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A semi-oriented radial measure for measuring the efficiency of decision making units with negative data, using DEA. (English) Zbl 1183.90230

Summary: Data Envelopment Analysis (DEA) is a nonparametric method for measuring the efficiency of a set of decision making units such as firms or public sector agencies, first introduced into the operational research and management science literature by A. Charnes, W. W. Cooper and E. L. Rhodes (CCR) [Eur. J. Oper. Res. 2, 429–444 (1978; Zbl 0416.90080)]. The original DEA models were applicable only to technologies characterized by positive inputs/outputs. In subsequent literature there have been various approaches to enable DEA to deal with negative data.In this paper, we propose a semi-oriented radial measure, which permits the presence of variables which can take both negative and positive values. The model is applied to data on a notional effluent processing system to compare the results with those yielded by two alternative methods for dealing with negative data in DEA: The modified slacks-based model suggested by J. A. Sharp et al. [A modified slacks-based measure model for data envelopment analysis with ‘natural’ negative outputs and inputs. J. Oper. Res. Soc. 57, No. 11, 1–6 (2006)] and the range directional model developed by M. C. A. S. Portela et al. [J. Oper. Res. Soc. 55, No. 10, 1111–1121 (2004; Zbl 1095.90063)]. A further example explores the advantages of using the new model.

MSC:

90B50 Management decision making, including multiple objectives
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[1] Ali, A.; Seiford, L. M., Translation invariance in data envelopment analysis, Operations Research Letters, 9, 403-405 (1990) · Zbl 0711.90006
[2] Banker, R. D.; Charnes, A.; Cooper, W. W., Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science, 30, 1078-1092 (1984) · Zbl 0552.90055
[3] Chambers, R. G.; Chung, Y.; Fare, R., Benefit and distance functions, Journal of Economic Theory, 70, 407-419 (1996) · Zbl 0866.90027
[4] Chambers, R. G.; Chung, Y.; Fare, R., Profit, directional distance functions, and Nerlovian efficiency, Journal of Optimization Theory and Applications, 98, 2, 351-364 (1998) · Zbl 0909.90040
[5] Charnes, A.; Cooper, W. W.; Rhodes, E., Measuring the efficiency of decision making units, European Journal of Operational Research, 2, 429-444 (1978) · Zbl 0416.90080
[6] Charnes, A.; Clark, T.; Cooper, W. W.; Golany, B., A developmental study of data envelopment analysis in measuring the efficiency of maintenance units in US. Air forces, Annals of Operational Research, 2, 95-112 (1985)
[7] Charnes, A.; Cooper, W. W.; Golany, B.; Seiford, L. M.; Stutz, J., Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions, Journal of Econometrics, 30, 1-2, 91-107 (1985) · Zbl 0582.90007
[8] Cooper, W. W.; Seiford, LM.; Tone, K., Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software (2000), Kluwer Academic Publishers
[9] Emrouznejad, A.; Parker, B. R.; Tavares, G., Evaluation of research in efficiency and productivity: A survey and analysis of the first 30years of scholarly literature in DEA, Socio-Economic Planning, 42, 3, 151-157 (2008)
[10] Lovell, C. A.K., Measuring the macroeconomic performance of the Taiwanese economy, International Journal of Production Economic, 39, 165-178 (1995)
[11] Lovell, C. A.K.; Pastor, J. T., Units invariant and translation invariant DEA models, Operations Research Letters, 18, 147-151 (1995) · Zbl 0855.90004
[12] Pastor, J.T., 1994. How to discount environmental effects in DEA: An application to bank branches. Working paper No. 011/94, Depto. De Estadistica e Investigacion Operativa, Universidad de Alicante, Spain.; Pastor, J.T., 1994. How to discount environmental effects in DEA: An application to bank branches. Working paper No. 011/94, Depto. De Estadistica e Investigacion Operativa, Universidad de Alicante, Spain.
[13] Pastor, J. T., Translation invariance in data envelopment analysis: A generalization, Annals of Operations Research, 66, 93-102 (1996) · Zbl 0863.90005
[14] Portela, M. C.A. S.; Thanassoulis, E.; Simpson, G., A directional distance approach to deal with negative data in DEA: An application to bank branches, Journal of Operational Research Society, 55, 10, 1111-1121 (2004) · Zbl 1095.90063
[15] Scheel, H., Undesirable outputs in efficiency valuations, European Journal of Operational Research, 132, 400-410 (2001) · Zbl 0985.90053
[16] Seiford, L. M.; Zhu, J., Modeling undesirable factors in efficiency evaluation, European Journal of Operational Research, 142, 16-20 (2002) · Zbl 1079.90565
[17] Sharp, J. A.; Liu, W. B.; Meng, W., A modified slacks-based measure model for data envelopment analysis with ‘natural’ negative outputs and inputs, Journal of Operational Research Society, 57, 11, 1-6 (2006)
[18] Thanassoulis, E., Introduction to the Theory and Application of Data Envelopment Analysis: A Foundation Text with Integrated Software (2001), Kluwer Academic Publishers: Kluwer Academic Publishers Boston
[19] Tone, K., A slacks-based measure of efficiency in data envelopment analysis, European Journal of Operational Research, 130, 498-509 (2001) · Zbl 0990.90523
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