Analytic hierarchy process
The Analytic Hierarchy Process and Analytical Hierarchy Process (AHP), also Saaty method , is one of the mathematician Thomas L. Saaty developed method to support decision-making.
The Analytic Hierarchy Process is a method from prescriptive decision theory to aid decision- making, similar to utility value analysis , in order to simplify complex decisions and make them more rational. The AHP is a systematic procedure for structuring and solving decision-making processes. The possible uses are diverse.
The goals of the AHP are:
- Support decisions in teams.
- To find the jointly portable solution and to minimize the time required for it.
- To make the decision-making and the result comprehensible.
- Uncover any inconsistencies in decision-making.
The AHP serves:
- For checking and supplementing subjective “gut decisions”.
- To work out qualitative weighting decisions based on comparative decisions.
- For the structured and hierarchical representation of a final decision using a decision tree.
The results allow a more detailed discussion of the decision.
The mathematician Thomas Saaty had theoretically developed and published the method as early as 1980. See literature sources on the web links . The method did not come into practical use until the 1990s. The AHP gained popularity particularly in North America, Scandinavia and the Far Eastern countries. In the German-speaking area, the AHP has so far received particular attention in Austria and Switzerland.
definition
The AHP is “hierarchical”, since criteria that are used to solve a problem are always brought into a hierarchical structure. The names for these criteria are characteristics, attributes, alternatives or similar, as required . Elements of a hierarchy can be divided into groups, whereby each group only influences one other ("higher") group of hierarchy elements and is only influenced by one other ("lower").
The AHP is called “analytical” because it is suitable for comprehensively analyzing a problem constellation in all its dependencies.
It is called a "process" because it specifies a procedural sequence of how decisions are structured and analyzed. This process is in principle always the same, which means that the AHP becomes an easy-to-use decision-making tool that is equivalent to routine action when it is used several times.
context
The use of quantitative models and methods for decision support in business administration is called Operations Research (OR); Operations research is shaped by the collaboration between applied mathematics , economics and computer science . (see also business informatics )
Decision support models and methods are the subject of research in decision theory . In applied probability theory, this is a branch for evaluating the consequences of decisions ; it is widely used as a business instrument.
Business administration and other social sciences deal, among other things, with how decisions are made in organizations. In companies, the department provides Controlling often data models and methods for planning and decision making (see also decision support system (Engl. Decision Support System ) statistical information system ).
Thanks to the increased IT capabilities, certain relationships ( correlations ) can now be determined more cheaply and more quickly than before from large databases (see also " Data Mining ", Data Warehouse ).
Practical process and methodology
The decision-making process is broken down into three phases. The mathematical and scientific relationships of the AHP are not dealt with in more detail below.
1st phase: collecting the data
In this phase, the decision maker collects all the data that are relevant for his decision-making.
The first step requires the decision maker to formulate a specific question about 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 names unsorted all criteria (viewpoints) that appear to be important for solving the question. The collection often takes the form of a previous brainstorming session . The order of the criteria according to their importance is done in a later step.
In the third step, the decision maker names all the alternatives (suggested solutions) that are shortlisted and realistic for him, with which his problem can be solved or the question asked at the beginning can be answered.
This completes the first phase of collecting and formulating all the data relevant to the decision.
2nd phase: Compare and weight data
After the first phase of collecting and formulating, there is now a comparison, comparison and evaluation of all criteria or alternatives in two sub-steps:
In the fourth step, the decision maker has to contrast and compare each criterion with each other. The decision maker notes which of the two criteria appears to be more important to him. This method of pairwise comparisons allows the decision maker to obtain a very precise assessment from the multitude of competing criteria. This leads to a ranking in which the criteria are ordered according to their importance.
A scale with a range from 1 to 9 points is used for evaluation. In practice, the assessment can best be imagined in the form of a virtual slider that is located between two criteria. In this process, one criterion is contrasted with the other, compared and rated with a number of points.
In the fifth step, the decision maker must examine and evaluate his alternatives for their suitability. He compares two alternatives and evaluates which alternative best suits the fulfillment of the respective criterion.
