Solving data envelopment analysis models with sum-of-fractional objectives: a global optimal approach based on the multiparametric disaggregation technique

doi:10.1007/s10479-021-04026-y

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	Solving data envelopment analysis models with sum-of-fractional objectives: a global optimal approach based on the multiparametric disaggregation technique
	Xie, Jianhui 4; Xie, Qiwei 3,5; Li, Yongjun 1; Liang, Liang 2
刊名	ANNALS OF OPERATIONS RESEARCH
	2021-04-12
页码	28
关键词	Data envelopment analysis Mixed-integer linear programming Global optimal solution Fractional programming
ISSN号	0254-5330
DOI	10.1007/s10479-021-04026-y
通讯作者	Li, Yongjun(lionli@ustc.edu.cn)
英文摘要	The majority of data envelopment analysis (DEA) models can be linearized via the classical Charnes-Cooper transformation. Nevertheless, this transformation does not apply to sum-of-fractional DEA efficiencies models, such as the secondary goal I (SG-I) cross efficiency model and the arithmetic mean two-stage network DEA model. To solve a sum-of-fractional DEA efficiencies model, we convert it into bilinear programming. Then, the obtained bilinear programming is relaxed to mixed-integer linear programming (MILP) by using a multiparametric disaggregation technique. We reveal the hidden mathematical structures of sum-of-fractional DEA efficiencies models, and propose corresponding discretization strategies to make the models more easily to be solved. Discretization of the multipliers of inputs or the DEA efficiencies in the objective function depends on the number of multipliers and decision-making units. The obtained MILP provides an upper bound for the solution and can be tightened as desired by adding binary variables. Finally, an algorithm based on MILP is developed to search for the global optimal solution. The effectiveness of the proposed method is verified by using it to solve the SG-I cross efficiency model and the arithmetic mean two-stage network DEA model. Results of the numerical applications show that the proposed approach can solve the SG-I cross efficiency model with 100 decision-making units, 3 inputs, and 3 outputs in 329.6 s. Moreover, the proposed approach obtains more accurate solutions in less time than the heuristic search procedure when solving the arithmetic mean two-stage network DEA model.
资助项目	National Natural Science Foundation of China[71701220] ; National Natural Science Foundation of China[72071192] ; National Natural Science Foundation of China[71671172] ; National Natural Science Foundation of China[71631006] ; Natural Science Foundation of Beijing[9202002] ; GreatWall Scholar Training Program of Beijing Municipality[CITTCD20180305] ; Social Science Foundation of Beijing[16JDGLC005]
WOS研究方向	Operations Research & Management Science
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000639514600005
资助机构	National Natural Science Foundation of China ; Natural Science Foundation of Beijing ; GreatWall Scholar Training Program of Beijing Municipality ; Social Science Foundation of Beijing
内容类型	期刊论文
源URL	[http://ir.ia.ac.cn/handle/173211/44356]
专题	类脑智能研究中心_微观重建与智能分析
通讯作者	Li, Yongjun
作者单位	1.Univ Sci & Technol China, Sch Management, Hefei 230026, Anhui, Peoples R China 2.Hefei Univ Technol, Sch Management, 193 TunXi Rd, Hefei 230009, Anhui, Peoples R China 3.Beijing Univ Technol, Res Base Beijing Modern Mfg Dev, Beijing 100124, Peoples R China 4.Sun Yat Sen Univ, Int Sch Business & Finance, Zhuhai 519082, Guangdong, Peoples R China 5.Chinese Acad Sci, Inst Automat, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Xie, Jianhui,Xie, Qiwei,Li, Yongjun,et al. Solving data envelopment analysis models with sum-of-fractional objectives: a global optimal approach based on the multiparametric disaggregation technique[J]. ANNALS OF OPERATIONS RESEARCH,2021:28.
APA	Xie, Jianhui,Xie, Qiwei,Li, Yongjun,&Liang, Liang.(2021).Solving data envelopment analysis models with sum-of-fractional objectives: a global optimal approach based on the multiparametric disaggregation technique.ANNALS OF OPERATIONS RESEARCH,28.
MLA	Xie, Jianhui,et al."Solving data envelopment analysis models with sum-of-fractional objectives: a global optimal approach based on the multiparametric disaggregation technique".ANNALS OF OPERATIONS RESEARCH (2021):28.