Column Generation with Free Replicability in DEA

Abstract

The evaluation of efficiency scores in data envelopment analysis is based on the construction of artificial decision making units subject to some assump- tions, usually requiring convexity of the production possibility set. This demands divisibility in input and output, which is not always possible. The so-called free replicability model, proposed by Henry Tulkens, permits input and output to enter in only discrete amounts. The model is of a mixed integer programming type, for which the number of variables, here corre- sponding to the decision making units, may be critical in order to reach an optimal solution. We suggest to use column generation techniques to include only those decision making units that may contribute to the creation of an optimal solution.