A scale with a range from 1 to 9 is also used for the evaluation. In practice, the idea of a virtual slider that lies between two alternatives is also suitable here. Similar to the criteria in the fourth step, this leads to a ranking of the alternatives.
3rd phase: processing data
The third and last phase is the answer to the question asked at the beginning. According to Thomas Saaty, there are various evaluation scenarios for this.
From the individual evaluations of the second step, the AHP determines a precise weighting of all criteria according to a mathematical model (see under web links "AHP Introduction") and puts them together in a percentage order.
On this occasion, the AHP uses the so-called “inconsistency factor” to measure the logic of the evaluations in relation to one another. A statement about the quality of the determined decision is thus available. The lower the inconsistency factor, the more conclusive their evaluations and the fewer contradictions they contain. In order to be able to present a contradiction at all, at least three different evaluations are required by definition, which must be used for consideration.
The stability of the solution found can be viewed by gradually changing the percentage values determined for the criteria.
Overview
(The focus of this article is currently on the presentation of the practical process for the specific user. The following scientific part has not yet been described in all its entirety. More about theory and mathematics can be found on the web links .)
Multi-level target hierarchies occur predominantly in the decision-making process. To resolve this, AHP was developed. The AHP goes through the following steps:
- Establishing the target hierarchy
- Determination of priorities
- Calculation of the weighting vectors
- Consistency check
- Calculate the overall hierarchy
The individual steps
The individual steps are run through in the order in which they are performed, with a return to the priority setting if inconsistencies are found.
Establishing the target hierarchy
An important goal of a company is success. This goal has, among other things, the "sub-goals" market share , stability and profit . In order to achieve the goal of stability, further sub-goals are set, for example employee fluctuation and the like.
These goals can be displayed as a graph with different levels.
Determination of priorities
To this end, the decision maker makes comparisons in pairs in which the importance of two sub-goals is compared with an overall goal. The following rating scale is used.
| Scale value | meaning |
|---|---|
| 1 | same meaning |
| 3 | slightly greater importance |
| 5 | significantly greater importance |
| 7th | much greater importance |
| 9 | absolutely dominating |
| 2, 4, 6, 8 | Intermediate values |
If the sub-goals to be compared are closer together than this scale indicates, the 1.1; 1.2; . . . . . 1.9 scale can be used. In principle, you can differentiate as finely as you like, but this rarely brings any meaningful added value.
After determining the priorities, the following matrix results, for example:
| decision | Attribute 1 | Attribute 2 | Attribute 3 |
|---|---|---|---|
| Attribute 1 | 1 | 7th | 4th |
| Attribute 2 | 1/7 | 1 | 1/5 |
| Attribute 3 | 1/4 | 5 | 1 |
Calculation of the weighting vectors
From this matrix, the eigenvector and the maximum eigenvalue can be calculated using a simplified method and are decisive.
For the example mentioned this would be:
| decision | Attribute 1 | Attribute 2 | Attribute 3 | priorities |
|---|---|---|---|---|
| Attribute 1 | 1 | 7th | 4th | 67.5% |
| Attribute 2 | 1/7 | 1 | 1/5 | 7.3% |
| Attribute 3 | 1/4 | 5 | 1 | 25.2% |
Software support
In principle, the process can also be mapped in a spreadsheet program. A corresponding instruction can be found on the web links. However, the mathematical principles of the AHP are much more complex and therefore much more time-consuming to program than z. B. in utility analysis . Especially the hierarchical variant and its inconsistency factors or also evaluation scenarios derived from the AHP such as B. the stability or sensitivity analysis can only be represented with difficulty with simple tools. Just as difficult is the presentation of various evaluations within the coordination processes in teams. This usually requires software support specially programmed for the AHP.
Comparison with the utility analysis and criticism
The Analytic Hierarchy Process is mathematically more demanding than the utility value analysis (NWA). When using the NWA, pen and paper are sufficient for the calculation. That is why the NWA was already used at a time when there was no IT. The AHP method is mathematically based on a chain of matrix multiplications. Of course, these required computing power, which in practice was actually only successfully available to the AHP from 1990 onwards.
