Production trade-offs in free disposal hull technologies

In data envelopment analysis, production trade-offs are value judgements that represent simultaneous changes to the inputs and outputs assumed to be technologically possible for any production unit in the technology. The specification of production trade-offs generally leads to an enlargement of the model of technology and increasing its discriminating power on efficiency. In conventional convex variable and constant returns-to-scale models, production trade-offs are the dual forms of weight restrictions. In this paper, we extend the use of production trade-offs to the free disposal hull model of technology and its constant, non-increasing and non-decreasing returns-to-scale variants, in a single unifying development. We provide an axiomatic definition of the new nonconvex technologies, explore the notion of consistent trade-offs in such technologies and develop methods for its testing. We further develop different computational approaches for nonconvex models with production trade-offs. We illustrate the new models by an application in the context of higher education.