Determining a common set of weights in a DEA problem using a separation vector

A separation method to be used for locating a set of weights, also known as a common set of weights (CSW), in the Data Envelopment Analysis (DEA) is proposed in this work. To analyze the methods of finding the CSW, it is necessary to solve a particular form of a multiple objectives fractional linear programming problem (MOFP). One of the characteristics of this particular MOFP is that the decision variables can be separated into two parts; one part of variables present in the numerator and the other part of variables present in the denominator. Based on this characteristic, this research utilized an auxiliary vector to convert the MOFP to a single objective linear programming to obtain a CSW for calculating the DMU’s efficiency ratio. Finally, the developed method is applied to analyze the data of the last Beijing Olympic Games.