EFFICIENCY DECOMPOSITION WITH SHARED INPUTS AND OUTPUTS IN TWO-STAGE DEA

• Published in: Journal of systems science and systems engineering Vol. 25; no. 1; pp. 23 - 38
• Main Authors: Li, Lin, Dai, Qianzhi, Huang, Haijun, Wang, Shouyang
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-03-2016; Springer Nature B.V; School of Economics and Management, Beihang University, Beijing, 100191, China; Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China%Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China%School of Economics and Management, Beihang University, Beijing, 100191, China%Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China
• Subjects: Complexity; Data envelopment analysis; DEA方法; Decomposition; Economic Theory/Quantitative Economics/Mathematical Methods; Efficiency; Engineering; Measurement methods; Operations Research/Decision Theory; Patient satisfaction; Performance evaluation; 信息技术系统; 决策单元; 分解模型; 多输入多输出; 数据包络分析; 网络共享; 资源使用; shared inputs; efficiency decomposition; shared outputs; centralized model; Data envelopment analysis; Data envelopment analysis,efficiency decomposition; shared inputs,shared outputs,centralized model
• ISSN: 1004-3756; 1861-9576
• DOI: 10.1007/s11518-016-5298-0

Data envelopment analysis （DEA） is an effective non-parametric method for measuring the relative efficiencies of decision making units （DMUs） with multiple inputs and outputs. In many real situations, the internal structure of DMUs is a two-stage network process with shared inputs used in both stages and common outputs produced by the both stages. For example, hospitals have a two-stage network structure. Stage 1 consumes resources such as information technology system, plant, equipment and admin personnel to generate outputs such as medical records, laundry and housekeeping. Stage 2 consumes the same set of resources used by stage 1 （named shared inputs） and the outputs generated by stage 1 （named intermediate measures） to provide patient services. Besides, some of outputs, for instance, patient satisfaction degrees, are generated by the two individual stages together （named shared outputs）. Since some of shared inputs and outputs are hard split up and allocated to each individual stage, it needs to develop two-stage DEA methods for evaluating the performance of two-stage network processes in such problems. This paper extends the centralized model to measure the DEA efficiency of the two-stage process with non split-table shared inputs and outputs. A weighted additive approach is used to combine the two individual stages. Moreover, additive efficiency decomposition models are developed to simultaneously evaluate the maximal and the minimal achievable efficiencies for the individual stages. Finally, an example of 17 city branches of China Construction Bank in Anhui Province is employed to illustrate the proposed approach.