# Analytics Hierarchy Process

of analytics Hierarchy Process (AHP) are one of the mathematician Thomas Saaty developed method, in order to support decision-making processes.

## introduction

of analytics Hierarchy Process are similar a method from the decision theory to the decision making aid the efficiency analysis, in order to simplify and more rationally make complex decisions. The AHP forms a systematic procedure, in order to structure and solve decision-making processes. The application type are various.

A goal of the AHP is it with difficult decisions in teams the optimal to find together portable solution and to minimize the expenditure of time necessary for it.

The AHP does not only serve for the examination and addition of subjective „belly decisions “, it can by new, unexpected aspects for more founded insights across those to crucial topic lead. Despite structured methodology also a decision remains with the help of the AHP a subjective procedure of individual, small belly decisions. Only over the result of the evaluations and/or. the representation of the offered solution can be reported clearly more objectively and/or. discuss.

The mathematician Thomas Saaty had already developed and had published the method 1980 theoretically. See sources of literature with Web on the left of. To the field use the method came however only into the 1990er years. Popularity won the AHP particularly in North America, in Scandinavia and in the eastern countries. In the German linguistic area the AHP found so far particularly in Austria and in Switzerland attention.

## definition

of the AHP is hierarchical „“, since criteria, which are consulted for the solution of a problem, are always brought into a hierarchical structure. The names for these criteria read depending upon need of characteristics, attributes, alternatives or similarly. Elements of a hierarchy can be divided in groups, whereby each group only in each case another („higher “) group is affected by hierarchy elements and only by another („lower “) affected.

When „analytically “the AHP because of its fortune designated to analyze a problem constellation in all their dependence comprehensively.

It is called „process “, because it gives a prozessualen operational sequence, how decisions are structured and analyzed. This expiration is always alike in principle remaining, whereby the AHP becomes with repeated employment an easily applicable, a routine action equaling Entscheidungstool.

## practical operational sequence

the expiration of decision is divided shortened represented into three phases. In that the following section the methodology of the AHP is represented. It is not dealt more in greater detail in this section with the mathematical-scientific connections of the AHP.

### 1. Phase: Collect the data

in this phase collect the Entscheider all data, which are substantial for its decision making.

The first step requires of the Entscheider that it formulates a concrete question for problem definition. A goal of the question is it to find the best solution and/or answer to the problem.

In the second step the Entscheider designates unsorted all criteria (criteria), which appear to it for the solution of the question as important. The collection takes place frequently in form preceding brainstorming. The order of the criteria after their importance takes place however only in a later step.

In the third step the Entscheider designates all alternatives (proposals for solution), which for it into the closer, realistic choice comes, with which its problem solve or question the asked at the beginning be answered can.

Thus the first phase of collecting and formulating all underlying data is final.

### 2. Phase: Data compare and to weights

after the first phase of collecting and formulating follow now the confrontation, comparison and evaluation of all criteria and/or alternatives in two fallen below:

In the fourth step the Entscheider must compare each criterion every other opposite racks and. Here the Entscheider notes, which the two criteria for it appears more important in each case. By this method of the comparisons in pairs to the Entscheider a very exact evaluation from the multiplicity of competitive criteria can be drawn. This leads to an order of rank, in which the criteria are arranged according to their importance.

To the evaluation a scale consulted with a range from 1 to 9 points. For practice one can imagine the evaluation at the best in form of a virtual slidegate valve automatic controller, which is between two criteria. With this expiration criterion is against-practice-suppl.-placed, compared to the other criterion and evaluated with a score.

In the fifth step the Entscheider must examine and evaluate its alternatives on their suitability. It confronts in each case two alternatives and evaluates, which alternative at the best to the fulfilment of the respective criterion fits.

To the evaluation likewise a scale consulted with a range from 1 to 9. For practice is suitable also also here the conception of a virtual sliding control, which lies between in each case two alternatives. This leads comparably to the criteria in the fourth step to an order of rank of the alternatives.

### 3. Phase: Data process

the answer of the question asked at the beginning in the sieved and last step stand. In addition there are different analysis scenarios after Thomas Saaty.

From the individual evaluations of step five the AHP determines a precise weighting of all criteria according to a mathematical model (see under Web on the left of „AHP introduction “) and joins these into a proportional order.

