Maximally productive input–output units

Technical or Pareto–Koopmans efficiency models can be based on ratios of weighted sums of outputs to weighted sums of inputs. Differing meanings have been considered for such factor weights. In this paper, we use value or cost rate meanings depending on model orientation. These meanings permit considering the simultaneous assignment of input and output factor weights along with optimal intensity values for a virtual composite unit constructed from the observed units. An optimization principle we call the winners-take-all criterion is proposed for determining the maximally productive unit(s). No assumptions are required on the internal transformation processes of the units. The model simultaneously determines the intensities and factor weights and results in indefinite quadratic programming problems that simplify to linear programming in certain cases. For the general case, genetic search is applied. Numerical illustrations are provided for faculty merit scoring and for the 15 hospital dataset of Sherman.