A B-convex production model for evaluating performance of firms

Some 30 years ago Charnes, Cooper and Rhodes [A. Charnes, W.W. Cooper, E. Rhodes, Measuring the efficiency of decision making units, European J. Oper. Res. 2 (6) (1978) 429–444] proposed DEA (Data Envelopement Analysis) as a mean of measuring and evaluating performance of firms. This paper proposes a model for production technologies which differs from the traditional DEA production model. The usual convex framework of the DEA model is replaced by an order theoretical condition: if two input vectors can produce a given output then the maximum coordinatewise of these two vectors can produce that same output. In this model, technologies are dually linked by a min–max cost function that is dual to the Shephard's distance function. Assuming free disposal of outputs these technologies can be completely described and the Shephard's distance function can be given in closed form.