IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v72y2017icp1-14.html
   My bibliography  Save this article

Graph productivity change measure using the least distance to the pareto-efficient frontier in data envelopment analysis

Author

Listed:
  • Aparicio, Juan
  • Garcia-Nove, Eva M.
  • Kapelko, Magdalena
  • Pastor, Jesus T.

Abstract

This paper proposes a new method to measure productivity change of decision making units in the full input-output space. The new approach is based on the calculation of the least distance to the Pareto-efficient frontier and hence provides the closest targets for evaluated decision making units to reach the strongly efficient frontier with least effort. Another advantage of the new methodology is that it always leads to feasible solutions. The productivity change in the new approach is operationalized as a Luenberger-type indicator in the Data Envelopment Analysis framework and it is decomposed into efficiency change and technical change. The paper empirically illustrates the new method using recent data on the Spanish quality wine sector.

Suggested Citation

  • Aparicio, Juan & Garcia-Nove, Eva M. & Kapelko, Magdalena & Pastor, Jesus T., 2017. "Graph productivity change measure using the least distance to the pareto-efficient frontier in data envelopment analysis," Omega, Elsevier, vol. 72(C), pages 1-14.
    • Handle: RePEc:eee:jomega:v:72:y:2017:i:c:p:1-14
    DOI: 10.1016/j.omega.2016.10.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305048316308234
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.omega.2016.10.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Tarja Joro & Pekka Korhonen & Jyrki Wallenius, 1998. "Structural Comparison of Data Envelopment Analysis and Multiple Objective Linear Programming," Management Science, INFORMS, vol. 44(7), pages 962-970, July.
    2. Simar, L. & Wilson, P.W., 1998. "Productivity Growth in Industrialized Countries," Papers 9810, Catholique de Louvain - Institut de statistique.
    3. Leopold Simar & Valentin Zelenyuk, 2006. "On Testing Equality of Distributions of Technical Efficiency Scores," Econometric Reviews, Taylor & Francis Journals, vol. 25(4), pages 497-522.
    4. C. Lovell, 2003. "The Decomposition of Malmquist Productivity Indexes," Journal of Productivity Analysis, Springer, vol. 20(3), pages 437-458, November.
    5. Jose Zofio & Jesus Pastor & Juan Aparicio, 2013. "The directional profit efficiency measure: on why profit inefficiency is either technical or allocative," Journal of Productivity Analysis, Springer, vol. 40(3), pages 257-266, December.
    6. W. Briec & K. Kerstens, 2009. "Infeasibility and Directional Distance Functions with Application to the Determinateness of the Luenberger Productivity Indicator," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 55-73, April.
    7. Robert G. Chambers & Rulon D. Pope, 1996. "Aggregate Productivity Measures," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 78(5), pages 1360-1365.
    8. S Lozano & G Villa, 2005. "Determining a sequence of targets in DEA," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(12), pages 1439-1447, December.
    9. Jean‐Philippe Boussemart & Walter Briec & Kristiaan Kerstens & Jean‐Christophe Poutineau, 2003. "Luenberger and Malmquist Productivity Indices: Theoretical Comparisons and Empirical Illustration," Bulletin of Economic Research, Wiley Blackwell, vol. 55(4), pages 391-405, October.
    10. Briec, Walter & Kerstens, Kristiaan, 2009. "The Luenberger productivity indicator: An economic specification leading to infeasibilities," Economic Modelling, Elsevier, vol. 26(3), pages 597-600, May.
