Cost, Revenue and Profit Efficiency in multi-period network system: A DEA-R based Approach

It has been proven that Data Envelopment Analysis is an efficient method to compare different decision making units with multiple inputs and outputs, but traditional Data Envelopment Analysis models suffers some difficulties: (a)-the inputs and outputs are not supposed to be given in terms of ratio. Thus, when the data are partially available, the decision maker will be unable to access missing data from the present data; (b) in measuring the efficiency of a set of decision making units for some periods, the conventional Data Envelopment Analysis based technique cannot handle the problem posed in a periodic form where the costs, profits and revenue efficiency of the main problems in the network structures are required. The contribution of this paper is four folded: (1) the cost, revenue and profit efficiency of each stages are calculated from the proposed method depends on the performance of the unit in both stages. (2) Our method evaluates the total cost, revenue and profit efficiency in a whole t (t = 1, ... , T) time periods derived from all periodic and every stage efficiency, (3) The proposed method in this study yields the efficiency measures deals with ratio data, (4) To elucidate the details of the proposed method, the proposed multi-period DEA-R method was employed to measure the efficiency of ten units in three separate time periods. Numerical examples are also provided to explain the presented methods.