Selective convexity in data envelopment analysis models

In this paper we introduce a concept of selective convexity into the models of data envelopment analysis (DEA). In this development, each input and output can be judged individually with respect to its compliance with the convexity assumption. The decision making units can be used to form convex combinations provided they are different only on the inputs and outputs for which the convexity assumption is accepted. The free disposal hull, standard variable returns-to-scale and quasi-concave DEA models are all special cases in the range of models obtained in this paper. Operationally, the new models are solved as mixed integer linear programs, both in the input- and output-oriented scenarios.