Article DOI: 10.1111/exsy.12112 A new data envelopment analysis method for ranking decision making units: an application in industrial parks Mohammad Izadikhah 1 and Reza Farzipoor Saen 2 (1) Department of Mathematics, College of Science, Arak Branch, Islamic Azad University, Arak, Iran E-mail: m_izadikhah@yahoo.com (2) Department of Industrial Management, Faculty of Management and Accounting, Karaj Branch, Islamic Azad University, Karaj, Iran E-mail: farzipour@yahoo.com Abstract: Relative efficiency of decision-making units (DMUs) is assessed by classical data envelopment analysis (DEA) models. DEA is a popular technique for efficiency evaluation. There might be a couple of efficient DMUs. Classical DEA models cannot fully rank efficient DMUs. In this paper, a novel technique for fully ranking all DMUs based on changing reference set using a single virtual inefficient DMU is proposed. To this end, the first concept of virtual DMU is defined as average of all inefficient DMUs. Virtual DMU is a proxy of all inefficient DMUs. This new method proposes a new ranking method that takes into account impact of efficient DMUs on virtual DMU and impact of efficient DMUs on influences of other efficient DMUs. A case study is given to show applicability of the proposed approach. Keywords: data envelopment analysis (DEA), reference set, efficiency, ranking, industrial parks 1. Introduction Industrial parks are known as one of the centres for improving and training knowledge and economy in each country. Industrial park is a place within a given area for establishing a set of industry, research, technology and support services such as design, engineering, education, information, counselling and commerce (Loftsen & Lindelof, 2003; Chen & Huang, 2004). Given the increasing number of industrial parks, measuring efficiency of industrial parks becomes an important issue for practitioners and academicians. Performance evaluation of industrial parks is a complex task. Lofsten and Lindelof (2003) extended prior researches on science parks by developing measures of whether resources, innovation, risk and strategies affect growth and profitability of firms. Chen and Huang (2004) used analytic hierarchy process (AHP) method to evaluate high-tech industries in industrial park of Taiwan. Nosratabadi et al. (2011) presented a fuzzy expert system to evaluate industrial parks. Tian et al. (2014) assessed economic and environmental performance of 17 accredited sector-eco-industrial parks. Data envelopment analysis (DEA) is a nonparametric methodology for calculating the relative efficiency of decision-making units (DMUs). The first DEA model, that is, Charnes–Cooper–Rhodes (CCR) model, was proposed by Charnes et al. (1978) and is based on the work of Farrell (1957). Dinc and Haynes (1999) developed an integrated set of models to investigate sources of inefficiencies in regional industry sectors by DEA. Afonso et al. (2005) computed public sector performance and efficiency indicators in 23 developed countries. They measured input and output efficiency of public sectors by DEA. Chen et al. (2006) applied DEA and Malmquist index to analyse comparative performance of six industries in a science park of Taiwan. Hu et al. (2009) analysed the efficiency of 57 industrial parks in Taiwan from 2000 to 2004 by DEA. Hu et al. (2010) assessed efficiency of 53 Science and Technology Industrial Parks (STIP) in China from 2004 to 2006. They applied a four-stage DEA approach to eliminate different operational conditions beyond STIPs’ control. Obadic and Aristovnik (2011) presented a method using DEA models for measuring relative efficiency of government expenditures on higher education in selected new European Union members in comparison with selected Organization for Economic Cooperation and Development (OECD) countries. Aristovnik (2012) proposed a DEA-based methodology to measure relative efficiency in utilizing public education and research and development (R&D) expenditures in new EU member states in comparison with the selected EU and OECD countries. Aristovnik (2014) proposed a DEA-based methodology for measuring relative efficiency of R&D sectors. Aristovnik et al. (2014) presented a three-stage DEA model to measure relative efficiency of police units. Farzipoor Saen (2009) developed an innovative DEA model to select technologies in the presence of imprecise data, weight restrictions and nondiscretionary factors. Khodakarami et al. (in press) proposed a gradual efficiency © 2015 Wiley Publishing Ltd 596 Expert Systems, October 2015, Vol. 32, No. 5