    11. Rafael Cuesta & José Zofío, 2005. "Hyperbolic Efficiency and Parametric Distance Functions: With Application to Spanish Savings Banks," Journal of Productivity Analysis, Springer, vol. 24(1), pages 31-48, September.
    12. W. Briec & J. B. Lesourd, 1999. "Metric Distance Function and Profit: Some Duality Results," Journal of Optimization Theory and Applications, Springer, vol. 101(1), pages 15-33, April.
    13. Juan Aparicio & José Ruiz & Inmaculada Sirvent, 2007. "Closest targets and minimum distance to the Pareto-efficient frontier in DEA," Journal of Productivity Analysis, Springer, vol. 28(3), pages 209-218, December.
    14. Pastor, J. T. & Ruiz, J. L. & Sirvent, I., 1999. "An enhanced DEA Russell graph efficiency measure," European Journal of Operational Research, Elsevier, vol. 115(3), pages 596-607, June.
    15. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
    16. Robert G. Chambers, 2002. "Exact nonradial input, output, and productivity measurement," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(4), pages 751-765.
    17. Chambers, Robert G. & Fare, Rolf & Grosskopf, Shawna, 1996. "Productivity Growth in APEC Countries," Working Papers 197843, University of Maryland, Department of Agricultural and Resource Economics.
    18. Maria Portela & Emmanuel Thanassoulis, 2006. "Malmquist Indexes Using a Geometric Distance Function (GDF). Application to a Sample of Portuguese Bank Branches," Journal of Productivity Analysis, Springer, vol. 25(1), pages 25-41, April.
    19. William Cooper & Kyung Park & Jesus Pastor, 1999. "RAM: A Range Adjusted Measure of Inefficiency for Use with Additive Models, and Relations to Other Models and Measures in DEA," Journal of Productivity Analysis, Springer, vol. 11(1), pages 5-42, February.
    20. Maria Silva Portela & Pedro Borges & Emmanuel Thanassoulis, 2003. "Finding Closest Targets in Non-Oriented DEA Models: The Case of Convex and Non-Convex Technologies," Journal of Productivity Analysis, Springer, vol. 19(2), pages 251-269, April.
    21. W. Briec, 1997. "Minimum Distance to the Complement of a Convex Set: Duality Result," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 301-319, May.
    22. Walter Briec & Hervé Leleu, 2003. "Dual Representations of Non-Parametric Technologies and Measurement of Technical Efficiency," Journal of Productivity Analysis, Springer, vol. 20(1), pages 71-96, July.
    23. Aparicio, Juan & Pastor, Jesus T., 2014. "Closest targets and strong monotonicity on the strongly efficient frontier in DEA," Omega, Elsevier, vol. 44(C), pages 51-57.
    24. Jesus Pastor & C. Lovell & Juan Aparicio, 2012. "Families of linear efficiency programs based on Debreu’s loss function," Journal of Productivity Analysis, Springer, vol. 38(2), pages 109-120, October.
    25. Kerstens, Kristiaan & Hachem, Bouye Ahmed Moulaye & Van de Woestyne, Ignace, 2010. "Malmquist and Hicks-Moorsteen Productivity Indices: An Empirical Comparison Focusing on Infeasibilities," Working Papers 2010/31, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
    26. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity," Econometrica, Econometric Society, vol. 50(6), pages 1393-1414, November.
    27. Frances Frei & Patrick Harker, 1999. "Projections Onto Efficient Frontiers: Theoretical and Computational Extensions to DEA," Journal of Productivity Analysis, Springer, vol. 11(3), pages 275-300, June.
