Least-distance approach for efficiency analysis: A framework for nonlinear DEA models

We propose a class of nonlinear data envelopment analysis (DEA) models, including variants of the Russell graph measure (RM), BRWZ measure, slack-based measure (SBM), and geometric distance function (GDF). Based on linear programming, this class of DEA models provides a monotonic maximum efficiency measure and an efficient target that achieves the least Manhattan distance from the weakly efficient frontier of the production possibility set. We show that the maximum efficiency measure in this class can be explicitly expressed as a decreasing function of the least Manhattan distance. Furthermore, by adding certain consistent weight restrictions to this class of DEA models, the maximum efficiency measures satisfy strong monotonicity.