IDEAS home Printed from https://ideas.repec.org/a/eee/oprepe/v12y2024ics2214716024000113.html
   My bibliography  Save this article

Chance constrained directional models in stochastic data envelopment analysis

Author

Listed:
  • Bolós, V.J.
  • Benítez, R.
  • Coll-Serrano, V.

Abstract

We construct a new family of chance constrained directional models in stochastic data envelopment analysis, generalizing the deterministic directional models and the chance constrained radial models. We prove that chance constrained directional models define the same concept of stochastic efficiency as the one given by chance constrained radial models and, as a particular case, we obtain a stochastic version of the generalized Farrell measure. Finally, we give some examples of application of chance constrained directional models with stochastic and deterministic directions, showing that inefficiency scores obtained with stochastic directions are less or equal than those obtained considering deterministic directions whose values are the means of the stochastic ones.

Suggested Citation

  • Bolós, V.J. & Benítez, R. & Coll-Serrano, V., 2024. "Chance constrained directional models in stochastic data envelopment analysis," Operations Research Perspectives, Elsevier, vol. 12(C).
    • Handle: RePEc:eee:oprepe:v:12:y:2024:i:c:s2214716024000113
    DOI: 10.1016/j.orp.2024.100307
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S2214716024000113
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.orp.2024.100307?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. William Cooper & Zhimin Huang & Vedran Lelas & Susan Li & Ole Olesen, 1998. "Chance Constrained Programming Formulations for Stochastic Characterizations of Efficiency and Dominance in DEA," Journal of Productivity Analysis, Springer, vol. 9(1), pages 53-79, January.
    2. TAVANA, Madjid & SHIRAZ, Rashed Khanjani & HATAMI-MARBINI, Adel & AGRELL, Per J., 2013. "Chance-constrained DEA models with random fuzzy inputs and outputs," LIDAM Reprints CORE 2531, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. W. Briec, 1997. "A Graph-Type Extension of Farrell Technical Efficiency Measure," Journal of Productivity Analysis, Springer, vol. 8(1), pages 95-110, March.
    4. 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.
    5. Fare, Rolf & Knox Lovell, C. A., 1978. "Measuring the technical efficiency of production," Journal of Economic Theory, Elsevier, vol. 19(1), pages 150-162, October.
    6. 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.
    7. 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.
    8. 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.
    9. A. Charnes & W. W. Cooper & E. Rhodes, 1981. "Evaluating Program and Managerial Efficiency: An Application of Data Envelopment Analysis to Program Follow Through," Management Science, INFORMS, vol. 27(6), pages 668-697, June.
    10. tone, Kaoru, 2010. "Variations on the theme of slacks-based measure of efficiency in DEA," European Journal of Operational Research, Elsevier, vol. 200(3), pages 901-907, February.
    11. Alireza Amirteimoori & Biresh K. Sahoo & Vincent Charles & Saber Mehdizadeh, 2022. "Stochastic Benchmarking," International Series in Operations Research and Management Science, Springer, number 978-3-030-89869-4, July-Dece.
    12. Rashed Khanjani Shiraz & Madjid Tavana & Hirofumi Fukuyama, 2021. "A joint chance-constrained data envelopment analysis model with random output data," Operational Research, Springer, vol. 21(2), pages 1255-1277, June.
    13. O. B. Olesen & N. C. Petersen, 1995. "Chance Constrained Efficiency Evaluation," Management Science, INFORMS, vol. 41(3), pages 442-457, March.
    14. 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.
    15. 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.
    16. Olesen, Ole B. & Petersen, Niels Christian, 2016. "Stochastic Data Envelopment Analysis—A review," European Journal of Operational Research, Elsevier, vol. 251(1), pages 2-21.
    17. W W Cooper & H Deng & Z Huang & S X Li, 2002. "Chance constrained programming approaches to technical efficiencies and inefficiencies in stochastic data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(12), pages 1347-1356, December.
    18. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    19. 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.
    20. Rajiv D. Banker, 1993. "Maximum Likelihood, Consistency and Data Envelopment Analysis: A Statistical Foundation," Management Science, INFORMS, vol. 39(10), pages 1265-1273, October.
    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. Rafael Benítez & Vicente Coll-Serrano & Vicente J. Bolós, 2021. "deaR-Shiny: An Interactive Web App for Data Envelopment Analysis," Sustainability, MDPI, vol. 13(12), pages 1-19, June.
    2. Cherchye, L. & Post, G.T., 2001. "Methodological Advances in Dea," ERIM Report Series Research in Management ERS-2001-53-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    3. 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.
    4. 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.
    5. Qunwei Wang & Ye Hang & Jin‐Li Hu & Ching‐Ren Chiu, 2018. "An alternative metafrontier framework for measuring the heterogeneity of technology," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(5), pages 427-445, August.
    6. 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.
    7. Aparicio, Juan & Monge, Juan F. & Ramón, Nuria, 2021. "A new measure of technical efficiency in data envelopment analysis based on the maximization of hypervolumes: Benchmarking, properties and computational aspects," European Journal of Operational Research, Elsevier, vol. 293(1), pages 263-275.
    8. Barbero, Javier & Zofío, José L., 2023. "The measurement of profit, profitability, cost and revenue efficiency through data envelopment analysis: A comparison of models using BenchmarkingEconomicEfficiency.jl," Socio-Economic Planning Sciences, Elsevier, vol. 89(C).
    9. Christian Hernández-Guedes & Jorge V Pérez-Rodríguez & Casiano Manrique-de-Lara-Peñate, 2024. "Input inefficiencies in the hotel industry. A non-radial directional performance measurement," Tourism Economics, , vol. 30(7), pages 1753-1779, November.
    10. Fukuyama, Hirofumi & Weber, William L., 2009. "A directional slacks-based measure of technical inefficiency," Socio-Economic Planning Sciences, Elsevier, vol. 43(4), pages 274-287, December.
    11. 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.
    12. Halická, Margaréta & Trnovská, Mária & Černý, Aleš, 2024. "A unified approach to radial, hyperbolic, and directional efficiency measurement in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 312(1), pages 298-314.
    13. Akther, Syed & Fukuyama, Hirofumi & Weber, William L., 2013. "Estimating two-stage network Slacks-based inefficiency: An application to Bangladesh banking," Omega, Elsevier, vol. 41(1), pages 88-96.
    14. Lampe, Hannes W. & Hilgers, Dennis, 2015. "Trajectories of efficiency measurement: A bibliometric analysis of DEA and SFA," European Journal of Operational Research, Elsevier, vol. 240(1), pages 1-21.
    15. 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.
    16. Chambers, Robert G., 2024. "Numeraire choice, shadow profit, and inefficiency measurement," European Journal of Operational Research, Elsevier, vol. 319(2), pages 658-668.
    17. Pastor, Jesus T. & Lovell, C.A. Knox & Aparicio, Juan, 2020. "Defining a new graph inefficiency measure for the proportional directional distance function and introducing a new Malmquist productivity index," European Journal of Operational Research, Elsevier, vol. 281(1), pages 222-230.
    18. Aparicio, Juan & Kapelko, Magdalena, 2019. "Accounting for slacks to measure dynamic inefficiency in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 278(2), pages 463-471.
    19. 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.
    20. 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.

    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:oprepe:v:12:y:2024:i:c:s2214716024000113. 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.journals.elsevier.com/operations-research-perspectives .

    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.