# Sensitivity and stability in stochastic data envelopment analysis

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## Abstract

Sensitivity and stability for Banker's model of Stochastic Data Envelopment Analysis (SDEA) is studied in this paper. In the case of the DEA model, necessary and sufficient conditions to preserve the efficiency of efficient decision-making units (DMUs) and the inefficiency of inefficient DMUs are obtained for different perturbations of data in the model. The cases of perturbations of all inputs, of perturbations of output and of the simultaneous perturbations of output and all inputs are considered. An illustrative example is provided.

## Keywords

data envelopment analysis linear programming stochastic DEA model sensitivity and stability analysis perturbations of data preserving the efficiency and inefficiency of DMUs## Notes

### Acknowledgements

This research was partly supported by Grant No. 067-0000000-1076 of the Ministry of Science, Education and Sports of the Republic of Croatia. The authors are grateful to two anonymous referees whose suggestions improved the paper.

## References

- Asgharian M, Khodabakhshi M and Neralić L (2010). Congestion in stochastic data envelopment analysis: An input relaxation approach. International Journal of Statistics and System Science 5 (1–2): 84–106.Google Scholar
- Banker RD (1988). Stochastic data envelopment analysis. Working Paper, Carnegie Mellon University, http://astro.temple.edu/~banker/DEA/18.pdf, accessed 27 November 2012.
- Banker RD (1993). Maximum likelihood, consistency and data envelopment analysis: A statistical foundation. Management Science 39 (10): 1265–1273.CrossRefGoogle Scholar
- Banker RD, Das S and Datar SM (1989). Analysis of cost variances for management control in hospitals. Research in Governmental and Nonprofit Accounting 5: 269–292.Google Scholar
- Banker RD, Datar SM and Kemerer CF (1991). A model to evaluate variables impacting the productivity of software maintenance projects. Management Science 37 (1): 1–18.CrossRefGoogle Scholar
- Charnes A and Neralić L (1990). Sensitivity analysis of the additive model in data envelopment analysis. European Journal of Operational Research 48 (3): 332–341.CrossRefGoogle Scholar
- Charnes A and Neralić L (1992a). Sensitivity analysis in data envelopment analysis 3. Glasnik Matematički 27 (1): 191–201.Google Scholar
- Charnes A and Neralić L (1992b). Sensitivity analysis of the proportionate change of inputs (or outputs) in data envelopment analysis. Glasnik Matematički 27 (2): 393–405.Google Scholar
- Charnes A, Cooper WW, Lewin AY, Morey RC and Rousseau J (1985). Sensitivity and stability analysis in DEA. Annals of Operations Research 2 (1): 139–156.CrossRefGoogle Scholar
- Collier T, Johnson AL and Ruggiero J (2011). Technical efficiency estimation with multiple inputs and multiple outputs using regression analysis. European Journal of Operational Research 208 (2): 153–160.CrossRefGoogle Scholar
- Cooper WW, Huang ZM, Lelas V, Li SX and Olesen OB (1998). Chance constrained programming formulations for stochastic characterizations of efficiency and dominance in DEA. Journal of Productivity Analysis 9 (1): 53–79.CrossRefGoogle Scholar
- Cooper WW, Li S, Seiford LM, Tone K, Thrall RM and Zhu J (2001). Sensitivity and stability analysis in DEA: Some recent developments. Journal of Productivity Analysis 15 (3): 217–246.CrossRefGoogle Scholar
- Cooper WW, Deng H, Huang ZM and Li SX (2002). Chance constrained programming approaches to technical efficiencies and inefficiencies in stochastic data envelopment analysis. Journal of the Operational Research Society 53 (12): 1347–1356.CrossRefGoogle Scholar
- Cooper WW, Deng H, Huang ZM and Li SX (2004). Chance constrained programming approaches to congestion in stochastic data envelopment analysis. European Journal of Operational Research 155 (2): 487–501.CrossRefGoogle Scholar
- Cooper WW, Seiford LM and Tone K (2006). Introduction to Data Envelopment Analysis and Its Uses with DEA-Solver Software and References. Springer Science+Business Media: New York.Google Scholar
- Desai A, Ratick SJ and Shinar AP (2005). Data envelopment analysis with stochastic variations in data. Socio-Economic Planning Sciences 39 (2): 147–164.CrossRefGoogle Scholar
- Golub GH and Van Loan CF (1983). Matrix Computations. Johns Hopkins University Press: Baltimore, MD.Google Scholar
- Grosskopf S (1996). Statistical inference and nonparametric efficiency: A selective survey. Journal of Productivity Analysis 7 (2–3): 161–176.CrossRefGoogle Scholar
