Convex Input and Output Projections of Nonconvex Production Possibility Sets
In this paper we characterize the smallest production possibility set that contains a specified set of (input, output) combinations. In accordance with neoclassical production economics, this possibility set has convex projections into the input and output spaces (convex isoquants), and it satisfies the assumption of free disposability. We obtain it by means of a possibly infinite recursion which builds the possibility set as an ever larger union of convex sets. We remark on the nature of the approximations obtained by truncating the recursion, and we obtain a necessary and sufficient condition, checkable in one iteration for the recursion to stop in the next. For the case in which the recursion stops, we provide a succinct characterization of the dominance relations among the constituent sets produced by the procedure. Finally, we present examples of both finite and infinite cases. The example for the finite case illustrates the construction of the possibility set along with its associated production and consumption sets.
Volume (Year): 46 (2000)
Issue (Month): 6 (June)
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- Banker, Rajiv D. & Thrall, R. M., 1992. "Estimation of returns to scale using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 62(1), pages 74-84, October.
- Banker, Rajiv D., 1984. "Estimating most productive scale size using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 17(1), pages 35-44, July.
- Russell, R. Robert, 1985. "On the Axiomatic Approach to the Measurement of Technical Efficiency," Working Papers 85-33, C.V. Starr Center for Applied Economics, New York University.
- Henry Tulkens, 1993. "On FDH efficiency analysis: Some methodological issues and applications to retail banking, courts, and urban transit," Journal of Productivity Analysis, Springer, vol. 4(1), pages 183-210, June.
- KERSTENS, Kristiaan & VANDEN EECKAUT, Philippe, 1997.
"Estimating returns to scale using nonparametric deterministic technologies : a new method based on goodness-of-fit,"
CORE Discussion Papers
1997013, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Kerstens, Kristiaan & Vanden Eeckaut, Philippe, 1999. "Estimating returns to scale using non-parametric deterministic technologies: A new method based on goodness-of-fit," European Journal of Operational Research, Elsevier, vol. 113(1), pages 206-214, February.
- Peter Bogetoft, 1996. "DEA on Relaxed Convexity Assumptions," Management Science, INFORMS, vol. 42(3), pages 457-465, March.
- 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.
- Seiford, Lawrence M. & Thrall, Robert M., 1990. "Recent developments in DEA : The mathematical programming approach to frontier analysis," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 7-38.
- Robert Russell, R., 1985. "Measures of technical efficiency," Journal of Economic Theory, Elsevier, vol. 35(1), pages 109-126, February.
- Niels Christian Petersen, 1990. "Data Envelopment Analysis on a Relaxed Set of Assumptions," Management Science, INFORMS, vol. 36(3), pages 305-314, March.
- DE BORGER, Bruno & KERSTENS, Kristiaan, 1994.
"Cost efficiency of Belgian local governments: A comparative analysis of FDH, DEA and econometric approaches,"
SESO Working Papers
1994002, University of Antwerp, Faculty of Applied Economics.
- De Borger, Bruno & Kerstens, Kristiaan, 1996. "Cost efficiency of Belgian local governments: A comparative analysis of FDH, DEA, and econometric approaches," Regional Science and Urban Economics, Elsevier, vol. 26(2), pages 145-170, April.
- 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.
- Chang, Kuo-Ping & Guh, Yeah-Yuh, 1991. "Linear production functions and the data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 52(2), pages 215-223, May.
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