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Integrated data envelopment analysis: Global vs. local optimum

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  • Lim, Sungmook
  • Zhu, Joe

Abstract

Chiou et al. (2010) (A joint measurement of efficiency and effectiveness for non-storable commodities: integrated data envelopment analysis approaches. European Journal of Operational Research 201, 477–489) propose an integrated data envelopment analysis model in measuring decision making units (DMUs) that have a two-stage internal network structure with multiple inputs, outputs, and consumptions. They claim that any optimal solutions determined by their DEA model are a global optimum, not a local optimum. We show that such a conclusion is a false statement due to their misuse of Hessian matrix in examining the concavity of the objective function, and their DEA model is actually a non-convex optimization problem. As a result, their DEA model is unusable in practice due to a lack of efficient algorithm for this particular non-convex DEA model. We further show that Chiou et al.’s (2010) model is a special case of a well-known two-stage network DEA model, and it can be transformed into a parametric linear program for which an approximate global optimal solution can be obtained by solving a sequence of linear programs in combination with a simple search algorithm.

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  • Lim, Sungmook & Zhu, Joe, 2013. "Integrated data envelopment analysis: Global vs. local optimum," European Journal of Operational Research, Elsevier, vol. 229(1), pages 276-278.
    • Handle: RePEc:eee:ejores:v:229:y:2013:i:1:p:276-278
    DOI: 10.1016/j.ejor.2013.02.023
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    1. 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.
    2. 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.
    3. 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.
    4. Chiou, Yu-Chiun & Lan, Lawrence W. & Yen, Barbara T.H., 2010. "A joint measurement of efficiency and effectiveness for non-storable commodities: Integrated data envelopment analysis approaches," European Journal of Operational Research, Elsevier, vol. 201(2), pages 477-489, March.
    5. 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.
    6. 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.
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    2. Qingyou Yan & Fei Zhao & Xu Wang & Guoliang Yang & Tomas Baležentis & Dalia Streimikiene, 2019. "The network data envelopment analysis models for non-homogenous decision making units based on the sun network structure," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(4), pages 1221-1244, December.
    3. Jiao, Hong-Wei & Liu, San-Yang, 2015. "A practicable branch and bound algorithm for sum of linear ratios problem," European Journal of Operational Research, Elsevier, vol. 243(3), pages 723-730.
    4. Phung, Manh-Trung & Cheng, Cheng-Ping & Guo, Chuanyin & Kao, Chen-Yu, 2020. "Mixed Network DEA with Shared Resources: A Case of Measuring Performance for Banking Industry," Operations Research Perspectives, Elsevier, vol. 7(C).
    5. Angelo Earvin Sy Choi & Benny Marie B. Ensano & Jurng-Jae Yee, 2021. "Fuzzy Optimization for the Remediation of Ammonia: A Case Study Based on Electrochemical Oxidation," IJERPH, MDPI, vol. 18(6), pages 1-17, March.
    6. Lingguang Li & Weixin Yang, 2018. "Total Factor Efficiency Study on China’s Industrial Coal Input and Wastewater Control with Dual Target Variables," Sustainability, MDPI, vol. 10(7), pages 1-22, June.
    7. Mohsen Khodakarami & Amir Shabani & Reza Farzipoor Saen, 2016. "Concurrent estimation of efficiency, effectiveness and returns to scale," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(5), pages 1202-1220, April.
    8. Zhang, Linyan & Chen, Kun, 2019. "Hierarchical network systems: An application to high-technology industry in China," Omega, Elsevier, vol. 82(C), pages 118-131.
    9. Guo, Chuanyin & Abbasi Shureshjani, Roohollah & Foroughi, Ali Asghar & Zhu, Joe, 2017. "Decomposition weights and overall efficiency in two-stage additive network DEA," European Journal of Operational Research, Elsevier, vol. 257(3), pages 896-906.
    10. Shen, Peiping & Zhu, Zeyi & Chen, Xiao, 2019. "A practicable contraction approach for the sum of the generalized polynomial ratios problem," European Journal of Operational Research, Elsevier, vol. 278(1), pages 36-48.
    11. Yin, Pengzhen & Chu, Junfei & Wu, Jie & Ding, Jingjing & Yang, Min & Wang, Yuhong, 2020. "A DEA-based two-stage network approach for hotel performance analysis: An internal cooperation perspective," Omega, Elsevier, vol. 93(C).
    12. Khoveyni, Mohammad & Fukuyama, Hirofumi & Eslami, Robabeh & Yang, Guo-liang, 2019. "Variations effect of intermediate products on the second stage in two-stage processes," Omega, Elsevier, vol. 85(C), pages 35-48.
    13. Zhang, Linyan & Chen, Yao, 2018. "Equivalent solutions to additive two-stage network data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1189-1191.
    14. Mahdiloo, Mahdi & Toloo, Mehdi & Duong, Thach-Thao & Farzipoor Saen, Reza & Tatham, Peter, 2018. "Integrated data envelopment analysis: Linear vs. nonlinear model," European Journal of Operational Research, Elsevier, vol. 268(1), pages 255-267.
    15. Chen, Kun & Zhu, Joe, 2020. "Additive slacks-based measure: Computational strategy and extension to network DEA," Omega, Elsevier, vol. 91(C).

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