## Example 148

The mini-max approach can be illustrated using the decision matrix presented in Table 14.5. The minimum performance value for each alternative is indicated in boldface type in Table 14.9. The minimum performance values for each alternative are as follows:

 Alternative Attribute 1: LTE 2: STE 3: TMV 4: IMP 5: Cost 1 0.4 0.3 0.0 0.5 1.0 2 0.6 0.3 0.25 1.0 0.75 3 0.8 0.9 0.5 0.5 0.0 4 0.5 0.8 0.5 0.75 1.0

Since alternative 4 has the largest minimum value (the best of the worst outcomes), it is selected. This technique does not consider the importance of an attribute in selecting the preferred alternative.

14.3.3.5 Dimensional Scoring Simple additive weighting is probably the most commonly used dimensional scoring method. The relative merit of each alternative is determined using an additive function, which sums the performance values for each attribute. The function that yields the composite-weighted score is known as the merit function. If different attributes have different degrees of importance, appropriate weights must be applied to the performance values. The merit function is given by

where i takes on values from 1 to N, MF, is the value of the merit function for alternative Ah wk the weighting constant for attribute k, and zik the scaled performance value for alternative i and attribute k. It is further required that

A potential problem in applying this technique is that the relative weights for each attribute may be controversial and difficult to determine. Since numerical values of the weights must be determined rather than just the order of importance of the attributes, these issues are more difficult than for the sequential method.