IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v64y2016i1p236-250.html
   My bibliography  Save this article

Marginal Values and Returns to Scale for Nonparametric Production Frontiers

Author

Listed:
  • Victor V. Podinovski

    (School of Business and Economics, Loughborough University, Loughborough LE11 3TU, United Kingdom)

  • Robert G. Chambers

    (Department of Agricultural and Resource Economics, University of Maryland, College Park, Maryland 20742)

  • Kazim Baris Atici

    (Department of Business Administration, Hacettepe University, Ankara 06800, Turkey)

  • Iryna D. Deineko

    (Warwick Business School, University of Warwick, Coventry CV4 7AL, United Kingdom)

Abstract

We present a unifying linear programming approach to the calculation of various directional derivatives for a very large class of production frontiers of data envelopment analysis (DEA). Special cases of this include different marginal rates, the scale elasticity, and a spectrum of partial and mixed elasticity measures. Our development applies to any polyhedral production technology including, to name a few, the conventional variable and constant returns-to-scale DEA technologies, their extensions with weight restrictions, technologies with weakly disposable undesirable outputs, and network DEA models. Furthermore, our development provides a general method for characterization of returns to scale (RTS) in any polyhedral technology. The new approach effectively removes the need to develop bespoke models for the RTS characterization and calculation of marginal rates and elasticity measures for each particular technology.

Suggested Citation

  • Victor V. Podinovski & Robert G. Chambers & Kazim Baris Atici & Iryna D. Deineko, 2016. "Marginal Values and Returns to Scale for Nonparametric Production Frontiers," Operations Research, INFORMS, vol. 64(1), pages 236-250, February.
    • Handle: RePEc:inm:oropre:v:64:y:2016:i:1:p:236-250
    DOI: 10.1287/opre.2015.1457
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.2015.1457
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.2015.1457?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
    ---><---

