Data envelopment analysis: theory and applications

The common weights approach is one of the most prominent methods to further prioritize the subset of DEA efficient units. This approach can be modeled as a multiobjective problem, where one seeks for a common set of weights that locates the efficiency ratio of each unit as close as possible to the target score of 1. In such a setting, different metrics can be applied to measure the distance of the efficiency ratios from target, such as the L1, L2 and L∞. When L1 and L2 metrics are used the models derived are non-linear. In case of the L∞ metric, the problem can be heuristically solved by the bisection method and a series of linear programs. We investigate in this paper the ability of genetic algorithms to solve the problem for estimating efficiency scores, by using an evolutionary optimization method based on a variant of the Nondominated Sorted Genetic Algorithm.