Analytic Hierarchy Process

The Analytic Hierarchy Process and Analytic Hierarchy Process (AHP ) is a technology developed by the mathematician Thomas L. Saaty method to support decision-making.

The Analytic Hierarchy Process is a method from the prescriptive decision theory to decision support similar to the cost-benefit analysis to simplify complex decisions and to take rational. The AHP is a systematic procedure to structure decision-making processes and to solve. The possibilities are endless.

The goal of the AHP is to:

• To support decisions in teams.
• Finding the common portable solution and to minimize the requisite amount of time.
• The decision-making and to make the result understandable.
• Any inconsistencies in the decision to uncover.

The AHP is used:

• In order to verify and supplement of subjective "gut " decisions.
• For working out qualitative weighting decisions based on comparative decisions.
• For structured and hierarchical representation of a final decision by a decision tree.

The results allow a more detailed discussion of the decision.

The mathematician Thomas Saaty, the method had already been theoretically developed and published in 1980. See Sources at the links. For practical use, however, this method was applied only in the 1990s. Gained popularity AHP especially in North America, Scandinavia and the Far East. In the German -speaking area of the AHP previously found primarily in Austria and Switzerland compliance.

Definition

The AHP is " hierarchical" as criteria that are used to solve a problem, are always placed in a hierarchical structure. The names of these criteria are as required features, attributes, alternatives or similar. Members of a hierarchy may be divided into groups, each group being influenced only one other ( "higher" ) group of elements and the hierarchy is influenced only by a different ( " lower ").

As an " analytical" AHP is called, because it is suitable to analyze a problem constellation in all its dependencies comprehensively.

It is called " process " because it claims a procedural sequence as decisions structured and analyzed. This procedure is in principle always consistent, so that the AHP easily deployable assay more than once to a, a routine action equaling decision tool.

Context

The use of quantitative models and methods for decision support in business administration is known as Operations Research (OR ); Operations Research is characterized by the cooperation of applied mathematics, economics and computer science. (see also economic computer science )

Models and methods for decision support are subject of research in decision theory. This is in applied probability theory, a branch to evaluate the consequences of decisions; it is often used as a business management tool.

Business economics and other social sciences are concerned, among other things, how decisions are made in organizations. In companies the controlling department often provides data, models and methods for planning and decision making (see also decision support system ( engl. Decision Support System), statistical information system ).

Thanks grown IT capabilities can now more cost effective and faster than in the past from large data sets certain relationships (correlations ) can be determined (see also " Data Mining ", Data Warehouse ).

Practical phases and methodology

The decision tree is divided shortened presented in three phases. The mathematical and scientific contexts of the AHP are discussed below in more detail.

Phase 1: Collect the data

In this phase, the decision maker collects all data that are relevant to its decision.

The first step requires the decision maker that he formulated a specific question to the problem. The aim of the question is to find the best solution or answer to the problem.

In the second step the decision maker identifies unsorted all criteria ( factors ), which appear to him to resolve the issue as important. The collection often takes the form of a previous brainstorming. The order of the criteria in order of importance is, however, only in a later step.

In the third step the decision maker identifies all alternatives ( solutions ) that come to him in the closer, more realistic choice, with the can solve his problem or answer the question asked at the beginning of question.

Thus the first phase of collecting and formulating of all relevant data has been completed.

Phase 2: compare data and weights

After the first phase of collecting and formulating now follows juxtaposition, comparison and evaluation of all criteria or alternatives in two sub-steps:

In the fourth step, the decision maker must face each criterion and compare each other. This listed the decider, which appears the two criteria for him each important. Through this method of pairwise comparisons can be the decision maker elicit a very accurate assessment of the plurality of competing criteria. This leads to a ranking in which are ordered according to the criteria of importance.

To evaluate a scale is used with a range 1-9 points. For practice you can best present the assessment in the form of a virtual slider, which is located between two criteria. In this procedure, which is a criterion compared with the other criterion, compared and rated with a score.

In the fifth step, the decision maker must study and evaluate through its alternatives for their suitability. He faces two alternatives and evaluate which alternative is best suited to fulfill the respective criteria.

To evaluate a scale is also used with a bandwidth 1 to 9 for the practice, here is the idea of ​​a virtual slider, which is between two alternatives. This results comparable to the criteria in the fourth step to rank the alternatives.

3rd phase: process data

In the third and last phase is the answer to the question posed at the beginning. There are, according to Thomas Saaty different evaluation scenarios.

From the individual ratings of the second step of the AHP determined using a mathematical model (see Web Links " AHP Introduction") a precise weighting of all the criteria and merges them into a percentage order.

