Bounded and discrete data and Likert scales in data envelopment analysis: application to regional energy efficiency in China

In data envelopment analysis (DEA), it is usually assumed that all data are continuous and not restricted by upper and/or lower bounds. However, there are situations where data are discrete and/or bounded, and where projections arising from DEAmodels are required to fall within those bounds. Such situations can be found, for example, in cases where percentage data are present and where projected percentages must not exceed the requisite 100% limit. Other examples include Likert scale data. Using existing integer DEA approaches as a backdrop, the current paper presents models for dealing with bounded and discrete data. Our proposed models address the issue of constraining DEA projections to fall within imposed Y. Chen School of Management, University of Science and Technology of China, 96 Jinzhai Road, Hefei 230026, Anhui, People’s Republic of China e-mail: [email protected] Wade D. Cook Schulich School of Business, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada e-mail: [email protected] J. Du School of Economics and Management, Tongji University, 1239 Siping Road, Shanghai 200092, People’s Republic of China e-mail: [email protected] H. Hu Southeast University, Nanjing 210096, People’s Republic of China e-mail: [email protected] J. Zhu International Center for Auditing and Evaluation, Nanjing Audit University, Nanjing, People’s Republic of China J. Zhu (B) Robert A. Foisie School of Business School of Business, Worcester Polytechnic Institute, Worcester, MA 01609, USA e-mail: [email protected]