- Huang ZM and Li SX (1996). Dominance stochastic models in data envelopment analysis. European Journal of Operational Research 95 (2): 390–403.CrossRefGoogle Scholar
- Huang ZM and Li SX (2001). Stochastic DEA models with different types of input-output disturbances. Journal of Productivity Analysis 15 (2): 95–113.CrossRefGoogle Scholar
- Kao C and Liu ST (2009). Stochastic data envelopment analysis in measuring the efficiency of Taiwan commercial banks. European Journal of Operational Research 196 (1): 312–322.CrossRefGoogle Scholar
- Khodabakhshi M (2009). Estimating most productive scale size with stochastic data in data envelopment analysis. Economic Modelling 26 (5): 968–973.CrossRefGoogle Scholar
- Khodabakhshi M (2010a). Chance constrained additive input relaxation model in stochastic data envelopment analysis. International Journal of Information and Systems Sciences 6 (1): 99–112.Google Scholar
- Khodabakhshi M (2010b). An output-oriented super-efficiency measure in stochastic data envelopment analysis: Considering Iranian electricity distribution companies. Computers & Industrial Engineering 58 (4): 663–671.CrossRefGoogle Scholar
- Khodabakhshi M and Asgharian M (2009). An input relaxation measure of efficiency in stochastic data envelopment analysis. Applied Mathematical Modelling 33 (4): 2010–2023.CrossRefGoogle Scholar
- Khodabakhshi M, Asgharian M and Gregoriu GN (2010). An input-oriented super-efficiency measure in stochastic data envelopment analysis: Evaluating chief executive officers of US public banks and thrifts. Expert Systems With Applications: An International Journal 37 (3): 2092–2097.CrossRefGoogle Scholar
- Kousmanen T and Johnson AL (2010). Data envelopment analysis as nonparametric least-squares regression. Operations Research 58 (1): 149–160.CrossRefGoogle Scholar
- Kousmanen T and Kortelainen M (2012). Stochastic non-smooth envelopment of data: Semi-parametric frontier estimation subject to shape constraints. Journal of Productivity Analysis 38 (1): 11–28.CrossRefGoogle Scholar
- Li SX (1998). Stochastic models and variable returns to scales in data envelopment analysis. European Journal of Operational Research 104 (3): 532–548.CrossRefGoogle Scholar
- Morita H and Seiford LM (1999). Characteristics on stochastic DEA efficiency—Reliability and probability being efficient. Journal of the Operations Research Society of Japan 42 (4): 389–404.CrossRefGoogle Scholar
- Murty KG (1983). Linear Programming. John Wiley & Sons: New York.Google Scholar
- Neralić L (1997). Sensitivity in data envelopment analysis for arbitrary perturbations of data. Glasnik Matematički 32 (2): 315–335.Google Scholar
- Neralić L (1998). Sensitivity analysis in models of data envelopment analysis. Mathematical Communications 3 (1): 41–59.Google Scholar
- Neralić L (2004). Preservation of efficiency and inefficiency classification in data envelopment analysis. Mathematical Communications 9 (1): 51–62.Google Scholar
- Neralić L and Wendell RE (2004). Sensitivity in data envelopment analysis using an approximate inverse matrix. Journal of the Operational Research Society 55 (11): 1187–1193.CrossRefGoogle Scholar
- Ray SC (2004). Data Envelopment Analysis Theory and Techniques for Economics and Operations Research. Cambridge University Press: Cambridge.CrossRefGoogle Scholar
- Ruggiero J (2004). Data envelopment analysis with stochastic data. Journal of the Operational Research Society 55 (9): 1008–1012.CrossRefGoogle Scholar
- Sengupta JK (1987). Data envelopment analysis for efficiency measurement in the stochastic case. Computers and Operations Research 14 (2): 117–129.CrossRefGoogle Scholar
- Sengupta JK (1998). Stochastic data envelopment analysis: A new approach. Applied Economics Letters 5 (5): 287–290.CrossRefGoogle Scholar
- Sengupta JK (2000a). Efficiency analysis by stochastic data envelopment analysis. Applied Economic Letters 7 (6): 379–383.CrossRefGoogle Scholar
- Sengupta JK (2000b). Dynamic and Stochastic Efficiency Analysis: Economics of Data Envelopment Analysis. World Scientific Publishing Company: Singapore.CrossRefGoogle Scholar
- Sueyoshi T (2000). Stochastic DEA for restructure strategy: An application to a Japanese petroleum company. Omega 28 (4): 385–398.CrossRefGoogle Scholar
- Watson J, Wickramanayke J and Premachandra IM (2011). The value of Morningstar ratings: Evidence using stochastic data envelopment analysis. Managerial Finance 37 (2): 94–116.CrossRefGoogle Scholar