.

Step 4: Scoring and consistency

To calculate the consistency, the average random consistency index is used. But before this is done, the matrix has to be normalized and the eigenvector has to be found. The vector is normalized by dividing each cell in the column with the total sum of the column. For the Lenovo computer in the former example the calculations will look like this:

By doing the calculations for all of the alternatives we end up with the following normalized matrix. Added to this matrix is the sum of the rows divided by the number of alternatives which gives us their priority:

Now the principal eigen vector is found as the matrix product of the sums from table 2 and the priorities from table 4. In the case for pairwise comparison of alternatives battery time the principal eigen vector is 3. The pricipal eigen vector is used to find the inconsistency which is given by:

Equation 1

Where n is the number of alternatives. The inconsistency is used combined with consistency index (RI), table 5, to make the inconsistency ratio, equation 2:

Equation 2

Step 5: Evaluation of the alternatives

Step 6: The ranking

Examples on the use of AHP

Criticism

Annotated bibliography

References used in the article

• Saaty, T. L. (1986). Axiomatic Foundation of the Analytic Hierarchy Process. Management Science, 32(7) ^[1]
  • This article is the foundation of analytical hierarchy process. Here the basic axioms for the method is presented

Video

A short video introducing the use of AHP by an example can be found here:

References

1. ↑ ^{1.0 1.1} Saaty, T. L. (1986). Axiomatic Foundation of the Analytic Hierarchy Process. Management Science, 32(7). http://doi.org/10.2307/2631765
2. ↑ Forman, E. H. (2001). The Analytic Hierarchy Process: An Exposition. Operations Research, 49(4). http://doi.org/10.2307/3088581
3. ↑ ^{3.0 3.1} Saaty, T. L., & Vargas, L. G. (2012). Models, Methods, Concepts & Applications of the Analytic Hierarchy Process (Vol. 175). Boston, MA: Springer US. http://doi.org/10.1007/978-1-4614-3597-6