The Malmquist Productivity Index with the Flexible Variables

The Malmquist productivity index (MPI) is one of the ways of signifying the progress and regressive the performances of units in the present time than the previous time. This index is using the classical DEA models for measures the productivity of decision making units by multiple inputs and outputs. But in the most of the measurement problems of the performance, the flexible measures are presented in addition to the input and output variables. Therefore, in this paper, we extend the Malmquist productivity index for cases that the problems can include the flexible variables.