Free disposal hull models of multicomponent technologies

Free disposal hull (FDH) is a nonparametric model of production technology based on the single assumption of free disposability of all inputs and outputs. In this paper, we consider multicomponent production technologies in which every decision making unit (DMU) consists of several parallel component processes that can in principle operate independently of each other, provided they have sufficient resources. An example is universities viewed as DMUs, with their departments or groups of departments viewed as component processes. Each component process uses its own set of inputs and an unknown part of the shared inputs in order to produce its own set of outputs and an unknown part of the shared outputs. We allow combinations of component processes taken from different DMUs in order to construct new hypothetical DMUs, and refer to the resulting model of technology as the multicomponent FDH (MFDH) model. We further develop a larger, and mathematically nontrivial, variant of MFDH for the case in which we can specify certain bounds on the proportions in which shared inputs and outputs are allocated to component processes. We use an illustrative example in the context of universities to demonstrate the increasing discriminatory power of the new MFDH models over the standard FDH models in the multicomponent setting.