IDEAS home Printed from https://ideas.repec.org/a/kap/jproda/v40y2013i3p271-283.html
   My bibliography  Save this article

Weight restrictions in DEA: misplaced emphasis?

Author

Listed:
  • Finn Førsund

Abstract

Measuring productive efficiency is an important research strand within fields of economics, management science and operations research. One definition of efficiency is the proportional scaling needed for observations of inefficient units to be projected onto an efficient production function and another definition is a ratio index of weighted outputs on weighted inputs. When linear programming is used to estimate efficiency the two definitions give identical results due to the fundamental duality of linear programming. Empirical applications of DEA using linear programming showed a prevalence of zero weights leading to questioning the consequence for the efficiency score estimate based on the ratio definition. Early literature on weight restrictions is exclusively based on the ratio efficiency. It was stated that variables with zero weights had no influence on the efficiency score, in spite of the alleged importance of the variables. This has been one motivation for introducing restrictions on weights. Another empirical result was that often there were too many efficient units. This problem could also be overcome by introducing weight restrictions. Weight restrictions were said to introduce values for inputs and outputs. The paper makes a critical examinations of these claims based on defining efficiency relative to a frontier production function. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Finn Førsund, 2013. "Weight restrictions in DEA: misplaced emphasis?," Journal of Productivity Analysis, Springer, vol. 40(3), pages 271-283, December.
    • Handle: RePEc:kap:jproda:v:40:y:2013:i:3:p:271-283
    DOI: 10.1007/s11123-012-0296-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11123-012-0296-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11123-012-0296-9?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. A. Bessent & W. Bessent & J. Elam & T. Clark, 1988. "Efficiency Frontier Determination by Constrained Facet Analysis," Operations Research, INFORMS, vol. 36(5), pages 785-796, October.
    2. 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.
    3. Charnes, A. & Cooper, W. W. & Huang, Z. M. & Sun, D. B., 1990. "Polyhedral Cone-Ratio DEA Models with an illustrative application to large commercial banks," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 73-91.
    4. Finn Førsund & Nikias Sarafoglou, 2002. "On the Origins of Data Envelopment Analysis," Journal of Productivity Analysis, Springer, vol. 17(1), pages 23-40, January.
    5. V V Podinovski, 2007. "Improving data envelopment analysis by the use of production trade-offs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(10), pages 1261-1270, October.
    6. Podinovski, V. V., 1999. "Side effects of absolute weight bounds in DEA models," European Journal of Operational Research, Elsevier, vol. 115(3), pages 583-595, June.
    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. R. Allen & A. Athanassopoulos & R.G. Dyson & E. Thanassoulis, 1997. "Weights restrictions and value judgements in Data Envelopment Analysis: Evolution, development and future directions," Annals of Operations Research, Springer, vol. 73(0), pages 13-34, October.
    9. Forsund, Finn R. & Sarafoglou, Nikias, 2005. "The tale of two research communities: The diffusion of research on productive efficiency," International Journal of Production Economics, Elsevier, vol. 98(1), pages 17-40, October.
    10. M. Stone, 2002. "How not to measure the efficiency of public services (and how one might)," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 165(3), pages 405-434, October.
    11. 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.
    12. 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.
    13. 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.
    14. Thompson, Russell G. & Langemeier, Larry N. & Lee, Chih-Tah & Lee, Euntaik & Thrall, Robert M., 1990. "The role of multiplier bounds in efficiency analysis with application to Kansas farming," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 93-108.
