Efficiency evaluation with convex pairs

AbstractIn this paper, we introduce a new approach to modeling technologiesin productivity analysis. The approach uses pairs of associated inputand output sets. It allows for different degrees of convexity in theoverall production possibility set. Using blocking and antiblockingtheory from combinatorial optimization, we also develop the dualrepresentation of the technology. We show how this modeling frame-work contains the classical FDH and BCC models together with avariety of new models, including FDH models with assurance regionsand models with diseconomies of scope (specialization gains). In allcases, the resulting Farrell efficiency programs can be formulated aslinear programming problems.Keywords: Productivity, convexity, duality, polarity.AMS mathematics subject classification: 91B02. 1 Introduction The mathematical programming approach to efficiency evaluation, most no-tably Data Envelopment Analysis (DEA), has proved useful in numerousapplications. Part of its success is due to the wide class of production

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