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Weight Restrictions and Free Production in Data Envelopment Analysis

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  • Victor V. Podinovski

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

  • Tatiana Bouzdine-Chameeva

    (BEM Bordeaux Management School, 33405 Talence Cedex, France)

Abstract

It is known that the incorporation of weight restrictions in models of data envelopment analysis may result in their infeasibility. In our paper we investigate this effect in detail. We show that the infeasibility is only one of several possible outcomes that point to a particular problem with weight restrictions. For example, the use of weight restrictions may also lead to zero or negative efficiency scores of some units. Removing problematic units from the data set does not necessarily remove the underlying problem caused by the weight restrictions and only makes it undetected. We prove that all such problems arise when weight restrictions induce free or unlimited production of outputs in the underlying technology. This is unacceptable from the production theory point of view and indicates that the weight restrictions need reassessing. We develop analytical criteria and computational methods that allow us to identify the above problematic situations.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:61:y:2013:i:2:p:426-437
    DOI: 10.1287/opre.1120.1122
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    2. Andreas Dellnitz & Andreas Kleine & Madjid Tavana, 2024. "An integrated data envelopment analysis and regression tree method for new product price estimation," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 46(4), pages 1189-1211, December.
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    4. Robin C. Sickles & Wonho Song & Valentin Zelenyuk, 2018. "Econometric Analysis of Productivity: Theory and Implementation in R," CEPA Working Papers Series WP082018, School of Economics, University of Queensland, Australia.
    5. Léopold Simar & Paul W. Wilson, 2023. "Another look at productivity growth in industrialized countries," Journal of Productivity Analysis, Springer, vol. 60(3), pages 257-272, December.
    6. 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.
    7. A. Guerrini & G. Romano & L. Carosi & F. Mancuso, 2017. "Cost Savings in Wastewater Treatment Processes: the Role of Environmental and Operational Drivers," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(8), pages 2465-2478, June.
    8. 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.
    9. Liesiö, Juuso & Andelmin, Juho & Salo, Ahti, 2020. "Efficient allocation of resources to a portfolio of decision making units," European Journal of Operational Research, Elsevier, vol. 286(2), pages 619-636.
    10. Podinovski, Victor V. & Wu, Junlin & Argyris, Nikolaos, 2024. "Production trade-offs in models of data envelopment analysis with ratio inputs and outputs: An application to schools in England," European Journal of Operational Research, Elsevier, vol. 313(1), pages 359-372.
    11. Podinovski, Victor V. & Bouzdine-Chameeva, Tatiana, 2015. "Consistent weight restrictions in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 244(1), pages 201-209.
    12. Podinovski, Victor V., 2016. "Optimal weights in DEA models with weight restrictions," European Journal of Operational Research, Elsevier, vol. 254(3), pages 916-924.
    13. Ma-Lin Song & Ron Fisher & Jian-Lin Wang & Lian-Biao Cui, 2018. "Environmental performance evaluation with big data: theories and methods," Annals of Operations Research, Springer, vol. 270(1), pages 459-472, November.
    14. Natalya Zelenyuk & Valentin Zelenyuk, 2021. "Bank Performance Analysis," CEPA Working Papers Series WP022021, School of Economics, University of Queensland, Australia.
    15. Podinovski, Victor V., 2017. "Returns to scale in convex production technologies," European Journal of Operational Research, Elsevier, vol. 258(3), pages 970-982.
    16. Podinovski, Victor V. & Bouzdine-Chameeva, Tatiana, 2017. "Solving DEA models in a single optimization stage: Can the non-Archimedean infinitesimal be replaced by a small finite epsilon?," European Journal of Operational Research, Elsevier, vol. 257(2), pages 412-419.
    17. 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.
    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. Ishizaka, Alessio & Lolli, Francesco & Balugani, Elia & Cavallieri, Rita & Gamberini, Rita, 2018. "DEASort: Assigning items with data envelopment analysis in ABC classes," International Journal of Production Economics, Elsevier, vol. 199(C), pages 7-15.
    20. 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.
    21. 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.
    22. 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.
    23. Quintano, Claudio & Mazzocchi, Paolo & Rocca, Antonella, 2021. "Evaluation of the eco-efficiency of territorial districts with seaport economic activities," Utilities Policy, Elsevier, vol. 71(C).
    24. Toloo, Mehdi & Ebrahimi, Bohlool & Amin, Gholam R., 2021. "New data envelopment analysis models for classifying flexible measures: The role of non-Archimedean epsilon," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1037-1050.
    25. Roets, Bart & Verschelde, Marijn & Christiaens, Johan, 2018. "Multi-output efficiency and operational safety: An analysis of railway traffic control centre performance," European Journal of Operational Research, Elsevier, vol. 271(1), pages 224-237.

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