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Efficiency decomposition and aggregation in network data envelopment analysis

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  • Kao, Chiang

Abstract

Network data envelopment analysis (DEA) is extended from conventional DEA to explore the internal structure of network production systems so that the efficiencies are measured more appropriately. There are two approaches for discussing the relationships between the system and division efficiencies, efficiency decomposition and efficiency aggregation. This paper develops a relational model from the viewpoint of efficiency decomposition to derive the relationships between the system and division efficiencies for network systems. The system efficiency can be decomposed into a weighted average of the division efficiencies adjusted by a factor, and the efficiency of the system is less than the weighted average of those of the divisions. The Major League Baseball example that has been discussed in the literature is used to illustrate the idea presented in this paper. The results of the efficiency decomposition model are compared to those obtained from an efficiency aggregation model that defines the aggregate efficiency of the divisions to be the system efficiency. This system efficiency is found to be very close to a measure contained in the proposed model. The proposed model can thus be used for both efficiency decomposition and aggregation.

Suggested Citation

  • Kao, Chiang, 2016. "Efficiency decomposition and aggregation in network data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 255(3), pages 778-786.
    • Handle: RePEc:eee:ejores:v:255:y:2016:i:3:p:778-786
    DOI: 10.1016/j.ejor.2016.05.019
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    1. Kao, Chiang, 2009. "Efficiency decomposition in network data envelopment analysis: A relational model," European Journal of Operational Research, Elsevier, vol. 192(3), pages 949-962, February.
    2. Kao, Chiang, 2013. "Dynamic data envelopment analysis: A relational analysis," European Journal of Operational Research, Elsevier, vol. 227(2), pages 325-330.
    3. Rolf Färe & Shawna Grosskopf & Gerald Whittaker, 2014. "Network DEA II," International Series in Operations Research & Management Science, in: Wade D. Cook & Joe Zhu (ed.), Data Envelopment Analysis, edition 127, chapter 0, pages 307-327, Springer.
    4. Rogge, Nicky & de Jaeger, Simon, 2012. "Evaluating the efficiency of municipalities in collecting and processing municipal solid waste: A shared input DEA-model," Working Papers 2012/22, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
    5. Castelli, Lorenzo & Pesenti, Raffaele & Ukovich, Walter, 2004. "DEA-like models for the efficiency evaluation of hierarchically structured units," European Journal of Operational Research, Elsevier, vol. 154(2), pages 465-476, April.
    6. Chen, Yao & Cook, Wade D. & Li, Ning & Zhu, Joe, 2009. "Additive efficiency decomposition in two-stage DEA," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1170-1176, August.
    7. Guan, Jiancheng & Chen, Kaihua, 2012. "Modeling the relative efficiency of national innovation systems," Research Policy, Elsevier, vol. 41(1), pages 102-115.
    8. Zha, Yong & Liang, Liang, 2010. "Two-stage cooperation model with input freely distributed among the stages," European Journal of Operational Research, Elsevier, vol. 205(2), pages 332-338, September.
    9. Chiang Kao, 2014. "Efficiency Decomposition in Network Data Envelopment Analysis," International Series in Operations Research & Management Science, in: Wade D. Cook & Joe Zhu (ed.), Data Envelopment Analysis, edition 127, chapter 0, pages 55-77, Springer.
    10. Tone, Kaoru & Tsutsui, Miki, 2009. "Network DEA: A slacks-based measure approach," European Journal of Operational Research, Elsevier, vol. 197(1), pages 243-252, August.
