IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v37y2009i5p943-950.html
   My bibliography  Save this article

Column generation with free replicability in DEA

Author

Listed:
  • Ehrgott, Matthias
  • Tind, Jørgen

Abstract

The evaluation of efficiency scores in data envelopment analysis is based on the construction of artificial decision making units subject to some assumptions, usually requiring convexity of the production possibility set. This demands divisibility in input and output, which is not always possible. The so-called free replicability model, proposed by Henry Tulkens, permits input and output to enter in only discrete amounts. The model is of a mixed integer programming type, for which the number of variables, here corresponding to the decision making units, may be critical in order to reach an optimal solution. We suggest to use column generation techniques to include only those decision making units that may contribute to the creation of an optimal solution.

Suggested Citation

  • Ehrgott, Matthias & Tind, Jørgen, 2009. "Column generation with free replicability in DEA," Omega, Elsevier, vol. 37(5), pages 943-950, October.
    • Handle: RePEc:eee:jomega:v:37:y:2009:i:5:p:943-950
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305-0483(08)00113-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Cook, Wade D. & Bala, Kamel, 2007. "Performance measurement and classification data in DEA: Input-oriented model," Omega, Elsevier, vol. 35(1), pages 39-52, February.
    2. Tarja Joro & Pekka Korhonen & Jyrki Wallenius, 1998. "Structural Comparison of Data Envelopment Analysis and Multiple Objective Linear Programming," Management Science, INFORMS, vol. 44(7), pages 962-970, July.
    3. Per Agrell & Jørgen Tind, 2001. "A Dual Approach to Nonconvex Frontier Models," Journal of Productivity Analysis, Springer, vol. 16(2), pages 129-147, September.
    4. Valter Boljunčić, 2006. "Sensitivity Analysis of an Efficient DMU in DEA Model with Variable Returns to Scale (VRS)," Journal of Productivity Analysis, Springer, vol. 25(1), pages 173-192, April.
    5. Henry Tulkens, 2006. "On FDH Efficiency Analysis: Some Methodological Issues and Applications to Retail Banking, Courts and Urban Transit," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 311-342, Springer.
    6. 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.
    7. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
    8. W. Cooper & Shanling Li & L. Seiford & Kaoru Tone & R. Thrall & J. Zhu, 2001. "Sensitivity and Stability Analysis in DEA: Some Recent Developments," Journal of Productivity Analysis, Springer, vol. 15(3), pages 217-246, May.
    9. Peter Bogetoft & Joseph M. Tama & Jørgen Tind, 2000. "Convex Input and Output Projections of Nonconvex Production Possibility Sets," Management Science, INFORMS, vol. 46(6), pages 858-869, June.
    10. Peter Bogetoft, 1996. "DEA on Relaxed Convexity Assumptions," Management Science, INFORMS, vol. 42(3), pages 457-465, March.
    11. Timo Kuosmanen, 2003. "Duality Theory of Non-convex Technologies," Journal of Productivity Analysis, Springer, vol. 20(3), pages 273-304, November.
    12. Vanderbeck, F. & Wolsey, L. A., 1996. "An exact algorithm for IP column generation," LIDAM Reprints CORE 1242, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Kleine, A., 2004. "A general model framework for DEA," Omega, Elsevier, vol. 32(1), pages 17-23, February.
    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. Kuosmanen, Timo & Kazemi Matin, Reza, 2011. "Duality of weakly disposable technology," Omega, Elsevier, vol. 39(5), pages 504-512, October.
    2. Kazemi Matin, Reza & Kuosmanen, Timo, 2009. "Theory of integer-valued data envelopment analysis under alternative returns to scale axioms," Omega, Elsevier, vol. 37(5), pages 988-995, October.
    3. Podinovski, Victor V. & Kuosmanen, Timo, 2011. "Modelling weak disposability in data envelopment analysis under relaxed convexity assumptions," European Journal of Operational Research, Elsevier, vol. 211(3), pages 577-585, June.
    4. Li, Xiangyong & Aneja, Y.P. & Huo, Jiazhen, 2012. "A robust branch-and-cut approach for the minimum-energy symmetric network connectivity problem," Omega, Elsevier, vol. 40(2), pages 210-217, April.
    5. Walter Briec & Kristiaan Kerstens & Ignace Van de Woestyne, 2022. "Nonconvexity in Production and Cost Functions: An Exploratory and Selective Review," Springer Books, in: Subhash C. Ray & Robert G. Chambers & Subal C. Kumbhakar (ed.), Handbook of Production Economics, chapter 18, pages 721-754, Springer.
    6. Li, Xiangyong & Aneja, Y.P. & Huo, Jiazhen, 2012. "Using branch-and-price approach to solve the directed network design problem with relays," Omega, Elsevier, vol. 40(5), pages 672-679.
    7. 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.

