Analytic hierarchy process (AHP)

The analytic hierarchy process (AHP) is a decision-making framework. The AHP involves breaking a complex decision or problem into a hierarchy of levels; assigning a rank or value to all criteria or alternatives within the various levels; and making comparisons and drawing conclusions from the results. Professor Thomas L. Saaty developed the AHP in the 1970s. Since then it has become a popular decision-making tool for governments, businesses, and other organizations.

Background

In the 1960s, Thomas L. Saaty was working for the US Arms Control and Disarmament Agency (ACDA). One of his roles was to advise the negotiators who were handling nuclear disarmament talks with the Soviet Union. During these meetings, Saaty noticed that negotiators from both sides failed to account for all aspects of the matter at hand. This is likely because when it comes to decision-making, humans tend to depend more on emotion and intuition than logic. Moreover, in group settings, humans are prone to influence one another's thinking.

In the early 1970s, Saaty left the ACDA and became a university professor, first teaching at the University of Pennsylvania and later teaching at the University of Pittsburgh. During this time, Saaty continued to think about his experiences with the disarmament negotiators and began to develop a decision-making framework, which became known as the analytic hierarchy process, or AHP. The AHP breaks any problem or decision into its component parts. These parts are then systematically compared and ranked, which results in numerical values that represent the priorities for each part. From these values, a set of overall priorities for the hierarchy can be determined, and a decision can be reached.

Today the AHP has applications in the public, private, and nonprofit sectors. Leaders in industries ranging from agriculture and manufacturing to financial services and education use the AHP to make decisions and solve problems. The AHP also can be used in everyday life, such as when trying to decide which school district to move into, which car to buy, or which college to attend.

Overview

The first step in using the AHP is to define the problem. Defining the problem means identifying a particular goal and all the criteria and alternatives associated with that goal. For instance, a woman is trying to decide between two refrigerators to buy, Model X and Model Y, and the criteria influencing her decision are price, consumer rating, and color.

The next step is to structure the problem into a hierarchy from top to bottom. At the top of the hierarchy is the objective: Choose a refrigerator. In the middle are the criteria on which the alternatives depend: Price, Rating, and Color. At the bottom are the alternatives: Model X and Model Y.

Once the hierarchy has been established, it is necessary to determine priorities by making judgments and pairwise comparisons. Pairwise comparison involves comparing criteria and ranking them based on importance or preference in relation to each other. The AHP scale generally uses the rankings 1 through 9, with 1 representing "equal importance" or "equal preference" and 9 representing "absolute importance" or "extreme preference." The rankings are recorded in a table of values with columns and rows that have the same headings.

The woman trying to choose a refrigerator would begin by comparing the criterion from Column A (Price) with the criterion from Row 1 (Price). Because these two criteria are identical, they are equal and receive a ranking of 1. If the woman decides that rating is moderately more important than price, she would record a 3 in Column B (Rating), Row 1. If she feels very strongly that color is more important than price, she would record a 7 in Column C (Color), Row 1. Once the woman has established these initial values, she can record a few reciprocal values in the table. For example, by establishing that color is 7 times more important than price, she establishes that price is 1/7 (0.143) as important as color. Therefore, she can record this reciprocal value in Column A, Row 3.

The next step in the AHP is normalizing the comparisons. To do this, one must first find the sum of each column. For example, the values in Column A are 1.000, 0.333, and 0.143, so the sum is 1.476. Each value in this column is then divided by the sum. Column A, Row 1 = 1.000/1.476 = 0.677. The other values in this column are 0.225 (Row 2) and 0.097 (Row 3). This step should be completed for all columns in the table.

Once all the comparisons have been normalized, it is possible to calculate priorities. Priorities are calculated by finding the average of the values in each row. For the price row, the values are 0.677, 0.714, and 0.538. The average is 0.677 + 0.714 + 0.538/3 = 0.643. In the decision to buy a new refrigerator, the value 0.643 represents the priority of the price of the refrigerator. This step should be repeated for the other two rows, rating and color.

Based on these values, it appears that price is the most important criterion in the woman's decision to buy a new refrigerator, followed by consumer rating, and then color. However, before the woman can make a decision, she must perform a similar analysis for each criterion in relation to each alternative.

Once the values of the priorities for all criteria and alternatives have been found, they can be used to determine the overall priorities for making a decision. For example, using the overall priority values, the woman can logically conclude which refrigerator is the best choice. Note that additional calculations of data from the various tables can reveal consistency and sensitivity of the results in the various levels of the AHP.

Bibliography

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