    28. Walter Briec & K. Kerstens, 2009. "Infeasibilities and directional distance functions: with application to the determinateness of the luenberger productivity indicator," Post-Print hal-00372560, HAL.
    29. Gonzalez, Eduardo & Alvarez, Antonio, 2001. "From efficiency measurement to efficiency improvement: The choice of a relevant benchmark," European Journal of Operational Research, Elsevier, vol. 133(3), pages 512-520, September.
    30. Charnes, A. & Cooper, W. W. & Golany, B. & Seiford, L. & Stutz, J., 1985. "Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 91-107.
    31. Aparicio, Juan & Mahlberg, Bernhard & Pastor, Jesus T. & Sahoo, Biresh K., 2014. "Decomposing technical inefficiency using the principle of least action," European Journal of Operational Research, Elsevier, vol. 239(3), pages 776-785.
    32. Juan Aparicio & Fernando Borras & Lidia Ortiz & Jesus T. Pastor, 2014. "Benchmarking in Healthcare: An Approach Based on Closest Targets," International Series in Operations Research & Management Science, in: Ali Emrouznejad & Emilyn Cabanda (ed.), Managing Service Productivity, edition 127, pages 67-91, Springer.
    33. Hirofumi Fukuyama & Hiroya Masaki & Kazuyuki Sekitani & Jianming Shi, 2014. "Distance optimization approach to ratio-form efficiency measures in data envelopment analysis," Journal of Productivity Analysis, Springer, vol. 42(2), pages 175-186, October.
    34. Hirofumi Fukuyama & Jens Leth Hougaard & Kazuyuki Sekitani & Jianming Shi, 2016. "Efficiency measurement with a non-convex free disposal hull technology," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(1), pages 9-19, January.
    35. Briec, W. & Lemaire, B., 1999. "Technical efficiency and distance to a reverse convex set," European Journal of Operational Research, Elsevier, vol. 114(1), pages 178-187, April.
    36. 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.
    37. Jose Zofio & C. A. Knox Lovell, 2001. "Graph efficiency and productivity measures: an application to US agriculture," Applied Economics, Taylor & Francis Journals, vol. 33(11), pages 1433-1442.
    38. Fukuyama, Hirofumi & Maeda, Yasunobu & Sekitani, Kazuyuki & Shi, Jianming, 2014. "Input–output substitutability and strongly monotonic p-norm least distance DEA measures," European Journal of Operational Research, Elsevier, vol. 237(3), pages 997-1007.
    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. Fukuyama, Hirofumi & Matousek, Roman & Tzeremes, Nickolaos G., 2023. "Estimating the degree of firms’ input market power via data envelopment analysis: Evidence from the global biotechnology and pharmaceutical industry," European Journal of Operational Research, Elsevier, vol. 305(2), pages 946-960.
    2. Henriques, C.O. & Chavez, J.M. & Gouveia, M.C. & Marcenaro-Gutierrez, O.D., 2022. "Efficiency of secondary schools in Ecuador: A value based DEA approach," Socio-Economic Planning Sciences, Elsevier, vol. 82(PA).
    3. Lozano, Sebastián & Khezri, Somayeh, 2021. "Network DEA smallest improvement approach," Omega, Elsevier, vol. 98(C).
    4. Fukuyama, Hirofumi & Matousek, Roman & Tzeremes, Nickolaos G., 2022. "Bank production with nonperforming loans: A minimum distance directional slack inefficiency approach," Omega, Elsevier, vol. 113(C).
    5. Somayeh Razipour-GhalehJough & Farhad Hosseinzadeh Lotfi & Gholamreza Jahanshahloo & Mohsen Rostamy-malkhalifeh & Hamid Sharafi, 2020. "Finding closest target for bank branches in the presence of weight restrictions using data envelopment analysis," Annals of Operations Research, Springer, vol. 288(2), pages 755-787, May.