    References listed on IDEAS

    as
    1. William W. Cooper & Lawrence M. Seiford & Joe Zhu (ed.), 2011. "Handbook on Data Envelopment Analysis," International Series in Operations Research and Management Science, Springer, number 978-1-4419-6151-8, July-Dece.
    2. Banker, Rajiv D. & Thrall, R. M., 1992. "Estimation of returns to scale using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 62(1), pages 74-84, October.
    3. 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.
    4. 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.
    5. Zelenyuk, Valentin, 2013. "A scale elasticity measure for directional distance function and its dual: Theory and DEA estimation," European Journal of Operational Research, Elsevier, vol. 228(3), pages 592-600.
    6. Banker, Rajiv D., 1984. "Estimating most productive scale size using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 17(1), pages 35-44, July.
    7. 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.
    8. F R Førsund & L Hjalmarsson, 2004. "Calculating scale elasticity in DEA models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(10), pages 1023-1038, October.
    9. Victor Podinovski, 2009. "Production technologies based on combined proportionality assumptions," Journal of Productivity Analysis, Springer, vol. 32(1), pages 21-26, August.
    10. 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.
    11. Podinovski, Victor V. & Førsund, Finn R. & Krivonozhko, Vladimir E., 2009. "A simple derivation of scale elasticity in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 197(1), pages 149-153, August.
    12. Timo Kuosmanen, 2005. "Weak Disposability in Nonparametric Production Analysis with Undesirable Outputs," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 87(4), pages 1077-1082.
    13. Victor V. Podinovski & Finn R. Førsund, 2010. "Differential Characteristics of Efficient Frontiers in Data Envelopment Analysis," Operations Research, INFORMS, vol. 58(6), pages 1743-1754, December.
    14. Atici, Kazim Baris & Podinovski, Victor V., 2015. "Using data envelopment analysis for the assessment of technical efficiency of units with different specialisations: An application to agriculture," Omega, Elsevier, vol. 54(C), pages 72-83.
    15. Rajiv D. Banker & William W. Cooper & Lawrence M. Seiford & Joe Zhu, 2011. "Returns to Scale in DEA," 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 41-70, Springer.
    16. J Ruggiero, 2000. "Nonparametric estimation of returns to scale in the public sector with an application to the provision of educational services," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(8), pages 906-912, August.
    17. 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.
    18. 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.
    19. Robert Chambers & Rolf Färe, 2008. "A “calculus” for data envelopment analysis," Journal of Productivity Analysis, Springer, vol. 30(3), pages 169-175, December.
    20. Bert Balk & Rolf Färe & Giannis Karagiannis, 2015. "On directional scale elasticities," Journal of Productivity Analysis, Springer, vol. 43(1), pages 99-104, February.
    21. Podinovski, Victor V. & Ismail, Ihsan & Bouzdine-Chameeva, Tatiana & Zhang, Wenjuan, 2014. "Combining the assumptions of variable and constant returns to scale in the efficiency evaluation of secondary schools," European Journal of Operational Research, Elsevier, vol. 239(2), pages 504-513.
    22. Dan Rosen & Claire Schaffnit & Joseph Paradi, 1998. "Marginal Rates and Two-dimensional Level Curves in DEA," Journal of Productivity Analysis, Springer, vol. 9(3), pages 205-232, March.
    23. repec:bla:scandj:v:87:y:1985:i:4:p:594-604 is not listed on IDEAS
    24. V E Krivonozhko & O B Utkin & A V Volodin & I A Sablin & M Patrin, 2004. "Constructions of economic functions and calculations of marginal rates in DEA using parametric optimization methods," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(10), pages 1049-1058, October.
    25. Emrouznejad, Ali & Anouze, Abdel Latef & Thanassoulis, Emmanuel, 2010. "A semi-oriented radial measure for measuring the efficiency of decision making units with negative data, using DEA," European Journal of Operational Research, Elsevier, vol. 200(1), pages 297-304, January.
    26. 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.
    27. Korhonen, Pekka J. & Soleimani-damaneh, Majid & Wallenius, Jyrki, 2011. "Ratio-based RTS determination in weight-restricted DEA models," European Journal of Operational Research, Elsevier, vol. 215(2), pages 431-438, December.
    28. Wade D. Cook & Joe Zhu, 2011. "Multiple Variable Proportionality in Data Envelopment Analysis," Operations Research, INFORMS, vol. 59(4), pages 1024-1032, August.
    29. O. B. Olesen & N. C. Petersen, 1996. "Indicators of Ill-Conditioned Data Sets and Model Misspecification in Data Envelopment Analysis: An Extended Facet Approach," Management Science, INFORMS, vol. 42(2), pages 205-219, February.
    30. Victor V. Podinovski & Tatiana Bouzdine-Chameeva, 2013. "Weight Restrictions and Free Production in Data Envelopment Analysis," Operations Research, INFORMS, vol. 61(2), pages 426-437, April.
    31. Sahoo, Biresh K. & Zhu, Joe & Tone, Kaoru & Klemen, Bernhard M., 2014. "Decomposing technical efficiency and scale elasticity in two-stage network DEA," European Journal of Operational Research, Elsevier, vol. 233(3), pages 584-594.
    32. 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.
    33. Rajiv D. Banker & Ajay Maindiratta, 1986. "Piecewise Loglinear Estimation of Efficient Production Surfaces," Management Science, INFORMS, vol. 32(1), pages 126-135, January.
    34. Kaoru Tone, 2001. "On Returns to Scale under Weight Restrictions in Data Envelopment Analysis," Journal of Productivity Analysis, Springer, vol. 16(1), pages 31-47, July.
    35. William W. Cooper & Lawrence M. Seiford & Kaoru Tone, 2007. "Data Envelopment Analysis," Springer Books, Springer, edition 0, number 978-0-387-45283-8, March.
    36. Atici, Kazim Baris & Podinovski, Victor V., 2012. "Mixed partial elasticities in constant returns-to-scale production technologies," European Journal of Operational Research, Elsevier, vol. 220(1), pages 262-269.
    37. C. N. Jones & E. C. Kerrigan & J. M. Maciejowski, 2008. "On Polyhedral Projection and Parametric Programming," Journal of Optimization Theory and Applications, Springer, vol. 138(2), pages 207-220, August.
    Full references (including those not matched with items on IDEAS)

