##
**Optimal criterion weights in multicriteria decision making.**
*(English)*
Zbl 0558.90052

Decision making with multiple objectives, Proc. 6th Int. Conf. Multiple criteria decision making, Cleveland/Ohio 1984, Lect. Notes Econ. Math. Syst. 242, 345-357 (1985).

[For the entire collection see Zbl 0552.00017.]

In repetitive judgmental discrete decision making with multiple criteria, the decision maker usually behaves as if there is a set of appropriate criterion weights such that the decisions chosen are based on the weighted sum of all the criteria. Many different procedures for estimating these implied criterion weights have been proposed. Most of these procedures emphasize on the preference trade-off among the multiple criteria of the decision maker and thus the criterion weights obtained are not directly related to the hit ratio of matching decisions. Based on past data, statistical discriminant analysis can be used to determine the implied criterion weights that would reflect the past decisions. The most interesting performance measure is the hit ratio. However, statistical discriminant analysis result is derived from maximizing the ratio of between-group to within-group variances. This is not exactly maximizing the hit ratio directly. In this work, we use the integer linear goal programming technique to determine optimal criterion weights which minimize the number of misclassification of decisions. The linear program of minimizing the amount of misclassification of decisions is a very close approximation of maximizing the hit ratio. The linear goal programming formulation has m constraints and \(m+k+1\) variables where m is the number of cases and k is the number of criteria. Empirical study is done by using two different procedures on the actual past MBA admission data of the Simon Fraser University. The hit ratios of the different procedures are compared.

In repetitive judgmental discrete decision making with multiple criteria, the decision maker usually behaves as if there is a set of appropriate criterion weights such that the decisions chosen are based on the weighted sum of all the criteria. Many different procedures for estimating these implied criterion weights have been proposed. Most of these procedures emphasize on the preference trade-off among the multiple criteria of the decision maker and thus the criterion weights obtained are not directly related to the hit ratio of matching decisions. Based on past data, statistical discriminant analysis can be used to determine the implied criterion weights that would reflect the past decisions. The most interesting performance measure is the hit ratio. However, statistical discriminant analysis result is derived from maximizing the ratio of between-group to within-group variances. This is not exactly maximizing the hit ratio directly. In this work, we use the integer linear goal programming technique to determine optimal criterion weights which minimize the number of misclassification of decisions. The linear program of minimizing the amount of misclassification of decisions is a very close approximation of maximizing the hit ratio. The linear goal programming formulation has m constraints and \(m+k+1\) variables where m is the number of cases and k is the number of criteria. Empirical study is done by using two different procedures on the actual past MBA admission data of the Simon Fraser University. The hit ratios of the different procedures are compared.

### MSC:

90B50 | Management decision making, including multiple objectives |