The use of Data Envelopment Analysis (DEA) in many fields is based on total flexibility of the weights. However, the problem of allowing total flexibility of the weights is that the values of the weights obtained by solving the unrestricted DEA program are often in contradiction to prior views or additional available information. Also, many applications of DEA assume complete discretionary of decision making criteria. However, they do not assume the conditions that some factors are nondiscretionary. To select the most efficient third-party reverse logistics (3PL) provider in the conditions that both weight restrictions and nondiscretionary factors are present, a methodology is introduced. A numerical example demonstrates the application of the proposed method.