a modified directional distance formulation of dea with malmquist index to assess bankruptcy

bankruptcy in the same amount of time and history is very rampant and therefore the vision of the future can be prevented. using data envelopment analysis (dea) and malmquist index can precise evaluating of the performances of many different kinds of decision making units (dmu) such as hospitals, universities, business firms, etc. in this paper, we will modify directional distance formulation of dea to assess bankruptcy with using malmquist index. this method is the most general non-radial directional distance model. the method measures worst relative efficiency within the interval of zero to one for various period times. model locates worst performing dmus and determines an inefficient frontier model simultaneously with decrease of output and increase of input. by using malmquist index we measure the productivity for various years .this study introduces a precise and comprehensive bankruptcy measure that could be used as an early warning system for bankruptcy assessment.