    15. Peter Smith, 1997. "Model misspecification in Data Envelopment Analysis," Annals of Operations Research, Springer, vol. 73(0), pages 233-252, October.
    16. Francisco Pedraja-Chaparro & Javier Salinas-Jimenez & Peter Smith, 1997. "On the Role of Weight Restrictions in Data Envelopment Analysis," Journal of Productivity Analysis, Springer, vol. 8(2), pages 215-230, May.
    17. V V Podinovski, 2005. "The explicit role of weight bounds in models of data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(12), pages 1408-1418, December.
    18. Allen, R. & Thanassoulis, E., 2004. "Improving envelopment in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 154(2), pages 363-379, April.
    19. T Joro & E-J Viitala, 2004. "Weight-restricted DEA in action: from expert opinions to mathematical models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(8), pages 814-821, August.
    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. Chia-Jung Tu & Ming-Chung Chang & Chiang-Ping Chen, 2016. "Progressive Time-Weighted Dynamic Energy Efficiency, Energy Decoupling Rate, and Decarbonization: An Empirical Study on G7 and BRICS," Sustainability, MDPI, vol. 8(9), pages 1-17, September.
    2. Afsharian, Mohsen & Bogetoft, Peter, 2023. "Limiting flexibility in nonparametric efficiency evaluations: An ex post k-centroid clustering approach," European Journal of Operational Research, Elsevier, vol. 311(2), pages 633-647.
    3. Aldanondo, Ana M. & Casasnovas, Valero L., 2015. "More is better than one: the impact of different numbers of input aggregators in technical efficiency estimation," MPRA Paper 64120, University Library of Munich, Germany.
    4. Subhash C. Ray, 2014. "Data Envelopment Analysis: An Overview," Working papers 2014-33, University of Connecticut, Department of Economics.
    5. Sen Subir, 2020. "Analysis of Cost Efficiency of Indian Life Insurers: A comparison of Quantity vs Value based DEA Approach," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 14(1), pages 1-25, January.
    6. Ray, Subhash C, 2019. "The transformation function, technical efficiency, and the CCR ratio," European Journal of Operational Research, Elsevier, vol. 278(2), pages 422-429.
    7. Aldanondo, Ana M. & Casasnovas, Valero L., 2016. "A note on the impact of multiple input aggregators in technical efficiency estimation," MPRA Paper 75290, University Library of Munich, Germany.
    8. Zuoren Sun & Rundong Luo & Dequn Zhou, 2015. "Optimal Path for Controlling Sectoral CO 2 Emissions Among China’s Regions: A Centralized DEA Approach," Sustainability, MDPI, vol. 8(1), pages 1-20, December.
    9. González, Eduardo & Cárcaba, Ana & Ventura, Juan, 2015. "How car dealers adjust prices to reach the product efficiency frontier in the Spanish automobile market," Omega, Elsevier, vol. 51(C), pages 38-48.
    10. Vladimir E. Krivonozhko & Finn R. Førsund & Andrey V. Lychev, 2017. "On comparison of different sets of units used for improving the frontier in DEA models," Annals of Operations Research, Springer, vol. 250(1), pages 5-20, March.
    11. Førsund, Finn R., 2018. "Economic interpretations of DEA," Socio-Economic Planning Sciences, Elsevier, vol. 61(C), pages 9-15.
    12. Costa, Marcelo Azevedo & Lopes-Ahn, Ana Lúcia & Kilger, Alexander de Carvalho & Micas, Artur Fontenelle, 2023. "Limitations of weight restrictions in data envelopment analysis for benchmarking Brazilian electricity distribution system operators," Utilities Policy, Elsevier, vol. 82(C).
    13. da Silva, Aline Veronese & Costa, Marcelo Azevedo & Ahn, Heinz & Lopes, Ana Lúcia Miranda, 2019. "Performance benchmarking models for electricity transmission regulation: Caveats concerning the Brazilian case," Utilities Policy, Elsevier, vol. 60(C), pages 1-1.
    14. Martin Bod’a & Martin Dlouhý & Emília Zimková, 2018. "Unobservable or omitted production variables in data envelopment analysis through unit-specific production trade-offs," 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. 26(4), pages 813-846, December.

