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

• Published in: Annals of operations research 2022-02, Vol.309 (1), p.143-162
• Main Authors: Kiaei, Hamid, Kazemi Matin, Reza
• Format: Article
• Language: English
• Subjects: Business and Management; Combinatorics; Data analysis; Data envelopment analysis; Decision making; Industrial equipment; Linear programming; Mathematical programming; Methods; Operations research; Operations Research/Decision Theory; Optimization; Original Research; Performance evaluation; Theory of Computation
• ISSN: 0254-5330; 1572-9338
• DOI: 10.1007/s10479-021-04304-9

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.