Analytic Hierarchy Process

The Analytic Hierarchy Process (AHP) is a technique for dealing with complex decisions where a number of competing factors demand consideration. It is especially suited to problems with high stakes, involving human perceptions and judgments, whose resolutions have long-term repercussions. AHP provides a comprehensive and rational framework for structuring a problem, for representing its elements and quantifying them, for relating those elements to overall goals, and for evaluating alternative solutions.

While it can be used by individuals working on straightforward problems, AHP is most commonly applied where teams of people are working on highly complex situations, particularly where some of the elements are difficult to quantify. Computer software is available to assist in the application of the process.

Developed in the 1970s by mathematician Thomas L. Saaty, AHP has been applied worldwide, in a wide variety of decision situations, in fields such as government, business, industry, healthcare, quality, and education.

The uses and applications of AHP

The applications of AHP to complex decision situations number in the thousands, typically where problems are important and complex. Many such applications are never reported to the outside world, because they take place at high levels of large organizations, where security and privacy considerations prohibit their disclosure. But some uses of AHP are discussed in the literature. Recently these have included:

• Deciding how best to reduce the impact of global climate change (Fondazione Eni Enrico Mattei)
• Quantifying the overall quality of software systems (Microsoft Corporation)
• Selecting university faculty (Bloomsburg University of Pennsylvania)
• Deciding where to locate offshore manufacturing plants (University of Cambridge)
• Assessing risk in operating cross-country petroleum pipelines (American Society of Civil Engineers)
• Deciding how best to manage U.S. watersheds (U.S. Department of Agriculture)

AHP 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, then to justify its budget to lawmakers.

The process is widely used in countries around the world. At a recent international conference on AHP, over 90 papers were presented from 19 countries, including the U.S., Germany, Japan, Chile, Malaysia, and Nepal. Topics covered ranged from Establishing Payment Standards for Surgical Specialists, to Strategic Technology Roadmapping, to Infrastructure Reconstruction in Devastated Countries. AHP was introduced in China in 1982, and its application has expanded greatly since then—its methods are highly compatible with the traditional Chinese decision making framework, and it has been used for many decisions in the fields of economics, energy, management, environment, traffic, agriculture, industry, and the military.

Though using AHP requires no specialized academic training, the subject is widely taught at the university level—one AHP software provider lists over a hundred colleges and universities among its clients. AHP is considered an important subject in many institutions of higher learning, including schools of engineering and graduate schools of business. AHP is also an important subject in the quality field, and is taught in many specialized courses including Six Sigma and QFD.

In China, nearly a hundred schools offer courses in AHP, and many doctoral students choose AHP as the subject of their research and dissertations. Over 900 papers have been published on the subject in that country, and there is at least one Chinese scholarly journal devoted exclusively to AHP.

Description of the process

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AHP is a method that breaks complexity into manageable pieces, works with each piece, then collectively evaluates all the pieces. The steps are...

Express the problem as a hierarchy

The first step in the Analytic Hierarchy Process is to express the problem as a hierarchy. In doing this, participants explore the aspects of the problem at levels from general to detailed, then express it in the multileveled way the AHP requires. As they build the hierarchy, they increase their understanding of the problem, of its context, and of each other's thoughts and feelings about both.

Hierarchies defined

A hierarchy is a system of ranking and organizing people, things, ideas, etc., where each element of the system, except for the top one, is subordinate to a single other element.

In the world of ideas, we use hierarchies to help us get detailed knowledge of complex reality: we structure the reality into its constituent parts, and these in turn into their own constituent parts, proceeding to as many levels as we need to or care to. As we do so, we increase our understanding of the nature of the complex reality.

Think of the hierarchy that medical students use while learning anatomy—they separately consider the musculoskeletal system (and its parts and subparts), the circulatory system (and its many levels and branches), the nervous system (and its many components and subsystems), etc., until they've covered all the systems and the important subdivisions of each. Advanced students continue the subdivision all the way to the cellular or molecular level. In the end, the students have a comprehensive understanding of anatomy. They understand the "big picture," and they understand the relation of the individual parts to the whole.

