User:Louis F. Sander/Analytic Hierarchy Process

DO NOT DELETE: This is a development page for the article on the Analytic Hierarchy Process.
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Left out of the lead for various reasons, but must be covered:

• AHP primarily used in groups
• Homogeneity
• Consistency checking (check the matrix, OR check the results for "looking right")

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From previous Citizendium leads:

It not only allows the decision to be considered more rationally and objectively, but it encourages communication that leads to a better global understanding of the problem and its possible solutions.

Constructing this hierarchy not only requires the participants to examine the decision problem very carefully, but also promotes extensive communication among them, both of which improve their collective understanding of the problem and its possible solutions.

As the participants construct the hierarchy and prepare for the next step, they refine their understanding of the problem and its possible solutions.

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Old Wikipedia lead:

The Analytic Hierarchy Process (AHP) is a technique for decision making where there are a limited number of choices, but where each has a number of different attributes, some or all of which may be difficult to formalize. It is especially applicable when decisions are being made by a team.

AHP can assist with identifying and weighting selection criteria, analyzing the data collected for the criteria, and expediting the decision-making process. It helps capture both subjective and objective evaluation measures, providing a useful mechanism for checking the consistency of the evaluation measures and alternatives suggested by the team.

The process is based on a series pairwise comparisons which are checked for internal consistency and then combined.

Underlying philosophy

Under Construction

There is a lot of good material on this in the books. If it can be put here in a suitable way, this maybe should be the first section of the article, or at least somewhere way up at the top.

Maybe this should be "history and philosophy." At least there should be a little history somewhere.

Early on, we need to convey the meaning of priorities.

There is philosophical stuff here about A) psychology, and B) measurement.

There is underlying mathematical rigor.

Mind mapping could be a good way to construct a hierarchy. Tony Buzan.

In the 1960s, the U.S. and the Soviet Union were negotiating to reduce the number of nuclear weapons held by both parties. On the U.S. side, the study of this problem was assigned to the State Department's Arms Control and Disarmament Agency. Over several years, this agency spent significant resources to tap the knowledge of some of the world's leading thinkers in mathematical economics, utility theory, game theory, and conflict resolution. It was found, unfortunately, that negotiators and other nontechnical people could neither learn nor apply the findings of these scholars. There was a two culture chasm in thought and language that could not be bridged.

The quest to understand and bridge such chasms led to the search for a decision making method that

• Does not require inordinate specialization to master
• Can incorporate both intuitive and analytical judgments
• Is adaptable to both groups and individuals, and
• Encourages compromise and consensus building

Three principles guide one in using the AHP:

• Decomposition
• Comparative judgments
• Synthesis of priorities

Decision making is a process that involves these steps:

• Structure a problem as a hierarchy or as a system with dependence loops
• Elicit judgments that reflect ideas, feelings or emotions
• Represent those judgments with meaningful numbers
• Use these numbers to calculate the priorities of the elements in the hierarchy
• Synthesize these results to determine an overall outcome
• Analyze the sensitivity to changes in judgment

People find AHP easy to use because:

• People find it natural and ar usually attracted rather than alienated by it
• It does not need advanced technical knowledge and nearly everyone can use it
• It takes into consideration judgments based on people's feelings and emotions as well as their thoughts
• It deals with intangibles side by side with tangibles. What we perceive with the senses is dealt with by the mind in a similar way to what we feel.
• It derives scales through reciprocal comparison rather than by assigning numbers pulled from the mind directly
• It does not take for granted the measurements on scales, but asks that scale values be interpreted according to the values of the problem
• It relies on simple-to-elaborate hierarchic structures to represent decision problems. With such appropriate representation, it is able to handle problems of risk, conflict, and prediction
• It can be used to make direct resource allocation, benefit/cost analysis, resolve conflicts, design and optimize systems
• It is an approach that describes how good decisions are made rather than prescribes how they should be made. No one living at a certain time knows what is good for people for all time.
• It provides a simple and effective procedure to arrive at an answer, even in group decision making where diverse expertise and preferences must be considered
• It can be applied in negotiating conflicts by focusing on relations between relative benefits to costs for each of the parties

Uses and applications

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

The introductory material for this section is Under Construction
AHP is a method that breaks complexity into manageable pieces, works with each piece, then collectively evaluates all the pieces. The steps are...