    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. Podinovski, Victor V., 2017. "Returns to scale in convex production technologies," European Journal of Operational Research, Elsevier, vol. 258(3), pages 970-982.
    2. 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.
    3. Podinovski, Victor V., 2019. "Direct estimation of marginal characteristics of nonparametric production frontiers in the presence of undesirable outputs," European Journal of Operational Research, Elsevier, vol. 279(1), pages 258-276.
    4. Victor V. Podinovski & Finn R. Førsund, 2010. "Differential Characteristics of Efficient Frontiers in Data Envelopment Analysis," Operations Research, INFORMS, vol. 58(6), pages 1743-1754, December.
    5. Mehdiloo, Mahmood & Podinovski, Victor V., 2019. "Selective strong and weak disposability in efficiency analysis," European Journal of Operational Research, Elsevier, vol. 276(3), pages 1154-1169.
    6. Victor V. Podinovski & Ole Bent Olesen & Cláudia S. Sarrico, 2018. "Nonparametric Production Technologies with Multiple Component Processes," Operations Research, INFORMS, vol. 66(1), pages 282-300, January.
    7. Zelenyuk, Valentin, 2015. "Aggregation of scale efficiency," European Journal of Operational Research, Elsevier, vol. 240(1), pages 269-277.
    8. Papaioannou, Grammatoula & Podinovski, Victor V., 2023. "Multicomponent production technologies with restricted allocations of shared inputs and outputs," European Journal of Operational Research, Elsevier, vol. 308(1), pages 274-289.
    9. Chia-Yen Lee, 2017. "Directional marginal productivity: a foundation of meta-data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(5), pages 544-555, May.
    10. Papaioannou, Grammatoula & Podinovski, Victor V., 2024. "A single-stage optimization procedure for data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 313(3), pages 1119-1128.
    11. Podinovski, Victor V. & Bouzdine-Chameeva, Tatiana, 2019. "Cone extensions of polyhedral production technologies," European Journal of Operational Research, Elsevier, vol. 276(2), pages 736-743.
    12. Afsharian, Mohsen & Podinovski, Victor V., 2018. "A linear programming approach to efficiency evaluation in nonconvex metatechnologies," European Journal of Operational Research, Elsevier, vol. 268(1), pages 268-280.
    13. Ole Bent Olesen & Niels Christian Petersen & Victor V. Podinovski, 2022. "Scale characteristics of variable returns-to-scale production technologies with ratio inputs and outputs," Annals of Operations Research, Springer, vol. 318(1), pages 383-423, November.
    14. Zelenyuk, Valentin, 2013. "A scale elasticity measure for directional distance function and its dual: Theory and DEA estimation," European Journal of Operational Research, Elsevier, vol. 228(3), pages 592-600.
    15. Victor V. Podinovski & Tatiana Bouzdine-Chameeva, 2021. "Optimal solutions of multiplier DEA models," Journal of Productivity Analysis, Springer, vol. 56(1), pages 45-68, August.
    16. Dellnitz, Andreas & Tavana, Madjid, 2024. "Data envelopment analysis: From non-monotonic to monotonic scale elasticities," European Journal of Operational Research, Elsevier, vol. 318(2), pages 549-559.
    17. Mehdiloo, Mahmood & Podinovski, Victor V., 2021. "Strong, weak and Farrell efficient frontiers of technologies satisfying different production assumptions," European Journal of Operational Research, Elsevier, vol. 294(1), pages 295-311.
    18. Peixin Duan, 2022. "How large of a grant size is appropriate? Evidence from the National Natural Science Foundation of China," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-14, February.
    19. Atici, Kazim Baris & Podinovski, Victor V., 2012. "Mixed partial elasticities in constant returns-to-scale production technologies," European Journal of Operational Research, Elsevier, vol. 220(1), pages 262-269.
    20. Barnabé Walheer, 2020. "Output, input, and undesirable output interconnections in data envelopment analysis: convexity and returns-to-scale," Annals of Operations Research, Springer, vol. 284(1), pages 447-467, January.

    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:inm:oropre:v:64:y:2016:i:1:p:236-250. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.