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The Analytic Hierarchy Process is 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. The method of the AHP is based mathematically on a chain of stencil multiplications. 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).
Instead the Entscheider registers its proportional estimated value directly into the Ranking table manually. 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 must separate "the chaff e.g. from a multiplicity of alternatives from wheat ". 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.
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