The Continuous CCR Model in DEA

The inputs and outputs of decision making units (DMUs) in conventional CCR model of data envelopment analysis (DEA) are the separate limited data, thus the relative efficiency among decision making units is evaluated at one point of the time axis. But in many real world applications, DMUs have the inputs and outputs which are the continuous functions of a time interval. In this situation, how can we get the relative efficiency of the decision-making unit evaluated? At present, the systematic research on this point is lacking. So in the present paper, we first develop the continuous CCR model which is a fractional function programming in DEA, when the inputs and outputs of decision making units are continuous CCR functions on the interval. Then we establish a linear function programming equivalent to continuous model for effecting computations. At the same time, we get the dual model of the linear function programming for simplifying the primal one. At last we get the dual theories and raise the definitions of DEA efficiency for continuous CCR model.