    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. Fukuyama, Hirofumi & Shiraz, Rashed Khanjani, 2015. "Cost-effectiveness measures on convex and nonconvex technologies," European Journal of Operational Research, Elsevier, vol. 246(1), pages 307-319.
    2. Podinovski, Victor V. & Kuosmanen, Timo, 2011. "Modelling weak disposability in data envelopment analysis under relaxed convexity assumptions," European Journal of Operational Research, Elsevier, vol. 211(3), pages 577-585, June.
    3. Kuosmanen, Timo & Cherchye, Laurens & Sipilainen, Timo, 2006. "The law of one price in data envelopment analysis: Restricting weight flexibility across firms," European Journal of Operational Research, Elsevier, vol. 170(3), pages 735-757, May.
    4. 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.
    5. 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.
    6. Podinovski, V. V., 2005. "Selective convexity in DEA models," European Journal of Operational Research, Elsevier, vol. 161(2), pages 552-563, March.
    7. Jean-Paul Chavas & Kwansoo Kim, 2015. "Nonparametric analysis of technology and productivity under non-convexity: a neighborhood-based approach," Journal of Productivity Analysis, Springer, vol. 43(1), pages 59-74, February.
    8. Walter Briec & Kristiaan Kerstens & Ignace Van de Woestyne, 2022. "Nonconvexity in Production and Cost Functions: An Exploratory and Selective Review," Springer Books, in: Subhash C. Ray & Robert G. Chambers & Subal C. Kumbhakar (ed.), Handbook of Production Economics, chapter 18, pages 721-754, Springer.
    9. Kuosmanen, Timo, 2001. "DEA with efficiency classification preserving conditional convexity," European Journal of Operational Research, Elsevier, vol. 132(2), pages 326-342, July.
    10. Agrell, Per J. & Bogetoft, Peter & Tind, Jorgen, 2000. "Polarity in DEA Models," Unit of Economics Working Papers 24188, Royal Veterinary and Agricultural University, Food and Resource Economic Institute.
    11. Monge, Juan F. & Ruiz, José L., 2023. "Setting closer targets based on non-dominated convex combinations of Pareto-efficient units: A bi-level linear programming approach in Data Envelopment Analysis," European Journal of Operational Research, Elsevier, vol. 311(3), pages 1084-1096.
    12. Timo Kuosmanen, 2003. "Duality Theory of Non-convex Technologies," Journal of Productivity Analysis, Springer, vol. 20(3), pages 273-304, November.
    13. Post, Thierry, 2001. "Estimating non-convex production sets - imposing convex input sets and output sets in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 131(1), pages 132-142, May.
    14. Kristiaan Kerstens & Ignace Van de Woestyne, 2018. "Enumeration algorithms for FDH directional distance functions under different returns to scale assumptions," Annals of Operations Research, Springer, vol. 271(2), pages 1067-1078, December.
    15. Botti, Laurent & Briec, Walter & Cliquet, Gérard, 2009. "Plural forms versus franchise and company-owned systems: A DEA approach of hotel chain performance," Omega, Elsevier, vol. 37(3), pages 566-578, June.
    16. Harald Dyckhoff & Katrin Allen, 1999. "Theoretische Begründung einer Effizienzanalyse mittels Data Envelopment Analysis (DEA)," Schmalenbach Journal of Business Research, Springer, vol. 51(5), pages 411-436, May.
    17. H Leleu, 2009. "Mixing DEA and FDH models together," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(12), pages 1730-1737, December.
    18. Pham, Manh D. & Zelenyuk, Valentin, 2019. "Weak disposability in nonparametric production analysis: A new taxonomy of reference technology sets," European Journal of Operational Research, Elsevier, vol. 274(1), pages 186-198.
    19. Hougaard, Jens Leth & Tind, Jørgen, 2009. "Cost allocation and convex data envelopment," European Journal of Operational Research, Elsevier, vol. 194(3), pages 939-947, May.
    20. Castillo, Ignacio & Joro, Tarja & Li, Yong Yue, 2009. "Workforce scheduling with multiple objectives," European Journal of Operational Research, Elsevier, vol. 196(1), pages 162-170, July.

    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:jomega:v:37:y:2009:i:5:p:943-950. 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.elsevier.com/wps/find/journaldescription.cws_home/375/description#description .

    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.