Benchmarking with nonconvex production possibility set through data envelopment analysis: An application to China’s transportation system

Abstract

Convex production possibility set (PPS) is an implicit assumption in previous benchmarking studies. Some scholars point out that the implicit assumption is inconsistent with the classical economic theory although it facilitates operational analysis. Hence, the present study develops a new benchmarking approach on the basis of technology that assumes convexity on consumption correspondence instead of imposing convexity on PPS, in which the closest benchmark with the least effort is identified. First, the correlation between two classical technologies in benchmarking (convex PPS and free disposal hull technology), and two nonconvex PPS (production correspondence and consumption correspondence), are identified. Next, the extreme efficient DMUs are identified to describe Pareto-efficient points on the frontier of the consumption correspondence. Then, the closest benchmark is determined by selecting a Pareto-efficient point that minimizes the distance between the evaluated unit and the efficient frontier of consumption correspondence. In addition, this study employs the Manhattan distance for benchmarking, and the proposed approach is flexible to accommodate other distances to derive different economic interpretations. Besides, the proposed approach introduces a new non-radial efficiency measure and conceptualizes a benchmark index by relaxing the convexity assumption on PPS. Finally, the proposed approach is applied to select benchmarks and measure performance for China’s transportation system. The proposed approach contributes to relaxing convexity assumption on PPS in benchmarking using DEA and provides a powerful managerial instrument to improve the performance of China’s transportation system.