Research Specifications

Data Envelopment Analysis measures relative efficiency, in which the efficiency of the decision making units in a group is compared. In this approach, an efficient unit in one group may be considered inefficient compared to the units of other groups and vice versa. Therefore, researchers have tried to measure the productivity changes of units (or systems) over time. Two known productivity indexes, the Malmquist and Luenberger, have been introduced to evaluate units (or systems) from one period to another. In some Two-stage systems, outputs produced by the second division can also be used by the first. This system is called feedback. Examples of the feedback system are the recycling of waste materials and wastewater. Studying of feedback systems in the real world is very important. Therefore, in this article, we have evaluated and calculated the productivity changes of such systems over time by presenting a new model. The results of a structural numerical example show that the proposed model can evaluate the mentioned two-stage systems over time.