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.