Modelling efficient and anti-efficient frontiers in DEA without explicit inputs

Data envelopment analysis (DEA) is one of the most widely used tools in efficiency analysis of many business and non-profit organisations. Recently, more and more researchers investigated DEA models without explicit input (DEA-WEI). DEA-WEI models can divide DMUs into two categories: efficient DMUs and inefficient DMUs. Usually there is a set of DMUs, which are 'efficient' so that conventional DEA models could not rank them. In this paper, we first develop a performance index based on efficient and anti-efficient frontiers in DEA-WEI models. Further, the corresponding performance index in DEA-WEI models with quadratic utility terms (quadratic DEA-WEI) is proposed also. Finally, we present two case studies on performance assessment of basketball players and the evaluation of research institutes in Chinese Academy of Sciences (CAS) to show the applicability and usefulness of the performance indices developed in this paper.