A modified DDF-based super-efficiency modelhandling negative data

Abstract

In conventional DEA models, inputs and outputs are assumed to be non-negative while negative data may occur in some DEA application such as the performance analysis of socially responsible and mutual funds; and the macroeconomic performance where "rate of growth of GDP per capita" can be either negative or positive. To handle the negative data and provide a measure of efficiency for all units, many researches have been studied. In this paper, the radial super-efficiency model based on Directional Distance Function (DDF) is modified to provide a complete ranking order of the DMUs (including efficient and inefficient ones). The proposed model shows more reliability on differentiating efficient DMUs from inefficient ones via a new super-efficiency measure. The properties of proposed model include feasibility, monotonicity and unit invariance. Moreover, the model can produce positive outputs when data are non-negative. Apart from numerical examples, an empirical study in bank sector demonstrates the superiority of the proposed model.