From the individual evaluations of the steps six and five the AHP determines a precise weighting of all alternatives in purchase to the respective criteria according to its model also and joins these in a proportional order.

The AHP measures on this occasion over the so-called inconsistency factor the logic of the evaluations to each other. Thus a statement about the quality of the determined decision is available. The lower the inconsistency factor is, the more conclusively is your evaluations and the fewer contradictions carries it in itself. In order to be able, become to represent a contradiction at all by definition at least three different evaluations needs, which must be consulted for the view.

By gradual change of the determined percentages of the criteria the stability found of the solution can be regarded.

### overview

(the emphasis in this article lies at present in the representation of the practical operational sequence for the concrete user. The following scientific part for the time being still is in the “child shoes”. More to the theory and mathematics one finds with Web on the left of)

multi-level Zielhierachien actually always arises in decision-making process. Around these to dissolve AHP was developed. The AHP thereby goes through the following steps:

1. Set up the Zielhierachie
2. determination of the priorities
3. computation of the weighting vectors
4. Konsistenzprüfung
5. calculation of the Gesamthierachie

### the individual steps

the individual steps after the order will go through, whereby for priority regulation one jumps back, if inconsistencies are determined.

#### setting up the Zielhierachie

an important goal of an enterprise is success. This goal has among other things the Unterziele market share, stability and profit. In order to achieve the goal of stability, under it further Unterziele is set, for example coworker fluctuation and the like.

These goals can be represented as graph with different stages.

#### determination of the priorities

of the Entscheider in addition comparisons in pairs are employed in which importance is compared by in each case two Unterzielen with a main goal. The following evaluation scale is used.

Scale values meaning
1 equal meaning
3 somewhat greater importance
5 very much greater importance
7 substantially greater importance
of 9 absolutely dominating
2, 4, 6, 8 intermediate values

## summary and criticism

of analytics Hierarchy Process are mathematically more fastidious in the comparison to the efficiency analysis (NWA), but but also more precisely.

With application of the NWA pin and paper are sufficient for computation. Therefore the NWA was already used at times, when there was still no EDP. 거푸집 Methode des AHP basiert mathematisch auf einer Kette 폰 Matrizen-Multiplikationen. This necessary naturally computing power, which was to the AHP in practice actually only starting from 1990 - with beginning of the computer era - successfully at the disposal.

The NWA is against it only one additive approximation method and is content with the basic operations of arithmetic. With the NWA contrary to the AHP the criterion Ranking is already not determined usually by comparison in pairs (not each criterion with every other criterion).

Stattdessen trägt der Entscheider는 prozentualen 거푸집 순위 Tabelle manuell ein에 있는 Schätzwert direkt를 seinen. The alternative Ranking is even generally determined with the NWA without comparison in pairs. „Methodology “the NWA reduces thus to the fact that the sum of all weight factors may not result in any more than 100 per cent. The AHP against it „forces “to the comparison in pairs also with the alternatives.

Apart from the broader evaluation scale the AHP examines logic and quality of a decision contrary to the NWA also. From the not avoidable contradictions all comparison in pairs and/or. their subjective evaluations by a quasi unnecessary over regulation the so-called inconsistency factor and the stability of the Rankings of all alternatives are determined.

The sharpness of the classical AHP method is at the same time in addition, their weakness. Because one really needs more time for the evaluation all comparisons. It is one turns alternatively a shortened evaluation method of the AHP on („a criterion with every other criterion “), as soon as the Entscheider e.g. from a multiplicity of alternatives „the chaff from wheat “to separate must. But then inconsistency and stability cannot be naturally determined any longer for lack of over regulation.

Newer applications try to reduce the problem of the multiplicity of pair comparisons which can be evaluated by different procedures. The adaptive AHP strives to reduce the number of the pair comparisons clearly without concerning the quality of the result.

## literature

• multi-criteria decision making - the analytics hierarchy process: planning, priority setting, resource allocation, Thomas's L. Saaty, ISBN 0-9620317-2-0
• Decision Making for Leaders - The analytics Hierarchy Process for Decisions in A Complex World, Thomas's L. Saaty, 3. Edition, Pittsburgh 2001.
• On-line market study: A positioning in the method canon of the market study under employment Web-based analytics of a Hierarchy Process (webAHP), Holger of Lütters, Wiesbaden 2004. ISBN 3-8244-8201-0

## Web on the left of

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