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Efficiency intervals, rank intervals and dominance relations of decision-making units with fixed-sum outputs

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  • Chen, Lifan
  • Guo, Mengyu
  • Li, Yongjun
  • Liang, Liang
  • Salo, Ahti

Abstract

How to evaluate the performance of decision-making units (DMUs) with fixed-sum outputs is a timely and challenging question in data envelopment analysis (DEA). Two major challenges are (1) how to determine a common equilibrium efficient frontier and (2) how to deal with multiple feasible equilibrium efficient frontiers. This paper first uses a simple dataset to illustrate the possibility of multiple equilibrium efficient frontiers and the corresponding major differences in the DMUs’ efficiencies and rankings resulting from these frontiers. We address these challenges by considering all feasible equilibrium efficient frontiers and develop several models to obtain the corresponding efficiency intervals, ranking intervals and dominance relations for the DMUs with fixed-sum outputs. We illustrate the proposed approach with two numerical examples and show that it gives more informative results than previous DEA approaches. For example, there are interesting dominance relations between DMUs under the fixed-sum outputs; yet these relations do not exist when there are no fixed-sum outputs. In addition, the efficiency ranges and ranking intervals can be narrowed by accounting for policy suggestions such as adjustment constraints of fixed-sum outputs for DMUs.

Suggested Citation

  • Chen, Lifan & Guo, Mengyu & Li, Yongjun & Liang, Liang & Salo, Ahti, 2021. "Efficiency intervals, rank intervals and dominance relations of decision-making units with fixed-sum outputs," European Journal of Operational Research, Elsevier, vol. 292(1), pages 238-249.
    • Handle: RePEc:eee:ejores:v:292:y:2021:i:1:p:238-249
    DOI: 10.1016/j.ejor.2020.10.024
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    Citations

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    Cited by:

    1. Lozano, Sebastián, 2023. "Bargaining approach for efficiency assessment and target setting with fixed-sum variables," Omega, Elsevier, vol. 114(C).
    2. Chu, Junfei & Dong, Yanhua & Yuan, Zhe, 2024. "An improved equilibrium efficient frontier data envelopment analysis approach for evaluating decision-making units with fixed-sum outputs," European Journal of Operational Research, Elsevier, vol. 318(2), pages 592-604.
    3. Xi Xiong & Guo-liang Yang & Kai-di Liu & De-qun Zhou, 2022. "A proposed fixed-sum carryovers reallocation DEA approach for social scientific resources of Chinese public universities," Scientometrics, Springer;Akadémiai Kiadó, vol. 127(7), pages 4097-4121, July.
    4. Ding, Tao & Zhang, Yun & Zhang, Danlu & Li, Feng, 2023. "Performance evaluation of Chinese research universities: A parallel interactive network DEA approach with shared and fixed sum inputs," Socio-Economic Planning Sciences, Elsevier, vol. 87(PA).
    5. Bouzidis, Thanasis & Karagiannis, Giannis, 2022. "An alternative ranking of DMUs performance for the ZSG-DEA model," Socio-Economic Planning Sciences, Elsevier, vol. 81(C).
    6. Li, Feng & Zhang, Danlu & Zhang, Jinyu & Kou, Gang, 2022. "Measuring the energy production and utilization efficiency of Chinese thermal power industry with the fixed-sum carbon emission constraint," International Journal of Production Economics, Elsevier, vol. 252(C).

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