    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. 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.
    2. Ramón, Nuria & Ruiz, José L. & Sirvent, Inmaculada, 2010. "A multiplier bound approach to assess relative efficiency in DEA without slacks," European Journal of Operational Research, Elsevier, vol. 203(1), pages 261-269, May.
    3. 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.
    4. Førsund, Finn, 2015. "Economic Perspectives on DEA," Memorandum 10/2015, Oslo University, Department of Economics.
    5. Maria Portela & Emmanuel Thanassoulis, 2006. "Zero weights and non-zero slacks: Different solutions to the same problem," Annals of Operations Research, Springer, vol. 145(1), pages 129-147, July.
    6. 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.
    7. Cook, Wade D. & Seiford, Larry M., 2009. "Data envelopment analysis (DEA) - Thirty years on," European Journal of Operational Research, Elsevier, vol. 192(1), pages 1-17, January.
    8. Victor V. Podinovski & Wan Rohaida Wan Husain, 2017. "The hybrid returns-to-scale model and its extension by production trade-offs: an application to the efficiency assessment of public universities in Malaysia," Annals of Operations Research, Springer, vol. 250(1), pages 65-84, March.
    9. Aldanondo, Ana M. & Casasnovas, Valero L., 2015. "More is better than one: the impact of different numbers of input aggregators in technical efficiency estimation," MPRA Paper 64120, University Library of Munich, Germany.
    10. Ströhl, Florian & Borsch, Erik & Souren, Rainer, 2018. "Integration von Gewichtsrestriktionen in das DEA-Modell nach Charnes, Cooper und Rhodes: Exemplarische Optionen und Auswirkungen," Ilmenauer Schriften zur Betriebswirtschaftslehre, Technische Universität Ilmenau, Institut für Betriebswirtschaftslehre, volume 3, number 32018.
    11. Førsund, Finn & Krivonozhko, Vladimir W & Lychev, Andrey V., 2016. "Smoothing the frontier in the DEA models," Memorandum 11/2016, Oslo University, Department of Economics.
    12. HOSSEINZADEH LOTFI, Farhad & HATAMI-MARBINI, Adel & AGRELL, Per & GHOLAMI, Kobra, 2013. "Centralized resource reduction and target setting under DEA control," LIDAM Discussion Papers CORE 2013005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Khalili, M. & Camanho, A.S. & Portela, M.C.A.S. & Alirezaee, M.R., 2010. "The measurement of relative efficiency using data envelopment analysis with assurance regions that link inputs and outputs," European Journal of Operational Research, Elsevier, vol. 203(3), pages 761-770, June.
    14. Estellita Lins, M.P. & Moreira da Silva, A.C. & Lovell, C.A.K., 2007. "Avoiding infeasibility in DEA models with weight restrictions," European Journal of Operational Research, Elsevier, vol. 181(2), pages 956-966, September.
    15. Podinovski, Victor V., 2016. "Optimal weights in DEA models with weight restrictions," European Journal of Operational Research, Elsevier, vol. 254(3), pages 916-924.
    16. Zhou, P. & Ang, B.W. & Poh, K.L., 2008. "A survey of data envelopment analysis in energy and environmental studies," European Journal of Operational Research, Elsevier, vol. 189(1), pages 1-18, August.
    17. Mai, Nhat Chi, 2015. "Efficiency of the banking system in Vietnam under financial liberalization," OSF Preprints qsf6d, Center for Open Science.
    18. Podinovski, Victor V. & Bouzdine-Chameeva, Tatiana, 2016. "On single-stage DEA models with weight restrictions," European Journal of Operational Research, Elsevier, vol. 248(3), pages 1044-1050.
    19. Luis R. Murillo‐Zamorano, 2004. "Economic Efficiency and Frontier Techniques," Journal of Economic Surveys, Wiley Blackwell, vol. 18(1), pages 33-77, February.
    20. Aldanondo, Ana M. & Casasnovas, Valero L., 2016. "A note on the impact of multiple input aggregators in technical efficiency estimation," MPRA Paper 75290, University Library of Munich, Germany.

    More about this item

    Keywords

    Weight restrictions; DEA; Efficiency; Frontier production function; Primal and dual linear programming problems; C61; D20;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D20 - Microeconomics - - Production and Organizations - - - General

    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:kap:jproda:v:40:y:2013:i:3:p:271-283. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.