Though the AHP can be used by an individual, our discussion will assume it's used by a group.

Brainstorming goes on a lot in the early stages.

We say "decision problem," but there might be a more general term.

Make it clear that this is a simplified description, and that it is based on previously published information, especially Decision Making for Leaders, but also including lots and lots of other books and articles.

Include a summary of the main steps in the process (the steps further described below).

Hello again, Lou....

Establish Priorities

Once the hierarchy has been constructed, the participants use AHP to establish priorities for all its nodes. In doing so, information is elicited from the participants and processed mathematically. This activity is somewhat complex, and the participants have many options on the road to completing it. This and the following sections describe a simple, straightforward example of establishing priorities.

As our first step, we will define priorities and show how they interact.

Priorities are numbers associated with the nodes of the hierarchy. By definition, the priority of the Goal is 1.000. The priorities of the Criteria (which are the children of the Goal) can vary in magnitude, but will always add up to 1.000. The priorities of the children of any Criterion can also vary but will always add up to 1.000, as will those of their own children, and so on down the hierarchy.

This illustration shows some priorities for the Jones car buying hierarchy. We'll say more about them in a moment. For now, just observe that the priorities of the children of each parent node add up to 1.000, and that there are three such groups of children in the illustration.

AHP hierarchy for the Jones family car buying decision, with some associated priorities.

If you understand what has been said so far, you will see that if we were to add a "Handling" criterion to this hierarchy, giving it five Criteria instead of four, the priority for each would be .200. You will also know that if the Safety criterion had three children, each of them would have a priority of .333.

In our example as it stands, the priorities within every group of child nodes are equal. In this situation, the priorities are called default priorities. As the analytic hierarchy process continues, the default priorities will change to reflect our judgments about the various items in each group.

As you may have guessed by now, the priorities indicate the relative weights given to the items in a given group of nodes. Depending on the problem at hand, "weight" can refer to importance, or preference, or likelihood, or whatever factor is being considered by the participants.

If all the priorities in a group are equal, each member has equal weight. If one of the priorities is two times another, or three, (or whatever), that member has two, or three, (or whatever) times the weight of the other one. For example, if we judge cargo capacity to be three times as important as passenger capacity, cargo capacity's new priority will be .750, and passenger capacity's priority will be .250, because .750 = 3 × .250, and .750 + .250 = 1.000. (Don't worry—the AHP software keeps track of all this.)

AHP priorities have another important feature. The priority of any child node represents its contribution to the priority of its parent. In the diagram above, Cost, Safety, Style and Capacity each contribute .250 of the 1.000 priority of the Goal. Cargo capacity and passenger capacity each contribute half of the priority belonging to the Capacity criterion. Working through the arithmetic, Passenger Capacity contributes .500 × .250 = .125 of the 1.000 priority of the Goal.

As we move ahead through the Analytical Hierarchy Process, the priorities will change but will still add to 1.000 for each group of child nodes.

Make judgments

Under Construction
Establish priorities for the elements of the hierarchy. Includes inputting data. Be careful about data. There are scales involved. Some are meaningful to us and the problem, some are not. This includes the consistency check step (repeated at every level) (Rozann: pairwise comparisons using judgment)

Derive priorities

Under Construction
This is done by "AHP Magic Math." It turns your pairwise comparisons of items at one level into weights for the items at that level. Maybe we are "developing" priorities, or "calculating" them, or ????

Synthesize priorities throughout the structure

Under Construction
More "AHP Magic Math" It takes the priorities for the various items at the various levels and turns them into one big integrated set of priorities for the whole hierarchy.

Check sensitivity

Under Construction
Take a look at what would happen if your judgments changed.

The mathematics of AHP

Under Construction

New stuff goes here.

Validation examples

Under Construction

New stuff goes here.

Using AHP with groups

Under Construction

When you get to this part, go through the whole article and harmonize "user", "participants", etc.

Criticisms and drawbacks

Under Construction

See also

Multi Criteria Decision Making

References