The AHP measures on this occasion by the so called " Inkonsistenzfaktor " the logic of the reviews to each other. This is a statement about the quality of the established decision available. The lower the Inkonsistenzfaktor, the more coherent are their reviews and the less contradictions they carry. To be able to represent a contradiction at all, at least three different reviews are required by definition that must be used to determine.

By gradually changing the determined percentages of the criteria can be the stability of the found solution consider.

Survey

( The focus in this article is currently in the presentation of the practical process for the specific user. Following the scientific part is not described in all completeness. More to the theory and mathematics can be found in the web links. )

Multi-level hierarchies of objectives occur predominantly in the decision-making process. To resolve this AHP was developed. The AHP will go through these steps:

The individual steps

The individual steps are run in sequence, which is to jump back to the priority determining if inconsistencies are detected.

Setting up the goal hierarchy

An important goal of a business is success. This goal has, among other things, the " sub-goals " market share, stability and profit. To achieve the goal of stability, including more sub-objectives to be set, for example, employee turnover and the like.

These objectives can be represented as a graph with different levels.

Determination of priorities

Pairwise comparisons of the decision maker to employed, in which the importance of two sub-targets is compared with an overall objective. The following grading scale is used.

After determining the priorities which implies, for example, the following matrix:

Calculation of the weighting vectors

From this matrix and the eigenvector of the maximum eigenvalue of a simplified procedure is to calculate and decisive.

For the above example would be this:

Software support

The method can in principle be mapped into a spreadsheet program. A corresponding instructions can be found in the web links. However, the mathematical foundations of the AHP vastly more complex and much more time-consuming to program than for example in the cost-benefit analysis. Specifically, the hierarchical variant and its Inkonsistenzfaktoren or derived from the AHP Auswerteszenarien such as stability or sensitivity analysis can be represented only difficult with simple tools. Is equally difficult to presenting the plurality of reviews in coordination processes in teams. But usually on the AHP requires specially programmed through software support.

Comparison with the cost-benefit analysis and criticism

The Analytic Hierarchy Process is mathematically demanding compared to the cost-benefit analysis (NWA ). When applying the NWA suffice to calculate pen and paper. Therefore, the NWA has already been used at times when there was no computer. The method of AHP mathematically based on a chain of matrix multiplications. This of course required computing power, which is actually only from 1990 successfully became the AHP in practice available.

The NWA is an additive approximation method and uses only the basic arithmetic operations. In the NWA, in contrast to the AHP criteria ranking is not determined by pairwise comparison (not " each criterion to every other criterion "). Instead, the decision bears his percentage estimate directly in the ranking table manually. Alternatives ranking is determined at the NWA without pairwise comparison. The " methodology " of the NWA is thus reduced to the fact that the sum of all weight factors may not give more than 100 percent. The AHP against " forcing " for pairwise comparison even with the alternatives.

Other than the wider score AHP checked in contrast to the NWA and logic and a quality decision. From the unavoidable contradictions (see consistency ) for all pairwise comparisons and their subjective evaluations is determined by a quasi unnecessary over-determination of the so-called Inkonsistenzfaktor and the stability of the ranking of all alternatives.

The sharpness of the classical AHP method is at the same time but also its weakness. Because you really needed more time to evaluate all comparisons. Unless you used a shortened alternative valuation method (see heuristic ) of the AHP at ( " a criterion to every other criterion " ) as soon as the decision maker, the " wheat from the chaff " must separate, for example, from a variety of alternatives. But then can the absence of over-determination of course inconsistency and stability no longer be determined.

Newer applications attempt the problem of large number of pairwise comparisons to be evaluated by different methods to reduce. The Adaptive AHP strives to reduce the number of pairwise comparisons significantly without affecting the quality of the result.

Another weakness of the AHP is the so-called rank reversal. If after full evaluation, the order of the alternatives, for example, a < b < c, it can be rotated by adding a further alternative, the order, and come out as a result of d < b < a < c. This change order is considered by most critics to be not logical. If previously the alternative B was better than A, why should they by adding a further alternative D now be worse than A? This is a violation of the IIA criterion ( Independence of Irrelevant Alternatives ).

The violation of the IIA criterion occurs when the new alternative in certain criteria extremely well, in others is extremely poor. You can avoid the rank reversal when one of the top two fictitious " extreme alternatives," " having considered the cut each very good and very bad in all criteria Opponents of this review explain the phenomenon often associated with the following example:. " A woman goes into the only hat shop in one place. the seller shows her hat a hat and B. The first hat woman like a best, but the seller shows her after a short time a hat C, who looks like hat A. Thereupon chooses the woman but for hat B because they do not want a woman with the same hat running around in the place. " However, this example is so far poorly chosen, as this, for example, can not be guaranteed that the uniqueness of the hat already had played a role, as the only woman to choose a or B had.