Variable and Constant Returns-to-Scale Production Technologies with Component Processes

Efficiency Analysis for Multicomponent Production Processes Conventional models concerned with efficiency analysis of organizations typically consider a single production process, or technology, in which all inputs are used in the production of all outputs. This approach does not account well for the situations in which the organizations are involved in several component production processes whose inputs and outputs may be shared by different processes. The main difficulty in modeling such technologies is the fact that we often do not know the exact allocation of the shared inputs and outputs to individual processes. In “Variable and Constant Returns-to-Scale Production Technologies with Component Processes,” V. V. Podinovski shows how this problem can be overcome by the consideration of the worst-case scenario for the allocation of the shared inputs and outputs to different components of the technology. This approach leads to the development of multicomponent variants of two well-established nonparametric models. An application involving universities in England demonstrates the usefulness and improved discriminating power of the new models compared with their conventional analogues. We consider nonparametric production technologies characterized by several component production processes and allow both component-specific and shared inputs and outputs. Each process uses its specific inputs and an unknown part of the shared inputs to produce its specific outputs and an unknown part of the shared outputs. For the described setting, we develop two new models of production technologies, under the assumptions of variable and constant returns to scale (VRS and CRS). These models are based on the worst-case assumption about the allocation of the shared inputs and outputs to component processes and, therefore, do not require exact knowledge of the actual allocation. The new models are larger than the standard VRS and CRS technologies. We provide a formal axiomatic derivation of the new technologies, explore their dual interpretation, and demonstrate their usefulness in an application.