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Obtaining weights and checking consistency 417
Table 16.2 – Comparing the importance of the ‘Quality’ attributes
Reliability
After-Sales
Support
Speed of
Delivery Customization
Reliability 1 4 5 4
After-Sales Support 1 3 1/2
Speed of Delivery 1 1/3
Customization 1
Table 16.3 – Comparing the machines on
‘Purchase Cost’
Aztec Barton Congress
Aztec 1 1/3 2
Barton 1 6
Congress 1
attributes. For example, he will be asked to consider the purchase
costs of the machines and asked whether, in terms of purchase costs, the
Aztec and Barton are ‘equally preferred’. If he indicates that the Barton
is preferred he will then be asked whether it is ‘weakly preferred’,
‘strongly preferred’ or ‘extremely strongly preferred’ (with intermediate
responses allowed). This leads to the values in Table 16.3 which shows,
for example, that the Aztec is twice as preferable as the Congress on
purchase cost.
This process is repeated, yielding a table for each of the lowest-level
attributes to represent the manager’s preferences for the machines in
terms of that attribute.
Obtaining weights and checking consistency
After each table has been obtained the AHP converts it into a set of
weights, which are then automatically normalized to sum to 1. A number
of conversion methods are possible, but the AHP uses a mathematical
approach based on eigenvalues (see Saaty 3 for details of this method).
Because of the complexities of this method a computer package like
EXPERT CHOICE is essential to carry out the calculations if any of the
tables involves more than two rows or columns. Figure 16.2 shows the
weights obtained from all the tables in the hierarchy. For Table 16.1,