1647 Copyright © 2014, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Category: Data Envelopment Analysis DOI: 10.4018/978-1-4666-5202-6.ch146 Nonlinear Effciency in DEA Relative to “Ideal Reference” INTRODUCTION Since the original publication on Data Envelop- ment Analysis (DEA) by Charnes et al. (1978) measuring the efficiency of decision making units, there has been a rapid and continuous growth in this area of study. A considerable amount of research publications have appeared, a significant portion of which focusing on DEA applications of efficiency and productivity in the banking sector. For example, a comprehensive survey of litera- ture on bank efficiency could be found in Fethi and Pasiouras (2010). They have examined bank branch efficiencies in more than 30 studies over the period 1998-2009. All these studies are using DEA to estimate bank efficiency. Thompson et al. (1995) introduced nonlinear LC-AR efficiency measure to DEA literature, where they discussed the single-output multiple-inputs model subject to linked-cone (LC) assurance-regions (AR). A major criticism leveled against DEA is that DEA measures only relative efficiency of deci- sion making units (DMUs) participating in the study. While highlighting this as a drawback in DEA methodology, some authors in the past have suggested incorporating best-practice efficiency analysis by including an industrial benchmark among the DMUs. Lei Li et al. (2013), Dharmapala et al. (2007), Cook and Zhu (2006), Zhu (1996), Thanassoulis and Dyson (1992), and Golany (1998) are among those suggested. In this paper, we compute the nonlinear LC-AR measure against the linear radial measures of CCR (Charnes et al., 1978), BCC (Banker et al., 1984), CCR/AR and BCC/AR (Thompson et al., 1992), relative to an “ideal reference”- an industrial benchmark. We demonstrate the computations in an application to a set of banks and show that the nonlinear measure is stricter. To our knowledge, we may be the first to carry out such a comparative study. LITERATURE REVIEW As a nonparametric method based on linear programming, DEA has been used to assess per- formance efficiency in many areas of decision science. A comprehensive listing and analysis of DEA research that covers the first 30 years of its history could be found in Emrouznejad et al. (2008). But in this paper, we narrow our search to the banking sector. Ji et al. (2012) researched in rating and ranking Chinese commercial banks, us- ing DEA, in the presence of an undesirable output, non-performing loans. Minh et al. (2012) proposed a method to rank efficient units in DEA based on slack-based measure of efficiency, with an appli- cation to agricultural bank branches in Vietnam. Dharmapala and Edirisuriya (2011) reported a decision model to predict profitability of banks using LC-AR efficiency and profit ratios. Cooper et al. (2011) proposed a new method to measure and decompose profit inefficiency through the weighted additive model. Fadzlan (2010), using DEA, provided empirical evidence on the evolu- tion of the Indonesian banking sector’s efficiency during the post Asian financial crisis period of 1999-2008. His findings suggested that Indone- sian banking sector’s inefficiency stems largely from pure technical rather than scale. Malhotra et al. (2009), while claiming that during the recent financial crisis they had seen a substantial decline in the profitability and liquidity of the financial services, used DEA to evaluate the strength of P. Sunil Dharmapala College of Economics & Political Science, Sultan Qaboos University, Sultanate of Oman N