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A minimax approach for selecting the overall and stage-level most efficient unit in two stage production processes

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  • Volkan Soner Özsoy

    (Aksaray University)

  • Mediha Örkcü

    (Gazi University)

  • H. Hasan Örkcü

    (Gazi University)

Abstract

Data envelopment analysis (DEA) is a very effective management tool in assessing the performance of a set of decision making units (DMUs). In the efficiency evaluation using classic single stage DEA models, the internal processes of the DMUs are often neglected. In most real-world problems, it may be more realistic to evaluate the efficiency evaluation in two-stage production systems. In some cases: however, the decision-maker must need to identify the most efficient single unit. Numerous methods have been introduced to find the most efficient unit in single stage systems whereas no methods have been proposed for this aim in two stage production systems. Therefore, a new model based on mixed-integer programming was proposed to determine the most efficient DMU in two-stage systems and sub-stages in this study. The most important innovation of the suggested approach is that the most efficient DMUs of both stages can be found separately using only one model. Numerical examples for real world problems and a simulation study were provided for the validity of the proposed model.

Suggested Citation

  • Volkan Soner Özsoy & Mediha Örkcü & H. Hasan Örkcü, 2021. "A minimax approach for selecting the overall and stage-level most efficient unit in two stage production processes," Annals of Operations Research, Springer, vol. 300(1), pages 137-169, May.
    • Handle: RePEc:spr:annopr:v:300:y:2021:i:1:d:10.1007_s10479-020-03827-x
    DOI: 10.1007/s10479-020-03827-x
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    as
    1. Wang, Ying-Ming & Chin, Kwai-Sang, 2010. "Some alternative models for DEA cross-efficiency evaluation," International Journal of Production Economics, Elsevier, vol. 128(1), pages 332-338, November.
    2. Chen, Chialin & Zhu, Joe & Yu, Jiun-Yu & Noori, Hamid, 2012. "A new methodology for evaluating sustainable product design performance with two-stage network data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 221(2), pages 348-359.
    3. Plácido Moreno & Sebastián Lozano, 2014. "A network DEA assessment of team efficiency in the NBA," Annals of Operations Research, Springer, vol. 214(1), pages 99-124, March.
    4. Per Andersen & Niels Christian Petersen, 1993. "A Procedure for Ranking Efficient Units in Data Envelopment Analysis," Management Science, INFORMS, vol. 39(10), pages 1261-1264, October.
    5. Galagedera, Don U.A. & Roshdi, Israfil & Fukuyama, Hirofumi & Zhu, Joe, 2018. "A new network DEA model for mutual fund performance appraisal: An application to U.S. equity mutual funds," Omega, Elsevier, vol. 77(C), pages 168-179.
    6. Premachandra, I.M. & Zhu, Joe & Watson, John & Galagedera, Don U.A., 2012. "Best-performing US mutual fund families from 1993 to 2008: Evidence from a novel two-stage DEA model for efficiency decomposition," Journal of Banking & Finance, Elsevier, vol. 36(12), pages 3302-3317.
    7. Qingxian An & Haoxun Chen & Jie Wu & Liang Liang, 2015. "Measuring slacks-based efficiency for commercial banks in China by using a two-stage DEA model with undesirable output," Annals of Operations Research, Springer, vol. 235(1), pages 13-35, December.
    8. Li, Yongjun & Lei, Xiyang & Dai, Qianzhi & Liang, Liang, 2015. "Performance evaluation of participating nations at the 2012 London Summer Olympics by a two-stage data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 243(3), pages 964-973.
    9. Sueyoshi, Toshiyuki, 1999. "DEA non-parametric ranking test and index measurement: slack-adjusted DEA and an application to Japanese agriculture cooperatives," Omega, Elsevier, vol. 27(3), pages 315-326, June.
    10. Roza Azizi & Reza Kazemi Matin, 2016. "Ranking Two-Stage Production Units in Data Envelopment Analysis," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(01), pages 1-19, February.
    11. Thomas Sexton & Herbert Lewis, 2003. "Two-Stage DEA: An Application to Major League Baseball," Journal of Productivity Analysis, Springer, vol. 19(2), pages 227-249, April.
    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. 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.
    15. Liu, John S. & Lu, Wen-Min, 2010. "DEA and ranking with the network-based approach: a case of R&D performance," Omega, Elsevier, vol. 38(6), pages 453-464, December.
    16. Friedman, Lea & Sinuany-Stern, Zilla, 1997. "Scaling units via the canonical correlation analysis in the DEA context," European Journal of Operational Research, Elsevier, vol. 100(3), pages 629-637, August.
    17. Yande Gong & Joe Zhu & Ya Chen & Wade D. Cook, 2018. "DEA as a tool for auditing: application to Chinese manufacturing industry with parallel network structures," Annals of Operations Research, Springer, vol. 263(1), pages 247-269, April.
    18. Li, Xiao-Bai & Reeves, Gary R., 1999. "A multiple criteria approach to data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 115(3), pages 507-517, June.
    19. Jianhui Xie & Xiaoxuan Zhu & Liang Liang, 2020. "A multiplicative method for estimating the potential gains from two-stage production system mergers," Annals of Operations Research, Springer, vol. 288(1), pages 475-493, May.
    20. Zhu, Joe, 2000. "Multi-factor performance measure model with an application to Fortune 500 companies," European Journal of Operational Research, Elsevier, vol. 123(1), pages 105-124, May.
    21. Chien Wang & Ram Gopal & Stanley Zionts, 1997. "Use of Data Envelopment Analysis in assessing Information Technology impact on firm performance," Annals of Operations Research, Springer, vol. 73(0), pages 191-213, October.
    22. Kao, Chiang & Liu, Shiang-Tai, 2019. "Cross efficiency measurement and decomposition in two basic network systems," Omega, Elsevier, vol. 83(C), pages 70-79.
    23. J S Liu & W-M Lu & C Yang & M Chuang, 2009. "A network-based approach for increasing discrimination in data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(11), pages 1502-1510, November.
    24. Jon A. Chilingerian & H. David Sherman, 2011. "Health-Care Applications: From Hospitals to Physicians, from Productive Efficiency to Quality Frontiers," International Series in Operations Research & Management Science, in: William W. Cooper & Lawrence M. Seiford & Joe Zhu (ed.), Handbook on Data Envelopment Analysis, chapter 0, pages 445-493, Springer.
    25. Kao, Chiang & Hwang, Shiuh-Nan, 2014. "Multi-period efficiency and Malmquist productivity index in two-stage production systems," European Journal of Operational Research, Elsevier, vol. 232(3), pages 512-521.
    26. Ertay, Tijen & Ruan, Da, 2005. "Data envelopment analysis based decision model for optimal operator allocation in CMS," European Journal of Operational Research, Elsevier, vol. 164(3), pages 800-810, August.
    27. 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.
    28. Lawrence M. Seiford & Joe Zhu, 1999. "Profitability and Marketability of the Top 55 U.S. Commercial Banks," Management Science, INFORMS, vol. 45(9), pages 1270-1288, September.
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