Similarly, when we approach a complex decision problem, we can use a hierarchy to integrate large amounts of information into our understanding. As we build this information tree, we form a better and better picture of the problem as a whole.

AHP hierarchies explained

An AHP hierarchy is a structured means of describing the problem at hand. It consists of an overall goal, a group of options or alternatives for reaching the goal, and a group of factors or criteria that relate the alternatives to the goal. In most cases the criteria are further broken down into subcriteria, sub-subcriteria, and so on, in as many levels as the problem requires.

The hierarchy can be visualized as a diagram like the one below, with the goal at the top, the alternatives at the bottom, and the criteria filling up the middle.

A simple AHP hierarchy. To avoid clutter, the lines between the Alternatives and Criteria are often omitted or reduced in number. Regardless of any such changes to the diagram, every Alternative is connected to every Criterion and vice versa. In practice, many Criteria have one or more layers of subcriteria. These are not shown in this simplified diagram.

The specifics 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. of the participants in the process.

As the AHP proceeds through its other steps, the hierarchy can be changed to accommodate newly-thought-of criteria or criteria not originally considered to be important; alternatives can also be added, deleted, or changed.

An elementary example

In a hierarchy for the simple case of buying a vehicle, the goal might be to buy the best car for the Jones family. The criteria to be considered might be cost, capacity, safety, and stylishness. The cost criterion might be subdivided into purchase price, fuel costs, maintenance costs, and resale value. Capacity might be subdivided into passenger capacity and cargo capacity. The alternatives for the family, which for personal reasons always buys Hondas, might be the Accord Sedan, Accord Hybrid Sedan, Pilot SUV, CR-V SUV, Element SUV, and Odyssey Minivan.

The Jones' hierarchy could be diagrammed like this:

File:AHPHierarchy2.png

AHP hierarchy for the Jones family auto decision. The Goal is green, the Criteria are yellow, and the Alternatives are pink. The subcriteria for the Cost and Capacity criteria are indented below the names of the criteria. Though in the real-world hierarchy every Alternative is connected to every Criterion and vice versa, only the connections for the Accord Sedan are shown in this simplified diagram.

As they build their hierarchy, the Joneses should investigate the values or measurements of the different elements that make it up. If there are published safety ratings, for example, or manufacturer's specs for cargo capacity, they should be gathered as part of the process. This information will be needed later, when the criteria and alternatives are evaluated. Photos and other information about the Jones' alternatives can be found HERE.

Note that the measurements for some criteria, such as purchase price, can be stated precisely and with absolute certainty. Others, such as resale value, must be estimated, therefore stated with less confidence. Still others, such as stylishness, are in the eye of the beholder and are hard to state quantitatively at all. They might even have totally different meanings for different participants. The AHP can deal with all these types of criteria, even when they are present in a single problem.

Also note that the vehicle-buying hierarchy might be different for other families (ones who don't limit themselves to Hondas, or who care nothing about style, or who drive less than 5,000 miles a year, etc.). It would definitely be different for a 25-year-old playboy who has all the money in the world and knows he will never have an accident, but who is intensely interested in speed, handling, and the numerous aspects of style.

Additional information. More information about hierarchies, including further reading and some complex real-world examples, can be found HERE.

Assign priorities

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Check consistency and sensitivity

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Criticisms and drawbacks

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See also

Multi Criteria Decision Making

External links

• Short nontechnical summary from University of Cambridge
• Simple example with math from Carnegie Mellon Tepper School of Business
• Interactive demonstration of pairwise comparison from the Canadian Conservation Institute
• ISAHP - International Symposium on the Analytic Hierarchy Process
• Decision Lens AHP software
• ExpertChoice AHP software
• Vanguard Software AHP scripts for handhelds