Two non-radial measures of super-efficiency in DEA with data uncertainty

Issue title: Special Section: Best papers of the 2016 International Conference on Management and Operations Research - ICMOR 2016

Guest editors: Xiaoxia Huang, Qun Zhang and Qing Yang

Article type: Research Article

Authors: Xu, Xiaoning^{a; *} | Chen, Rong^a | He, Feng^{b; *} | Zhu, Liyun^c

Affiliations: [a] School of Economics and Management, Tsinghua University, Beijing, P.R. China | [b] Donlinks School of Economics and Management, University of Science and Technology Beijing, Beijing, P.R. China | [c] School of business, Hebei Agricultural University, Baoding, P.R. China

Correspondence: [*] Corresponding author. Xiaoning Xu, School of Economics and Management, Tsinghua University, No. 30 Shuangqing Road, Haidian District, Beijing 100084, P.R. China. E-mail: xuxn@sem.tsinghua.edu.cn and Feng He, Donlinks School of Economics and Management, University of Science and Technology Beijing, No. 30 Xueyuan Road, Haidian District, Beijing 100083, P.R. China. Tel.: +86 15210602249/+86 010 62333657; Fax: +86 010 62333450; E-mail: hefeng@manage.ustb.edu.cn.

Abstract: Measuring errors or uncertainties in inputs and outputs create difficulties for performance evaluation in data envelopment analysis (DEA). The literature deals with the uncertainty using fuzzy or stochastic approaches. However, specifying the membership function or probability distribution is not always easy. This paper proposes a new method by assuming the inputs and outputs vary within a bounded interval and using interval analysis to extend the classic radial DEA models to two non-radial DEA models with bounded uncertainty, respectively. One is used to obtain efficiencies on the basis of slacks-based measurement (SBM) of super-efficiency DEA model, and the other is used to identify specific inefficiencies on the basis of additive super-efficiency DEA model for the decision making units (DMU) under evaluation. To solve the interval non-radial DEA models, the paper adopts the optimization theory to transform the uncertain two-level programs into deterministic one-level programs, and an acceptability index to compare and rank any of the resulting interval efficiencies. Numerical analysis illustrates the advantage of this new approach against conventional methods.

Keywords: Data envelopment analysis, slacks, additive model, super-efficiency, interval efficiency

DOI: 10.3233/JIFS-169217

Journal: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 6, pp. 4533-4542, 2017