×

Translation invariance in data envelopment analysis. (English) Zbl 0711.90006

Summary: Conditions are established under which data envelopment analysis (DEA) models are translation invariant. Specifically, an affine displacement does not alter the efficient frontier for models incorporating the convexity constraint. This affords a ready solution to the problems of scaling and the presence of zero values which arise in DEA.

MSC:

91B06 Decision theory
91B38 Production theory, theory of the firm
90C05 Linear programming
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ahn, T.; Charnes, A.; Cooper, W. W., A note on the efficiency characterizations obtained in different DEA models, Socio-Econom. Plan. Sci., 6, 253-257 (1988)
[2] Banker, R. D.; Charnes, A.; Cooper, W. W., Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Sci., 30, 9, 1078-1092 (1984) · Zbl 0552.90055
[3] Banker, R. D.; Morey, R. C., Efficiency analysis for exogenously fixed inputs and outputs, Oper. Res., 34, 4 (1986) · Zbl 0609.90074
[4] Banker, R. D.; Morey, R. C., The use of categorical variables in data envelopment analysis, Management Sci., 32, 12, 1613-1627 (1986)
[5] Charnes, A.; Cooper, W. W., Preface to topics in DEA, Ann. Oper. Res., 2, 59-94 (1985)
[6] Charnes, A.; Cooper, W. W.; Golany, B.; Seiford, L.; Stutz, J., Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions, J. Econom., 30, 1/2, 91-107 (1985) · Zbl 0582.90007
[7] Charnes, A.; Cooper, W. W.; Rhodes, E., Measuring the efficiency of decision making units, Eur. J. Oper. Res., 2, 6, 429-444 (1978) · Zbl 0416.90080
[8] Charnes, A.; Cooper, W. W.; Rhodes, E., Short communication: Measuring the efficiency of decision making units, Eur. J. Oper. Res., 3, 4, 339 (1979) · Zbl 0425.90086
[9] Charnes, A.; Cooper, W. W.; Rousseau, J.; Semple, J., Data envelopment analysis and axiomatic notions of efficiency and reference sets, (Research Report CCS 558 (1987), Center for Cybernetic Studies, The University of Texas: Center for Cybernetic Studies, The University of Texas Austin, TX)
[10] Charnes, A.; Cooper, W. W.; Seiford, L.; Stutz, J., Invariant multiplicative efficiency and piecewise Cobb-Douglas envelopments, Oper. Res. Lett., 2, 3, 101-103 (1983) · Zbl 0521.90066
[11] Charnes, A.; Cooper, W. W.; Thrall, R. M., Classifying and characterizing efficiencies and inefficiencies in data envelopment analysis, Oper. Res. Lett., 5, 3, 105-110 (1986) · Zbl 0605.90082
[12] Charnes, A.; Cooper, W. W.; Thrall, R. M., A structure for classifying and characterizing efficiencies and inefficiencies in data envelopment analysis, (Research Report CCS 512 (1986), Center for Cybernetic Studies, The University of Texas at Austin: Center for Cybernetic Studies, The University of Texas at Austin TX) · Zbl 0605.90082
[13] Seiford, L. M., A bibliography of data envelopment analysis (1978-1989), Version 5.0, (Technical Report (1990), Department of Industrial Engineering and Operations Research, University of Massachusetts: Department of Industrial Engineering and Operations Research, University of Massachusetts Amherst, MA)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.