Optimal Criterion Weights in Repetitive Multicriteria Decision-Making

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Abstract
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 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. 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 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 admission data of an M.B.A. programme. The hit ratios of the different procedures are compared.

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