    11. Carvalho, Pedro & Marques, Rui Cunha, 2014. "Computing economies of vertical integration, economies of scope and economies of scale using partial frontier nonparametric methods," European Journal of Operational Research, Elsevier, vol. 234(1), pages 292-307.
    12. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    13. Kao, Chiang & Hwang, Shiuh-Nan, 2008. "Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan," European Journal of Operational Research, Elsevier, vol. 185(1), pages 418-429, February.
    14. C Kao, 2012. "Efficiency decomposition for parallel production systems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(1), pages 64-71, January.
    15. Charnes, A. & Cooper, W. W., 1984. "The non-archimedean CCR ratio for efficiency analysis: A rejoinder to Boyd and Fare," European Journal of Operational Research, Elsevier, vol. 15(3), pages 333-334, March.
    16. Kao, Chiang, 2014. "Efficiency decomposition in network data envelopment analysis with slacks-based measures," Omega, Elsevier, vol. 45(C), pages 1-6.
    17. Liang Liang & Zhao-Qiong Li & Wade Cook & Joe Zhu, 2011. "Data envelopment analysis efficiency in two-stage networks with feedback," IISE Transactions, Taylor & Francis Journals, vol. 43(5), pages 309-322.
    18. Kao, Chiang, 2014. "Network data envelopment analysis: A review," European Journal of Operational Research, Elsevier, vol. 239(1), pages 1-16.
    19. Wade Cook & Moez Hababou & Hans Tuenter, 2000. "Multicomponent Efficiency Measurement and Shared Inputs in Data Envelopment Analysis: An Application to Sales and Service Performance in Bank Branches," Journal of Productivity Analysis, Springer, vol. 14(3), pages 209-224, November.
    20. Cruz, Nuno Ferreira da & Carvalho, Pedro & Marques, Rui Cunha, 2013. "Disentangling the cost efficiency of jointly provided water and wastewater services," Utilities Policy, Elsevier, vol. 24(C), pages 70-77.
    21. Kao, Chiang, 2015. "Efficiency measurement for hierarchical network systems," Omega, Elsevier, vol. 51(C), pages 121-127.
    22. Liang Liang & Feng Yang & Wade Cook & Joe Zhu, 2006. "DEA models for supply chain efficiency evaluation," Annals of Operations Research, Springer, vol. 145(1), pages 35-49, July.
    23. Cook, Wade D. & Zhu, Joe & Bi, Gongbing & Yang, Feng, 2010. "Network DEA: Additive efficiency decomposition," European Journal of Operational Research, Elsevier, vol. 207(2), pages 1122-1129, December.
    24. Li, Yongjun & Chen, Yao & Liang, Liang & Xie, Jianhui, 2012. "DEA models for extended two-stage network structures," Omega, Elsevier, vol. 40(5), pages 611-618.
    25. Seiford, Lawrence M. & Zhu, Joe, 2002. "Modeling undesirable factors in efficiency evaluation," European Journal of Operational Research, Elsevier, vol. 142(1), pages 16-20, October.
    26. Yao Chen & Liang Liang & Feng Yang, 2006. "A DEA game model approach to supply chain efficiency," Annals of Operations Research, Springer, vol. 145(1), pages 5-13, July.
    27. Hiroyuki Kawaguchi & Kaoru Tone & Miki Tsutsui, 2014. "Estimation of the efficiency of Japanese hospitals using a dynamic and network data envelopment analysis model," Health Care Management Science, Springer, vol. 17(2), pages 101-112, June.
    28. Kao, Chiang, 2014. "Efficiency decomposition for general multi-stage systems in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 232(1), pages 117-124.
    29. Kao, Chiang, 2009. "Efficiency measurement for parallel production systems," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1107-1112, August.
    30. Jie Wu & Beibei Xiong & Qingxian An & Jiasen Sun & Huaqing Wu, 2017. "Total-factor energy efficiency evaluation of Chinese industry by using two-stage DEA model with shared inputs," Annals of Operations Research, Springer, vol. 255(1), pages 257-276, August.
    31. Cook, Wade D. & Green, Rodney H., 2004. "Multicomponent efficiency measurement and core business identification in multiplant firms: A DEA model," European Journal of Operational Research, Elsevier, vol. 157(3), pages 540-551, September.
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