Column generation with free replicability in DEA

• Published in: Omega (Oxford) Vol. 37; no. 5; pp. 943 - 950
• Main Authors: Ehrgott, Matthias, Tind, Jørgen
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.10.2009; Elsevier; Pergamon Press Inc
• Series: Omega
• Subjects: Applied sciences; Branch and bound; Column generation; Cutting plane; Data envelopment analysis; Data envelopment analysis Free replicable hull Branch and bound Cutting plane Column generation; Decision making; Decision making models; Decision making units; Decision theory. Utility theory; Exact sciences and technology; Firm modelling; Free replicable hull; Integer programming; Mathematical programming; Mathematics; Nonparametric inference; Operational research and scientific management; Operational research. Management science; Optimization; Probability and statistics; Sciences and techniques of general use; Statistics; Studies; Column generation; Free replicable hull; Branch and bound; Cutting plane; Data envelopment analysis; Performance evaluation; Input output; Decision support system; Branch and bound method; Decision making; Non parametric estimation; Mixed integer programming; Modeling; Cutting plane method; Convexity
• ISSN: 0305-0483; 1873-5274
• DOI: 10.1016/j.omega.2008.08.003

The evaluation of efficiency scores in data envelopment analysis is based on the construction of artificial decision making units subject to some assumptions, 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 corresponding 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.