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Multiplicative aggregation of division efficiencies in network data envelopment analysis

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  • Kao, Chiang

Abstract

Network systems have two basic structures, series and parallel, and a network system can be transformed into a series system of subsystems, where each has a parallel structure composed of a number of divisions. The efficiency of the system can thus be expressed as the product of those of the subsystems, and the efficiency of each subsystem is a weighted average of those of its component divisions, under a relational data envelopment analysis (DEA) model. A previous study showed that the efficiency of a network system can be expressed as an additive aggregation of those of the divisions adjusted by a factor, and the former is bounded from above by the latter. This paper shows that the efficiency of the system can be expressed as a multiplicative aggregation of those of the divisions multiplied by a factor of greater than one. The system efficiency is thus bounded from below by the multiplicative aggregation of the division efficiencies. An example is used to show how to calculate the efficiency bounds, and how to identify the divisions that have stronger effects on the performance of the system.

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  • Kao, Chiang, 2018. "Multiplicative aggregation of division efficiencies in network data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 270(1), pages 328-336.
    • Handle: RePEc:eee:ejores:v:270:y:2018:i:1:p:328-336
    DOI: 10.1016/j.ejor.2017.09.047
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    4. Bai, Xuejie & Sun, Xianzhen & Chiu, Yung-Ho, 2020. "Does China's higher education investment play a role in industrial growth?," Technology in Society, Elsevier, vol. 63(C).
    5. Ali Homayoni & Reza Fallahnejad & Farhad Hosseinzadeh Lotfi, 2022. "Cross Malmquist Productivity Index in Data Envelopment Analysis," 4OR, Springer, vol. 20(4), pages 567-602, December.
    6. Lee, Hsuan-Shih, 2021. "Efficiency decomposition of the network DEA in variable returns to scale: An additive dissection in losses," Omega, Elsevier, vol. 100(C).
    7. Antonio Peyrache & Maria C. A. Silva, 2023. "Efficiency decomposition for multi-level multi-components production technologies," Journal of Productivity Analysis, Springer, vol. 60(3), pages 273-294, December.
    8. Meng, Fanyong & Xiong, Beibei, 2021. "Logical efficiency decomposition for general two-stage systems in view of cross efficiency," European Journal of Operational Research, Elsevier, vol. 294(2), pages 622-632.
    9. Ming-Miin Yu & Li-Hsueh Chen, 2020. "A meta-frontier network data envelopment analysis approach for the measurement of technological bias with network production structure," Annals of Operations Research, Springer, vol. 287(1), pages 495-514, April.
    10. Gidion, Dickson K. & Hong, Jin & Adams, Magdalene Z.A. & Khoveyni, Mohammad, 2019. "Network DEA models for assessing urban water utility efficiency," Utilities Policy, Elsevier, vol. 57(C), pages 48-58.
    11. Kremantzis, Marios Dominikos & Beullens, Patrick & Kyrgiakos, Leonidas Sotirios & Klein, Jonathan, 2022. "Measurement and evaluation of multi-function parallel network hierarchical DEA systems," Socio-Economic Planning Sciences, Elsevier, vol. 84(C).

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