Improved Super-efficiency Models And Evaluation Methods In Data Envelopment Analysis

In real practice of social production, it is often necessary to evaluate the performances of homogeneous sections or organizations. Data envelopment analysis (DEA) is a methodology of quantitative analysis for evaluating the relative efficiencies of a set of homogeneous decision making units (DMUs) with multiple inputs and multiple outputs. DEA has inimitable advantages in efficiency evaluation since it does not require any prior parametric assumptions or non-dimensional treatments.The conventional DEA dichotomizes DMUs into efficient and inefficient groups and identifies the efficient production frontier. However, more than one DMU is often evaluated as efficient especially when the number of inputs and outputs is great. In practice, decision makers usually need to derive the most efficient DMU and a complete ranking within a given set of DMUs, in order to make a clearer and more accurate decision. As a result, many researchers have put efforts on evaluating and ranking the relative efficiencies of DMUs and developed various effective methods.Super-efficiency DEA is a commonly used method for further discriminating between efficient DMUs. The basic idea of super-efficiency DEA is to evaluate the efficiency of the DMU being observed relative to all the other DMUs after it is excluded from the reference set. On the basis of the previous studies, this paper develops modified super-efficiency DEA models based on simultaneous input-output projection and provides the associated efficiency evaluation methods. By comparisons with the conventional super-efficiency models, the proposed super-efficiency models are analyzed in depth and a series of properties and theorems related to them are attained. Theoretically, the modified models are proved to overcome the infeasibility problem arising from the conventional super-efficiency models, and the economic meaning of the efficiency evaluation results can be well interpreted. Based upon the provided procedure for model solving, an empirical example is studied in order to demonstrate the effectiveness and practicability of the modified models and evaluation methods. The comparisons of the evaluation results of using alternative modified super-efficiency methods show that the proposed methods provide some advantages over previously reported methods. The results of the empirical example also illustrate that the proposed models and methods can further prioritize efficient DMUs as well as provide reasonable decision basis for decision makers by identifying the room for the productivity improvement of inefficient DMUs.