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Modelling weak disposability in data envelopment analysis under relaxed convexity assumptions

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  • Podinovski, Victor V.
  • Kuosmanen, Timo

Abstract

The treatment of undesirable (bad) outputs in models of efficiency and productivity analysis often requires replacing the assumption of free disposability of outputs by their weak disposability. In a recent publication the authors showed that the Kuosmanen technology is the only correct representation of the fully convex technology exhibiting weak disposability of bad and good outputs. In this paper we relax the assumption of full convexity and consider two further possibilities: the case in which only the output sets are assumed convex and the case in which no convexity is assumed at all. In the first case we show that, although the traditional Shephard technology of nonparametric production analysis satisfies the assumption of convex output sets, it is larger than necessary. Based on the minimum extrapolation principle, we develop a correct model that is based on the assumed axioms. The second case leads to the development of a weakly disposable analogue of the free disposable hull. To complete our study, we give a full axiomatic definition of the Shephard technology.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:211:y:2011:i:3:p:577-585
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    1. Podinovski, V. V., 2005. "Selective convexity in DEA models," European Journal of Operational Research, Elsevier, vol. 161(2), pages 552-563, March.
    2. Timo Kuosmanen, 2003. "Duality Theory of Non-convex Technologies," Journal of Productivity Analysis, Springer, vol. 20(3), pages 273-304, November.
    3. Timo Kuosmanen, 2005. "Weak Disposability in Nonparametric Production Analysis with Undesirable Outputs," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 87(4), pages 1077-1082.
    4. 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.
    5. AGRELL, Per J. & BOGETOFT, Peter & BROCK, Michael & TIND, Jorgen, 2005. "Efficiency evaluation with convex pairs," LIDAM Reprints CORE 1828, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Yang, Hongliang & Pollitt, Michael, 2009. "Incorporating both undesirable outputs and uncontrollable variables into DEA: The performance of Chinese coal-fired power plants," European Journal of Operational Research, Elsevier, vol. 197(3), pages 1095-1105, September.
    7. Podinovski, V. V., 2004. "On the linearisation of reference technologies for testing returns to scale in FDH models," European Journal of Operational Research, Elsevier, vol. 152(3), pages 800-802, February.
    8. Walter Briec & Kristiaan Kerstens & Philippe Venden Eeckaut, 2004. "Non-convex Technologies and Cost Functions: Definitions, Duality and Nonparametric Tests of Convexity," Journal of Economics, Springer, vol. 81(2), pages 155-192, February.
    9. V V Podinovski, 2004. "Bridging the gap between the constant and variable returns-to-scale models: selective proportionality in data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(3), pages 265-276, March.
    10. 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.
    11. Rong, Aiying & Hakonen, Henri & Lahdelma, Risto, 2006. "An efficient linear model and optimisation algorithm for multi-site combined heat and power production," European Journal of Operational Research, Elsevier, vol. 168(2), pages 612-632, January.
    12. Niels Christian Petersen, 1990. "Data Envelopment Analysis on a Relaxed Set of Assumptions," Management Science, INFORMS, vol. 36(3), pages 305-314, March.
    13. 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.
    14. 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.
    15. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    16. Kuosmanen, Timo, 2001. "DEA with efficiency classification preserving conditional convexity," European Journal of Operational Research, Elsevier, vol. 132(2), pages 326-342, July.
    17. Peter Bogetoft, 1996. "DEA on Relaxed Convexity Assumptions," Management Science, INFORMS, vol. 42(3), pages 457-465, March.
    18. Dyson, R. G. & Allen, R. & Camanho, A. S. & Podinovski, V. V. & Sarrico, C. S. & Shale, E. A., 2001. "Pitfalls and protocols in DEA," European Journal of Operational Research, Elsevier, vol. 132(2), pages 245-259, July.
    19. 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.
    20. Seiford, Lawrence M. & Zhu, Joe, 2002. "Modeling undesirable factors in efficiency evaluation," European Journal of Operational Research, Elsevier, vol. 142(1), pages 16-20, October.
    21. Lahdelma, Risto & Hakonen, Henri, 2003. "An efficient linear programming algorithm for combined heat and power production," European Journal of Operational Research, Elsevier, vol. 148(1), pages 141-151, July.
    22. Hasenkamp, Georg, 1976. "A study of multiple-output production functions : Klein's railroad study revisited," Journal of Econometrics, Elsevier, vol. 4(3), pages 253-262, August.
    23. Dekker, David & Post, Thierry, 2001. "A quasi-concave DEA model with an application for bank branch performance evaluation," European Journal of Operational Research, Elsevier, vol. 132(2), pages 296-311, July.
    24. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    25. Ehrgott, Matthias & Tind, Jørgen, 2009. "Column generation with free replicability in DEA," Omega, Elsevier, vol. 37(5), pages 943-950, October.
    26. Panzar, John C & Willig, Robert D, 1981. "Economies of Scope," American Economic Review, American Economic Association, vol. 71(2), pages 268-272, May.
    27. 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.
    28. Scheel, Holger, 2001. "Undesirable outputs in efficiency valuations," European Journal of Operational Research, Elsevier, vol. 132(2), pages 400-410, July.
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