The NWA is an additive approximation method and only uses the basic arithmetic operations . With the NWA, in contrast to the AHP, the criteria ranking is not determined by pairwise comparison (not “every criterion with every other criterion”). Instead, the decision maker enters his estimated percentage directly in the ranking table. Also alternatives ranking is determined at the NWA without pairwise comparison. The "methodology" of the NWA is reduced to the fact that the sum of all weighting factors must not result in more than 100 percent. The AHP, on the other hand, “forces” a pairwise comparison even with the alternatives.
Apart from the broader evaluation scale, the AHP, unlike the NWA, also checks the logic and quality of a decision. From the unavoidable contradictions (see consistency ) of all pairwise comparisons or their subjective evaluations, the so-called inconsistency factor and the stability of the ranking of all alternatives are determined by a quasi unnecessary overdetermination .
The sharpness of the classic AHP method is also its weakness. Because you need more time for evaluating all comparisons. Unless you alternatively use a shortened evaluation method (see heuristics ) of the AHP ("one criterion with every other criterion"), as soon as the decision maker z. B. from a variety of alternatives that "separate the wheat from the chaff". But then, due to a lack of overdetermination, inconsistency and stability can of course no longer be determined.
Newer applications try to reduce the problem of the large number of pair comparisons to be assessed by different methods. The Adaptive-AHP tries to significantly reduce the number of pair comparisons without affecting the quality of the result.
Another weakness of the AHP is the so-called rank reversal . If, after the complete evaluation, the order of the alternatives is a <b <c, for example, the order can be reversed by adding a further alternative and the result is d <b <a <c. Most critics consider this change in the order to be not logical. If before alternative B was better than A, why should it be worse than A after adding another alternative D? This is a violation of the IIA criterion ( Independence of Irrelevant Alternatives ).
Violation of the IIA criterion occurs when the new alternative is extremely good in certain criteria and extremely bad in others. The Rank Reversal can be avoided if one includes two fictitious "extreme alternatives" "" which do very well or very badly in all criteria. The opponents of this criticism often explain the phenomenon with the following example: "A woman goes into the only hat shop in a town. The seller shows her hat A and hat B. The woman initially likes hat A best, but after a short time the seller shows her a hat C, which looks like hat A. Then the woman decides for hat B because she does not want a woman with the same hat to walk around the town. ”However, this example is badly chosen because it cannot guarantee, for example, that the uniqueness of the hat already exists had played a role when the woman only had A or B to choose from.
See also
- Analytic Network Process (ANP)
- Utility analysis
- Kepner-Tregoe
- Conjoint analysis
- TOPSIS (Technique for Order Preference by Similarity to Ideal Solution)
literature
- Thomas L. Saaty: Multicriteria decision making - the analytic hierarchy process. Planning, priority setting, resource allocation . 2nd Edition. RWS Publishing, Pittsburgh 1990, ISBN 0-9620317-2-0 .
- Thomas L. Saaty: Decision Making for Leaders - The Analytic Hierarchy Process for Decisions in a Complex World . 3. Edition. RWS Publishing, Pittsburgh 2001, ISBN 0-9620317-8-X .
- Holger Lütters: Online market research: A position determination in the method canon of market research using a web-based Analytic Hierarchy Process (webAHP) . Wiesbaden 2004, ISBN 3-8244-8201-0 .
- Holger Lütters: Analytic Hierarchy Process (AHP) in market research . 2008 ( marktforschung.de ).
- Holger Lütters, Jörg Staudacher: Strategic Control with the Analytic Hierarchy Process. Published in Marketing Review St. Gallen . 2008, doi : 10.1007 / s11621-008-0025-y .
Web links
- MSDN Magazine The Analytic Hierarchy Process: Test Run
- Methodological comparison with the utility value analysis
Individual evidence
- ^ Society for Operations Research: Operations Research .
- ↑ Thomas L. Saaty: How to make a decision: The Analytic Hierarchy Process . Ed .: European Journal of Operational Research 48. North-Holland 1990, p. 18 ( sciencedirect.com ).