# Analytic hierarchy process (Pair Wise)

**Skill level:** Advanced

**Description**

The analytic hierarchy process (AHP) is a method that breaks down decision making into series of pair-wise comparisons. It is most effective in determining the relative importance of evaluation criteria.

**Benefits**

- Converts subjective assessments of relative importance into a set of overall scores or weights
- Offers a team activity where members must decide on the relative importance of one factor against another
- Easily removes emotions and helps in making better decisions

**How to Use**

**Step 1.**List all the criteria of importance to be considered.**Step 2**. Create a table and list the criteria in the rows along the left side and in the columns across the top in the same sequence.**Step 3.**In the cells where identical criteria intercept (diagonal) enter a value of “1.”**Step 4.**Working row by row, determine whether the row is more important than the column and, if so, how much more important. Use the rating scale suggested below.**Step 5.**Enter the number (weight) if the row is more important than the column and, if so, how much more important. For example, enter “3” if the row is moderately more important.**Step 6.**If the column is more important than the row, use the inverse. For example, enter “1/3” if the column is moderately more important.**Step 7.**Continue until you have filled all of the cells in the table.**Step 8.**Calculate the relative weight of the criteria. The total of each column must be normalized, summing across the rows and normalizing those sums. See the example for more details.- *Note: Using a spreadsheet program for this step is easier, but you can complete it manually.
- First, sum the criteria columns.
- Next, determine the “sum of normalized ratings” and sum that column.
- Finally, compute the “weighting,”which is a ratio and gives a relative importance for each evaluation criterion.

- *Note: Using a spreadsheet program for this step is easier, but you can complete it manually.
**Step 9.**To select the best concept, you can use the Pugh Matrix.

**Rating Scale: **Thomas Saaty, the inventor of this tool, recommends the following rating scale:

- (1) Equally important
- (3) Moderately more important
- (5) Strongly more important
- (7) Very strongly more important
- (9) Overwhelmingly more important

**Relevant Definitions**

*Normalization: *A mathematical method of computing numbers that takes into account the overall values.

*Pugh Matrix: *A tool used to evaluate different concepts against a set of criteria and select the best one.

** Example **

A well-established retail business wishes to expand the number of stores it operates in different states and seeks to know which states will offer the best fit for its products and services. The task force has determined five major criteria for the success of the expansion. To determine a weighting for each criterion using a fact-based method rather than individual perception and emotion, the team uses the analytic hierarchy process. The table below illustrates the results:

From this table, the following criteria are listed in order of importance:

- States with “higher average income” (55%)
- States with a “large population” (19%)
- States with at least one “large university” (13%)