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Composite Network Data Envelopment Analysis Model

Author

Listed:
  • QUANLING WEI

    (School of Economics, Renmin University of China, Haidian District, Beijing, China)

  • HONG YAN

    (Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China)

  • LIYONG PANG

    (School of Economics, Renmin University of China, Haidian District, Beijing, China)

Abstract

This paper extends the DEA model to considering the decision-making unit (DMU) with the network structure. We define the networkDMUand its network DEA efficiency based on the postulate system. On the series structure of theDMU, we further discuss a sequential optimization model originally proposed by Sexton and Lewis.1,2Based on their work, we extend to theDMUwith general network ofkstages and propose a composite network DEA model which evaluate the network DEA efficiency by solving only one linear programming. We show that the network efficiency obtained from the composite model is equivalent to that obtained by the sequential optimization model. We show that a networkDMUis network-efficient if and only if it is efficient at all stages. That is, the network-efficientDMUfollows the "Bellman Optimal Principle." Our model shows that if a networkDMUis not DEA-efficient, then it is not efficient at one stage at least. We also define the projection of the networkDMUon the corresponding production possibility set of networkDMUs. Finally, we discuss other basic structures of the networkDMUand show that the overall network DEA model can be extended to the general networkDMU.

Suggested Citation

  • Quanling Wei & Hong Yan & Liyong Pang, 2011. "Composite Network Data Envelopment Analysis Model," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 613-633.
    • Handle: RePEc:wsi:ijitdm:v:10:y:2011:i:04:n:s0219622011004488
    DOI: 10.1142/S0219622011004488
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    References listed on IDEAS

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    1. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
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    Cited by:

    1. Kao, Chiang, 2014. "Network data envelopment analysis: A review," European Journal of Operational Research, Elsevier, vol. 239(1), pages 1-16.
    2. Kao, Chiang, 2017. "Efficiency measurement and frontier projection identification for general two-stage systems in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 261(2), pages 679-689.
    3. Wen-Min Lu & Qian Long Kweh & Kai-Chu Yang, 2022. "Multiplicative efficiency aggregation to evaluate Taiwanese local auditing institutions performance," Annals of Operations Research, Springer, vol. 315(2), pages 1243-1262, August.

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