New common set of weights method in black-box and two-stage data envelopment analysis

Data envelopment analysis (DEA) strives to evaluate the production units under their best conditions. DEA flexibility in selecting the appropriate input/output weights always results in unreal and zero weights. Treating decision-making units (DMUs) as black-box regardless of their internal structures misleads the DEA performance evaluation. While considering units as a network process, it is more likely to identify more inefficiency sources. This paper suggests using a new common set of weights (CSWs) approach to evaluate the units in both black-box and two-stage structures based on a unified criterion. Indeed, our contribution to this line of research is as follows: Firstly, we improve the model proposed by Kao and Hung (J Oper res Soc 56(10): 1196-1203, 2005) to calculate the CSWs in a linear-based optimization model. Secondly, a new CSWs method is suggested in the two-stage network DEA (NDEA) as multiple objectives fractional programming (MOFP) problem. Thirdly, the MOFP problem is converted into a single objective linear programming problem in the two-stage network case. Finally, an enlightening application is presented.

Automated summary

DEA analysis aims to evaluate production units under optimal conditions, but flexibility in weight selection may lead to unrealistic results. Treating decision units as a network process can help identify inefficiencies more effectively. This paper introduces a new method for efficiency evaluation and investigates improved models to address multi-objective problems.