Pliers master defines the efficiency analysis (NWA) as a "“analysis of a quantity of complex action alternatives with the purpose to arrange the elements of this quantity according to the preferences of the decision maker concerning a multi-dimensional target system. The illustration of the order takes place via the indication of the utilizable values (total values) of the alternatives."”

The objective of the NWA

A goal of a NWA is it to find an illustration of the alternatives on e.g. the real numbers which arranges the alternatives according to the preferences of the decision maker concerning a multi-dimensional target system. The NWA is usually used, if other methods of the operational research are not suitable like for example the cost benefit analysis for decision making.

This concerns a method, which supplies the utilizable value of different decision alternatives to each other in the comparison. The result at the beginning of perhaps somewhat technically seeming analysis is for each of the alternatives a number, which is called utilizable value. "„The optimal "“solution obtains thereby the highest utilizable value compared with the other alternatives.

It is suitably, if "„yield "“- thus in monetary value or numbers not representable - criteria are present, on the basis those between different alternatives a decision pleases will must.

Operational area

If several, with one another with difficulty comparable, different parameters are to be compared, the efficiency analysis represents an instrument for the selection of the use-richest variant. The NWA determines the efficiency, i.e. the relationship of the total contribution of the project to given goals. The application type of the NWA are very in principle various.

Use

By use the suitability and the extent of the suitability of a property are to be understood for the satisfaction of a need of a decision maker. For the size of the use five factors are decisive:

• that, which uses the property
• the purpose, for which the property is to be used
• the situation, in which the property is to be used
• the time, on which the property is to be used
• the property

Advantages

• Flexibility of the target system
• Adjustment to a large number of special requirements
• direct comparability of the individual alternatives

Disadvantages

• Subjectivity of the weighting - thereby large Transparency (political) of the preferences
• Comparability of the alternatives, since always it cannot be ensured that two alternatives in the same regard are compared.

Acceptance of the efficiency analysis

The following conditions must be fulfilled for the execution of an efficiency analysis:

• The quantity of the alternatives A can be arranged by the decision maker by a two digit relation P on the quantity of A.
• The decision maker is able, the question: "“Does y from A P (x, y) to x,"” to answer.
• The decision maker behaves during the questioning in the following sense consistently:
  • The preference order P is complete and
  • transitiv.

Completeness of the preference order P

The preference order is complete, if the decision maker between two arbitrary alternatives can indicate its preference or the alternatives is equivalent.

\ forall x, y \ in A: P (x, y) \ or P (y, x) 

Transitivity of the preference order P

Transitivity means that the decision maker behaves logically. Who likes goose rather than duck, duck rather than chicken, must rather like and not the chicken of the goose prefer goose than chicken. The transitivity is thus given, if a decision maker, who prefers the alternative x in relation to y and prefers y in relation to z, prefers also x in relation to z.

\ forall x, y, z \ in A \ colon (P (x, y) \ and P (y, z)) \ Rightarrow P (x, z)  

(after pliers master, page 63)

Use functions

A goal of the efficiency analysis is to be found a function u (the use function) over A on an arranged quantity of U, thus applies:

(u (x) \ geq u (y)) \ Leftrightarrow P (x, y) 

The function value of the function u is called utilizable value. It is dimensionless and serves excluding the order of the alternatives. Statements "“like alternative A is twice as well like alternative b"” are senseless therefore. A pupil with the note 6 is as good not half as a pupil with a 3. Therefore it is an error the utilizable value of an alternative in relation to its costs too set, which happens unfortunately frequently.

As arranged quantity of U the real numbers are usually used.

u \ colon A \ tons \ mathbb R 

If the alternatives can be completely described by several consequences AI regarding use, then applies:

 n \ in \ mathbb N; n \ geq 2; \ qquad A = K_1 \ times"… \ times K_n 

and the use function u receives the form:

u: K_1 \ times"… \ times K_n \ tons \ mathbb R; u (k_1,"…, k_n) 

The multi-linear use function

The multi-linear use function represents a special case, whose validity is to be verified in the context of the NWA.

u_i \ colon K_i \ tons \ mathbb R; \ qquad u (k_1,"…, k_n) = \ sum_ {i=1} ^n u_i (k_i) 

If weights so mentioned are assigned to the individual criteria, the also following form of the use function is used:

u (k_1,"…, k_n) = \ sum_ {i=1} ^n g_i \ times u_i (k_i) 

The weights gi are usually selected in such a way that its sum 1 or 100% results in.

\ sum_ {i=1} ^n g_i = 1 

With a NWA almost exclusively this form of the use function is used, without examining their applicability. It is however applicable only if the use contribution of the individual consequences is linear independent of the development of other consequences. This is to be examined with the NWA. See in addition R.L. Keeney and H. Raiffa.

Regularly this special case in evaluations of the goods test or magazines is used. Also the computation of the average note of a pupil is in the reason an efficiency analysis, with which each note with gi = 1/n is weighted.

Around wrong decisions at the edges of the ranges of values of the consequences additionally K.O will exclude. - Criteria defines. I.e. alternatives, whose consequences certain minima or maxima under/will not exceed not regarded.

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