Abstract
In conventional data envelopment analysis (DEA) models, the efficiency measurement is carried out by using deterministic data typically referring to past observations. However, in many operative contexts, decision makers are called to predict the future performance for planning and control purposes. In these situations, ignoring the stochastic nature of data might lead to misleading results. The paper proposes a stochastic DEA approach based on the chance constrained paradigm and accounts for risk measured in terms of tail \(\gamma \)-mean. A deterministic equivalent reformulation is presented under the assumption of discrete distributions. The computational experiments are carried out on an empirical case study related to the evaluation of the credit risk. The results demonstrate the validity of the proposed approach as proactive evaluation technique.
Similar content being viewed by others
References
Artzner, P., Delbaen, F., Eber, J.M., Heath, D.: Coherent measures of risk. Math. Finance 9, 203–228 (1999)
Banker, R.D.: Maximum likelihood, consistency and data envelopment analysis: a statistical foundation. Manag. Sci. 39(10), 1265–1273 (1993)
Beraldi, P., Bruni, M.E.: An exact approach for solving integer problems under probabilistic constraints with random technology matrix. Ann. Oper. Res. 177(1), 127–137 (2010)
Beraldi, P., Bruni, M.E.: Data envelopment analysis under uncertainty and risk. WASET 66, 837–842 (2012)
Beraldi, P., Bruni, M.E.: A clustering approach for scenario tree reduction: an application to a stochastic programming portfolio optimization problem. TOP 22, 934–949 (2014)
Beraldi, P., De Simone, F., Violi, A.: Generating scenario trees: a parallel integrated simulation–optimization approach. J. Comput. Appl. Math. 23(9), 2322–2331 (2010)
Beraldi, P., Bruni, M.E., Laganá, D.: The express heuristic for probabilistically constrained integer problems. J. Heurist. 19(3), 423–441 (2013)
Beraldi, P., Bruni, M.E., Iazzolino, G.: Lending decision under uncertainty: a DEA approach. Int. J. Prod. Res. 52(3), 766–775 (2014)
Bruni, M.E., Conforti, D., Beraldi, P., Tundis, E.: Probabilistically constrained models for efficiency and dominance in DEA. Int. J. Prod. Econ. 177(1), 219–228 (2009)
Chang, T.S., Tone, K., Wu, C.-H.: DEA models incorporating uncertain future performance. Eur. J. Oper. Res. 254(2), 532–549 (2016)
Charnes, A., Cooper, W.W.: Chance constrained programming. Manag. Sci. 5(1), 73–79 (1959)
Charnes, A., Cooper, W.W., Rhodes, E.: Measuring the efficiency of decision making units. Eur. J. Oper. Res. 6(2), 429–444 (1978)
Chen, K., Zhu, J.: Computational tractability of chance constrained data envelopment analysis. Eur. J. Oper. Res. 274(3), 1037–1046 (2019)
Cheng, J., Lisser, A.: A second-order cone programming approach for linear programs with joint probabilistic constraints. Oper. Res. Lett. 40(5), 325–328 (2012)
Cooper, W.W., Huang, Z., Li, S.: Satisficng DEA model under chance constraints. Ann. Oper. Res. 66(5), 79–295 (1996)
Cooper, W.W., Deng, H., Huang, Li S: Chance constrained programming approaches to congestion in stochastic data envelopment analysis. Eur. J. Oper. Res. 155(2), 487–501 (2004)
Iazzolino, G., Bruni, M.E., Beraldi, P.: Using DEA and financial ratios for credit risk evaluation: an empirical analysis. Appl. Econ. Lett. 20(14), 1310–1317 (2013)
Kao, C., Liu, S.-T.: Stochastic efficiency measures for production units with correlated data. Eur. J. Oper. Res. 273(1), 278–287 (2019)
Land, K.C., Lovell, C.A.K., Thore, S.: Chance-constrained data envelopment analysis. Manag. Decis. Econ. 14, 541–554 (1993)
Markowitz, H.M.: Portfolio selection. J. Finance 7, 77–91 (1952)
Ogryczak, W.: Tail mean and related robust solution concept. Int. J. Syst. Sci. 45, 29–38 (2014)
Ogryczak, W., Ruszczynski, A.: Dual stochastic dominance and related mean-risk models. SIAM J. Optim. 13, 60–78 (2002a)
Ogryczak, W., Ruszczynski, A.: Dual stochastic dominance and quantile risk measures. Int. Trans. Oper. Res. 9, 661–680 (2002b)
Olesen, O.B., Petersen, N.C.: Chance constrained efficiency evaluation. Manag. Sci. 41, 442–457 (1995)
Olesen, O.B., Petersen, N.C.: Stochastic data envelopment analysis: a review. Eur. J. Oper. Res. 251(1), 2–21 (2016)
Paradi, J.C., Asmild, M., Simak, P.: Using DEA and worst practice DEA in credit risk evaluation. J. Prod. Anal. 21, 153–165 (2004)
Post, T.: Performance evaluation in stochastic environments using mean–variance data envelopment analysis. Oper. Res. 49(2), 281–292 (2001)
Premachandra, I.M., Chen, Y., Watson, J.: DEA as a tool for predicting corporate failure and success: a case of bankruptcy assessment. Omega 39, 620–626 (2011)
Rockafellar, R.T., Uryasev, S.: Optimization of conditional value-at-risk. J. Risk 2, 21–41 (2000)
Sengupta, J.K.: Data envelopment analysis for efficiency measurement in the stochastic case. Comput. Oper. Res. 14, 117–129 (1987)
Sueyoshi, T.: Stochastic DEA for restructure strategy: an application to a Japanese petroleum company. Omega 28, 385–398 (2000)
Wei, G., Chen, J., Wang, J.: Stochastic efficiency analysis with a reliability consideration. Omega 48, 1–9 (2014)
Wu, D., Olson, D.: Enterprise risk management: a DEA VaR approach in vendor selection. Int. J. Prod. Res. 40(6), 4919–4932 (2010)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Beraldi, P., Bruni, M.E. Efficiency evaluation under uncertainty: a stochastic DEA approach. Decisions Econ Finan 43, 519–538 (2020). https://doi.org/10.1007/s10203-020-00295-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10203-020-00295-7