IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v190y2008i3p855-876.html
   My bibliography  Save this article

A bi-objective generalized data envelopment analysis model and point-to-set mapping projection

Author

Listed:
  • Wei, Quanling
  • Yan, Hong
  • Xiong, Lin

Abstract

This work introduces a bi-objective generalized data envelopment analysis (Bi-GDEA) model and defines its efficiency. We show the equivalence between the Bi-GDEA efficiency and the non-dominated solutions of the multi-objective programming problem defined on the production possibility set (PPS) and discuss the returns to scale under the Bi-GDEA model. The most essential contribution is that we further define a point-to-set mapping and the mapping projection of a decision making unit (DMU) on the frontier of the PPS under the Bi-GDEA model. We give an effective approach for the construction of the point-to-set-mapping projection which distinguishes our model from other non-radial models for simultaneously considering input and output. The Bi-GDEA model represents decision makers' specific preference on input and output and the point-to-set mapping projection provides decision makers with more possibility to determine different input and output alternatives when considering efficiency improvement. Numerical examples are employed for the illustration of the procedure of point-to-set mapping.

Suggested Citation

  • Wei, Quanling & Yan, Hong & Xiong, Lin, 2008. "A bi-objective generalized data envelopment analysis model and point-to-set mapping projection," European Journal of Operational Research, Elsevier, vol. 190(3), pages 855-876, November.
    • Handle: RePEc:eee:ejores:v:190:y:2008:i:3:p:855-876
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(07)00887-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ole Olesen & N. Petersen, 2003. "Identification and Use of Efficient Faces and Facets in DEA," Journal of Productivity Analysis, Springer, vol. 20(3), pages 323-360, November.
    2. 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.
    3. Thanassoulis, E. & Dyson, R. G., 1992. "Estimating preferred target input-output levels using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 56(1), pages 80-97, January.
    4. Fukuyama, Hirofumi, 2000. "Returns to scale and scale elasticity in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 125(1), pages 93-112, August.
    5. Wei, Quanling & Yu, Gang, 1997. "Analyzing properties of K-cones in the generalized data envelopment analysis model," Journal of Econometrics, Elsevier, vol. 80(1), pages 63-84, September.
    6. repec:bla:scandj:v:87:y:1985:i:4:p:594-604 is not listed on IDEAS
    7. M P Estellita Lins & L Angulo-Meza & A C Moreira Da Silva, 2004. "A multi-objective approach to determine alternative targets in data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(10), pages 1090-1101, October.
    8. Seiford, Lawrence M. & Zhu, Joe, 1999. "An investigation of returns to scale in data envelopment analysis," Omega, Elsevier, vol. 27(1), pages 1-11, February.
    9. Banker, Rajiv D. & Chang, Hsihui & Cooper, William W., 1996. "Equivalence and implementation of alternative methods for determining returns to scale in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 89(3), pages 473-481, March.
    10. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2007. "Measurement of returns to scale using a non-radial DEA model: A range-adjusted measure approach," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1918-1946, February.
    11. Banker, Rajiv D. & Cooper, William W. & Seiford, Lawrence M. & Thrall, Robert M. & Zhu, Joe, 2004. "Returns to scale in different DEA models," European Journal of Operational Research, Elsevier, vol. 154(2), pages 345-362, April.
    12. Seiford, Lawrence M. & Thrall, Robert M., 1990. "Recent developments in DEA : The mathematical programming approach to frontier analysis," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 7-38.
    13. Yu, Gang & Wei, Quanling & Brockett, Patrick & Zhou, Li, 1996. "Construction of all DEA efficient surfaces of the production possibility set under the Generalized Data Envelopment Analysis Model," European Journal of Operational Research, Elsevier, vol. 95(3), pages 491-510, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. V E Krivonozhko & O B Utkin & M M Safin & A V Lychev, 2009. "On some generalization of the DEA models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(11), pages 1518-1527, November.
    2. Tao Ding & Zhixiang Zhou & Qianzhi Dai & Liang Liang, 2020. "Analysis of China’s Regional Economic Environmental Performance: A Non-radial Multi-objective DEA Approach," Computational Economics, Springer;Society for Computational Economics, vol. 55(4), pages 1209-1231, April.
    3. Taleb, Mushtaq & Khalid, Ruzelan & Ramli, Razamin & Ghasemi, Mohammad Reza & Ignatius, Joshua, 2022. "An integrated bi-objective data envelopment analysis model for measuring returns to scale," European Journal of Operational Research, Elsevier, vol. 296(3), pages 967-979.
    4. Krivonozhko, Vladimir E. & Førsund, Finn R. & Lychev, Andrey V., 2012. "Identifying Suspicious Efficient Units in DEA Models," Memorandum 30/2012, Oslo University, Department of Economics.
    5. Vladimir Krivonozhko & Finn Førsund & Andrey Lychev, 2015. "Terminal units in DEA: definition and determination," Journal of Productivity Analysis, Springer, vol. 43(2), pages 151-164, April.
