The Calculation of the output price vectorby applying reverse linear programming: The novel approach in DEA

In the today’s world wherein every routine is based on economic factors, there is no doubt that theoretical sciences are driven by their capabilities and affordances in terms of economy. As a mathematical tool, data envelopment analysis (DEA) is provided to economics, so that one can investigate associated costs, prices and revenues of economic units. Data Envelopment Analysis (DEA) is a linear programming technique used for measuring the relative efficiency of decision making units based on input and output data. One of the applications of this technique is calculation of  revenue efficiency. Methods of revenue efficiency calculation in DEA are generally presented for obtaining maximum revenue from output selling, these methods are not sufficiently efficient for evaluation of all system including network systems due to ignoring the internal structure of units and their middle products. Therefore, in this article, in addition to introduction of inverse linear programming in DEA and its application in calculating   revenue efficiency, a new method is presented which considers the network structure of units, the ability to determine the optimal price and appropriate costs for efficiency of the unit. The proposed numerical examples demonstrated the superiority of the proposed methods over the traditional data envelopment analyses.