Sequential benchmark selection on Pareto-efficient frontiers with endogenous directions

Abstract

Directional distance function (DDF) has been a popular technique in performance evaluation and benchmark selection. However, one drawback of DDF in benchmark selection lies in its inability to ensure Pareto-efficient benchmarks because of the selection of directional vectors. In the current article, we develop an approach to identify endogenous directions to guarantee selected benchmarks on Pareto-efficient frontiers in sequential benchmark selection. The approach synthesizes DDF and context-dependent data envelopment analysis (CD-DEA). The endogenous directions are determined by a “trade-off” between potential reductions and expansions of inputs and outputs, respectively. We prove that the selected benchmarks are DEA-based strongly efficient (Pareto efficient) and affine invariant. Moreover, we conceptualize the effort of realizing the selected benchmarks as a benchmark index. We demonstrate that the benchmark index can be described by DDF and Euclidean distance between the evaluated decision-making unit and its benchmark. Several properties of the benchmark index, namely positive, weak monotonic, translation invariant, and reference-set dependent, are proven. Finally, a detailed analysis is conducted to select sequential benchmarks for China’s transportation system.