Analytic hierarchy process

Individual experts’ experiences are utilized to estimate the relative magnitudes of factors through pair-wise comparisons.

Each of the respondents compares the relative importance of each pair of items using a specially designed questionnaire.

Users of the AHP first decompose their decision problem into a hierarchy of more easily comprehended sub-problems, each of which can be analyzed independently.

[5] The AHP converts these evaluations to numerical values that can be processed and compared over the entire range of the problem.

These numbers represent the alternatives' relative ability to achieve the decision goal, so they allow a straightforward consideration of the various courses of action.

[15] It was recently applied to a project that uses video footage to assess the condition of highways in Virginia.

Highway engineers first used it to determine the optimum scope of the project, and then to justify its budget to lawmakers.

[20][21][22] The International Symposium on the Analytic Hierarchy Process (ISAHP) holds biennial meetings of academics and practitioners interested in the field.

Those in 2005 ranged from "Establishing Payment Standards for Surgical Specialists", to "Strategic Technology Roadmapping", to "Infrastructure Reconstruction in Devastated Countries".

[24] A similar number of papers were presented at the 2009 symposium in Pittsburgh, Pennsylvania, when 28 countries were represented.

[25] Subjects of the papers included Economic Stabilization in Latvia, Portfolio Selection in the Banking Sector, Wildfire Management to Help Mitigate Global Warming, and Rural Microprojects in Nepal.

As can be seen in the material that follows, using the AHP involves the mathematical synthesis of numerous judgments about the decision problem at hand.

While the math can be done by hand or with a calculator, it is far more common to use one of several computerized methods for entering and synthesizing the judgments.

In doing this, participants explore the aspects of the problem at levels from general to detailed, then express it in the multileveled way that the AHP requires.

As they work to build the hierarchy, they increase their understanding of the problem, of its context, and of each other's thoughts and feelings about both.

Human organizations are often structured as hierarchies, where the hierarchical system is used for assigning responsibilities, exercising leadership, and facilitating communication.

Familiar hierarchies of "things" include a desktop computer's tower unit at the "top", with its subordinate monitor, keyboard, and mouse "below."

Similarly, when we approach a complex decision problem, we can use a hierarchy to integrate large amounts of information into our understanding of the situation.

The design of any AHP hierarchy will depend not only on the nature of the problem at hand, but also on the knowledge, judgments, values, opinions, needs, wants, etc.

Such a hierarchy can be visualized as a diagram like the one immediately below, with the goal at the top, the three alternatives at the bottom, and the four criteria in between.

Once the hierarchy has been constructed, the participants analyze it through a series of pairwise comparisons that derive numerical scales of measurement for the nodes.

An important task of the decision makers is to determine the weight to be given each criterion in making the choice of a leader.

Depending on the problem at hand, "weight" can refer to importance, or preference, or likelihood, or whatever factor is being considered by the decision makers.

Priorities are distributed over a hierarchy according to its architecture, and their values depend on the information entered by users of the process.

The local priorities, shown in gray, represent the relative weights of the nodes within a group of siblings with respect to their parent.

As the Analytical Hierarchy Process moves forward, the priorities will change from their default values as the decision makers input information about the importance of the various nodes.

[26][31] One of them contains a handful of expanded examples, plus about 400 AHP hierarchies briefly described and illustrated with figures.

[28] Many examples are discussed, mostly for professional audiences, in papers published by the International Symposium on the Analytic Hierarchy Process.

[32][33][34][35][36] The AHP is included in most operations research and management science textbooks, and is taught in numerous universities; it is used extensively in organizations that have carefully investigated its theoretical underpinnings.

In the context of tournament matrices, it has been proven by Oskar Perron[51] that the principal right eigenvector method is not monotonic.