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# 管理科学代写|决策论代写Management Science Models for Decision Making代考|ECO100 Outranking

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## 管理科学代写|决策论代写Management Science Models for Decision Making代考|Outranking

Roy (1996) has suggested another approach to pairwise comparison based on what he calls ‘outranking relations’. He redefines dominance in a less demanding way than is conventional: Option A is said to outrank Option B if A is at least as good as B on enough criteria of enough importance and is not seriously worse than B in any respect. This method is more demanding than even swaps in that it requires ‘importance’ weights for the different criteria but generally requires fewer judgement-based comparisons.

The first test – enough criteria of enough importance – is assessed by a concordance index, which is simply the sum of the weights for the criteria on which A scores at least as highly as B.

The second test, which acts as a kind of veto on the concordance index in cases where an option performs particularly badly, even if only in one respect, is assessment by a discordance index. Calculation of this is more complex but if you are interested in finding out more, the formulae and some results can be seen in the file on your CD called Ch4MulCrit! on the spreadsheet called ‘Outranking’.

It is up to the decision makers to adjust the power of the analysis to discriminate, by choosing threshold values for the two indices. To see how this works, look at the spreadsheet. Assume the same set of criterion importance weights as in Activity $4.5$ (Table 4.5) and the shortlist of options in Table 4.6. Choose the threshold values $0.85$ and $0.80$ for the concordance and discordance indexes, in cells S6 and S18 respectively. It can be seen from the range $A B 30: A B 36$ in the spreadsheet that Option 1 is again eliminated following comparison with Option 10. However, Option 17 is also eliminated, because it ranks so poorly on staff acceptability. Lowering the discordance threshold to $0.70$ leads to Option 11 being eliminated by Option 10, and with concordance threshold at $0.70$, Option 7 becomes dominated by Option 18. At this stage only Options 6, 10 and 18 remain.

## 管理科学代写|决策论代写Management Science Models for Decision Making代考|The Analytical Hierarchy Process: importance weights based on pairwise preferences

The relative transparency of pairwise comparisons of options suggests that decision makers may find it easier to derive importance weights for criteria from pairwise comparisons of criteria than direct judgements. One method of doing this is part of a broader approach to multiple criteria decision making called the Analytical Hierarchy Process (AHP) (Saaty 1980). Similar methods may be used for determining option scores.

This involves an agreed scale for the comparison of pairs of criteria (criterion A and criterion B, say). Commonly a 9-point scale is used. The odd-numbered scale points are labelled, with the values of the interspersed even-numbered points left implicit:
$1=$ A and B equally preferred (i.e. to be given equal weight).
$3=$ A moderately preferred to $B$.
$5=$ A strongly preferred.
$7=$ A very strongly preferred.
$9=$ A extremely strongly preferred.

## 管理科学代写|决策论代写管理科学决策模型代考|Outranking

Roy(1996)提出了另一种基于他所谓的“优先关系”的成对比较方法。他以一种比传统方法要求更低的方式重新定义了支配地位:如果a在足够多的、足够重要的标准上至少与B一样好，并且在任何方面都不严重逊于B，那么就可以说a优于B。这种方法比交换方法要求更高，因为它需要不同标准的“重要性”权重，但通常需要较少的基于判断的比较

## 管理科学代写|决策论代写管理科学决策模型代考|层次分析法:基于两两偏好的重要性权重

$1=$ A和B同样优先(即给予相同的权重)。
$3=$比较喜欢$B$ .
$5=$非常喜欢。
$7=$强烈推荐。
$9=$强烈推荐

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