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Measuring and decomposing the overall efficiency of multi-period and -division systems associated with DEA


  • Chen, Kaihua


The combination way of component efficiencies into the overall efficiency is a central topic in the efficiency modeling of network systems based on data envelopment analysis (DEA). In terms of the feature and advantage of DEA modeling as the multiplier generation on inputs/outputs, it is desirable that the combination weights are derived from the data and self-generated in calculation process. The prior weights choice makes DEA modeling lose the objectivity and generalization in efficiency measures. This study proposes a new formulating approach of dynamic network DEA (DN-DEA) models to measure and decompose the overall efficiency of multi-period and -division systems without the pre-specified weights to combine component efficiencies into the overall efficiency. In our formulating approach, the double identities of carry-overs connecting consecutive periods and linkers connecting consecutive divisions are fully accounted for. This approach is applicable for the formulations of both radial measures (DN-CCR and DN-BCC) and non-radial measures (DN-SBM). This study extends Kao’s (in press) relational approach of dynamic DEA to dynamic network systems for empirical comparison. In contrast to Kao’s (in press) approach, our approach can present a weighted average decomposition of the overall (in)efficiency score into components ones by a set of endogenous weight sets which are the most favorable for the tested multi-period and -division system. This makes sense of the comparison between overall and component (in)efficiency scores. In this context, the overall efficiency score is less or more than all component ones. We applied our models to evaluate the innovation efficiency of OECD (Organization for Economic Co-operation and Development) countries.

Suggested Citation

  • Chen, Kaihua, 2014. "Measuring and decomposing the overall efficiency of multi-period and -division systems associated with DEA," MPRA Paper 55073, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:55073

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    References listed on IDEAS

    1. Wang, Eric C. & Huang, Weichiao, 2007. "Relative efficiency of R&D activities: A cross-country study accounting for environmental factors in the DEA approach," Research Policy, Elsevier, vol. 36(2), pages 260-273, March.
    2. 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.
    3. 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.
    4. Guan, Jiancheng & Chen, Kaihua, 2012. "Modeling the relative efficiency of national innovation systems," Research Policy, Elsevier, vol. 41(1), pages 102-115.
    5. 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.
    6. 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.
    7. Tone, Kaoru & Tsutsui, Miki, 2010. "Dynamic DEA: A slacks-based measure approach," Omega, Elsevier, vol. 38(3-4), pages 145-156, June.
    8. Kao, Chiang, 2014. "Efficiency decomposition in network data envelopment analysis with slacks-based measures," Omega, Elsevier, vol. 45(C), pages 1-6.
    9. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    10. 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.
    11. Tone, Kaoru, 2001. "A slacks-based measure of efficiency in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 130(3), pages 498-509, May.
    12. William Cooper & Kyung Park & Jesus Pastor, 2001. "The Range Adjusted Measure (RAM) in DEA: A Response to the Comment by Steinmann and Zweifel," Journal of Productivity Analysis, Springer, vol. 15(2), pages 145-152, March.
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    More about this item


    Dynamic network DEA; Multi-period and -division systems; Efficiency measurement and decomposition; Innovation efficiency; OECD countries;

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • O31 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Innovation and Invention: Processes and Incentives
    • P51 - Economic Systems - - Comparative Economic Systems - - - Comparative Analysis of Economic Systems

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