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Weight restrictions in DEA: misplaced emphasis?

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  • 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
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    3. 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.
    4. 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.
    5. 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.
    6. Førsund, Finn R., 2018. "Economic interpretations of DEA," Socio-Economic Planning Sciences, Elsevier, vol. 61(C), pages 9-15.
    7. 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).
    8. 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.
    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. Subhash C. Ray, 2014. "Data Envelopment Analysis: An Overview," Working papers 2014-33, University of Connecticut, Department of Economics.
    11. 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.
    12. 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.
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    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.

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    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

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