    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. Juan Aparicio & Jesus T. Pastor & Jose L. Sainz-Pardo & Fernando Vidal, 2020. "Estimating and decomposing overall inefficiency by determining the least distance to the strongly efficient frontier in data envelopment analysis," Operational Research, Springer, vol. 20(2), pages 747-770, June.
    2. Juan Aparicio & Magdalena Kapelko & Bernhard Mahlberg & Jose L. Sainz-Pardo, 2017. "Measuring input-specific productivity change based on the principle of least action," Journal of Productivity Analysis, Springer, vol. 47(1), pages 17-31, February.
    3. Aparicio, Juan & Cordero, Jose M. & Pastor, Jesus T., 2017. "The determination of the least distance to the strongly efficient frontier in Data Envelopment Analysis oriented models: Modelling and computational aspects," Omega, Elsevier, vol. 71(C), pages 1-10.
    4. Juan Aparicio & José L. Zofío & Jesús T. Pastor, 2023. "Decomposing Economic Efficiency into Technical and Allocative Components: An Essential Property," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 98-129, April.
    5. Kao, Chiang, 2022. "Closest targets in the slacks-based measure of efficiency for production units with multi-period data," European Journal of Operational Research, Elsevier, vol. 297(3), pages 1042-1054.
    6. Zhu, Qingyuan & Aparicio, Juan & Li, Feng & Wu, Jie & Kou, Gang, 2022. "Determining closest targets on the extended facet production possibility set in data envelopment analysis: Modeling and computational aspects," European Journal of Operational Research, Elsevier, vol. 296(3), pages 927-939.
    7. Aparicio, Juan & Pastor, Jesus T., 2014. "Closest targets and strong monotonicity on the strongly efficient frontier in DEA," Omega, Elsevier, vol. 44(C), pages 51-57.
    8. Juan Aparicio & Fernando Borras & Lidia Ortiz & Jesus T. Pastor & Fernando Vidal, 2019. "Luenberger-type indicators based on the weighted additive distance function," Annals of Operations Research, Springer, vol. 278(1), pages 195-213, July.
    9. Briec, Walter & Dumas, Audrey & Kerstens, Kristiaan & Stenger, Agathe, 2022. "Generalised commensurability properties of efficiency measures: Implications for productivity indicators," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1481-1492.
    10. Aparicio, Juan & Cordero, Jose M. & Gonzalez, Martin & Lopez-Espin, Jose J., 2018. "Using non-radial DEA to assess school efficiency in a cross-country perspective: An empirical analysis of OECD countries," Omega, Elsevier, vol. 79(C), pages 9-20.
    11. Juo, Jia-Ching & Fu, Tsu-Tan & Yu, Ming-Miin & Lin, Yu-Hui, 2016. "Non-radial profit performance: An application to Taiwanese banks," Omega, Elsevier, vol. 65(C), pages 111-121.
    12. Juan Aparicio & Magdalena Kapelko & Juan F. Monge, 2020. "A Well-Defined Composite Indicator: An Application to Corporate Social Responsibility," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 299-323, July.
    13. Zhu, Qingyuan & Wu, Jie & Ji, Xiang & Li, Feng, 2018. "A simple MILP to determine closest targets in non-oriented DEA model satisfying strong monotonicity," Omega, Elsevier, vol. 79(C), pages 1-8.
    14. Fangqing Wei & Junfei Chu & Jiayun Song & Feng Yang, 2019. "A cross-bargaining game approach for direction selection in the directional distance function," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(3), pages 787-807, September.
    15. Mette Asmild & Tomas Baležentis & Jens Leth Hougaard, 2016. "Multi-directional productivity change: MEA-Malmquist," Journal of Productivity Analysis, Springer, vol. 46(2), pages 109-119, December.
    16. Jradi, Samah & Bouzdine Chameeva, Tatiana & Aparicio, Juan, 2019. "The measurement of revenue inefficiency over time: An additive perspective," Omega, Elsevier, vol. 83(C), pages 167-180.
    17. Magdalena Kapelko, 2019. "Measuring productivity change accounting for adjustment costs: evidence from the food industry in the European Union," Annals of Operations Research, Springer, vol. 278(1), pages 215-234, July.
    18. Alcaraz, Javier & Anton-Sanchez, Laura & Aparicio, Juan & Monge, Juan F. & Ramón, Nuria, 2021. "Russell Graph efficiency measures in Data Envelopment Analysis: The multiplicative approach," European Journal of Operational Research, Elsevier, vol. 292(2), pages 663-674.
    19. J. Vakili, 2017. "New Models for Computing the Distance of DMUs to the Weak Efficient Boundary of Convex and Nonconvex PPSs in DEA," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(06), pages 1-20, December.
    20. Fangqing Wei & Yanan Fu & Feng Yang & Chun Sun & Sheng Ang, 2023. "Closest target setting with minimum improvement costs considering demand and resource mismatches," Operational Research, Springer, vol. 23(3), pages 1-29, September.

    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:jomega:v:72:y:2017:i:c:p:1-14. 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/wps/find/journaldescription.cws_home/375/description#description .

    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.