Variations on the theme of slacks-based measure of efficiency: Convex hull-based algorithms. (September 2021) - Xie, Qiwei; Zhu, Yuanchang; Shang, Haichao; Li, Yongjun
Highlights: Non-radial data envelopment analysis models always overestimate inefficiencies of decision-making units and bring them far benchmarks. This paper proposes several algorithms based on a convex hull algorithmand applies the algorithms to a real dataset. Abstract: Non-radial data envelopment analysis (DEA) models, such as the slacks-based measure (SBM) model, exert an important role in theoretical research and real applications on efficiency evaluation and improvement. However, those models maximize input and output slacks and may therefore find a rather far projection for each inefficient decision-making unit (DMU). This results in varying performance measures and inconveniences in improving the performance of inefficient DMUs. Tone (2016) proposed a new non-oriented SBM-Max model and several algorithms to overcome such limitations. However, those algorithms were computationally expensive and complicated, limiting their applications to different problems. In the present study, algorithms are proposed based on two convex hull algorithms to make a novel variation of (Tone, 2016) that is easily applicable to different problems. The proposal is based on the constant returns-to-scale (CRS) assumption. The algorithms can be further extended based on other assumptions of returns to scale. The used two convex hull algorithms were the Quickhull (Qhull) algorithm and the C++ (ANSI C) implementation of the double description (CDD) algorithm. The proposed algorithms were tested on a dataset from prior literature and a real dataset of Hong Kong hospitals. The results demonstrate that the proposed algorithms are effective for finding a close projection on efficiency evaluation, resulting in improvements in DMUs.