    6. Jie Wu & Zhixiang Zhou, 2015. "A mixed-objective integer DEA model," Annals of Operations Research, Springer, vol. 228(1), pages 81-95, May.
    7. Førsund, Finn & Krivonozhko, Vladimir W & Lychev, Andrey V., 2016. "Smoothing the frontier in the DEA models," Memorandum 11/2016, Oslo University, Department of Economics.
    8. Jie Wu & Xiang Lu & Dong Guo & Liang Liang, 2017. "Slacks-Based Efficiency Measurements with Undesirable Outputs in Data Envelopment Analysis," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(04), pages 1005-1021, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2009. "An occurrence of multiple projections in DEA-based measurement of technical efficiency: Theoretical comparison among DEA models from desirable properties," European Journal of Operational Research, Elsevier, vol. 196(2), pages 764-794, July.
    2. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2007. "Measurement of returns to scale using a non-radial DEA model: A range-adjusted measure approach," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1918-1946, February.
    3. Sahoo, Biresh K & Khoveyni, Mohammad & Eslami, Robabeh & Chaudhury, Pradipta, 2016. "Returns to scale and most productive scale size in DEA with negative data," European Journal of Operational Research, Elsevier, vol. 255(2), pages 545-558.
    4. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2007. "The measurement of returns to scale under a simultaneous occurrence of multiple solutions in a reference set and a supporting hyperplane," European Journal of Operational Research, Elsevier, vol. 181(2), pages 549-570, September.
    5. Banker, Rajiv D. & Cooper, William W. & Seiford, Lawrence M. & Thrall, Robert M. & Zhu, Joe, 2004. "Returns to scale in different DEA models," European Journal of Operational Research, Elsevier, vol. 154(2), pages 345-362, April.
    6. Hadjicostas, Petros & Soteriou, Andreas C., 2006. "One-sided elasticities and technical efficiency in multi-output production: A theoretical framework," European Journal of Operational Research, Elsevier, vol. 168(2), pages 425-449, January.
    7. Adel Hatami-Marbini & Zahra Ghelej Beigi & Jens Leth Hougaard & Kobra Gholami, 2014. "Estimating Returns to Scale in Imprecise Data Envelopment Analysis," MSAP Working Paper Series 07_2014, University of Copenhagen, Department of Food and Resource Economics.
    8. Amineh Ghazi & Farhad Hosseinzadeh Lotfı & Masoud Sanei, 2022. "Finding the strong efficient frontier and strong defining hyperplanes of production possibility set using multiple objective linear programming," Operational Research, Springer, vol. 22(1), pages 165-198, March.
    9. A. Davoodi & M. Zarepisheh & H. Rezai, 2015. "The nearest MPSS pattern in data envelopment analysis," Annals of Operations Research, Springer, vol. 226(1), pages 163-176, March.
    10. Victor Podinovski, 2004. "Efficiency and Global Scale Characteristics on the “No Free Lunch” Assumption Only," Journal of Productivity Analysis, Springer, vol. 22(3), pages 227-257, November.
    11. Zhang, Baocheng & Wu, Hao & Yang, Xinsheng & Zhai, Wenpeng & Xia, Qingjun & Li, Yafei, 2014. "An estimation of returns to scale of airport airsides under multiple optimal solutions in DEA," Journal of Air Transport Management, Elsevier, vol. 40(C), pages 149-156.
    12. Taleb, Mushtaq & Khalid, Ruzelan & Ramli, Razamin & Ghasemi, Mohammad Reza & Ignatius, Joshua, 2022. "An integrated bi-objective data envelopment analysis model for measuring returns to scale," European Journal of Operational Research, Elsevier, vol. 296(3), pages 967-979.
    13. Mostafa Omidi & Mohsen Rostamy-Malkhalifeh & Ali Payan & Farhad Hosseinzadeh Lotfi, 2019. "Estimation of Overall Returns to Scale (RTS) of a Frontier Unit Using the Left and Right RTS," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 633-655, February.
    14. Mehdiloozad, Mahmood & Mirdehghan, S. Morteza & Sahoo, Biresh K. & Roshdi, Israfil, 2015. "On the identification of the global reference set in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 245(3), pages 779-788.
    15. Kristof Witte & Rui Marques, 2011. "Big and beautiful? On non-parametrically measuring scale economies in non-convex technologies," Journal of Productivity Analysis, Springer, vol. 35(3), pages 213-226, June.
    16. Yun, Y. B. & Nakayama, H. & Tanino, T., 2004. "A generalized model for data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 157(1), pages 87-105, August.
    17. Jahanshahloo, G.R. & Shirzadi, A. & Mirdehghan, S.M., 2009. "Finding strong defining hyperplanes of PPS using multiplier form," European Journal of Operational Research, Elsevier, vol. 194(3), pages 933-938, May.
    18. Podinovski, Victor V., 2017. "Returns to scale in convex production technologies," European Journal of Operational Research, Elsevier, vol. 258(3), pages 970-982.
    19. A. Ghazi & F. Hosseinzadeh Lotfi, 2023. "Marginal rates in DEA using defining hyperplanes of PPS with CRS technology," Operational Research, Springer, vol. 23(1), pages 1-37, March.
    20. Krivonozhko, Vladimir E. & Førsund, Finn R. & Lychev, Andrey V., 2014. "Measurement of returns to scale using non-radial DEA models," European Journal of Operational Research, Elsevier, vol. 232(3), pages 664-670.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:190:y:2008:i:3:p:855-876. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.