An input relaxation measure of efficiency in stochastic data envelopment analysis. (English) Zbl 1205.90209
Summary: We introduce stochastic version of an input relaxation model in data envelopment analysis (DEA). The input relaxation model, recently developed in DEA, is useful to resource management. This model allows more changes in the input combinations of decision making units than those in the observed inputs of evaluating decision making units. Using this extra flexibility in input combinations we can find better outputs. We obtain a non-linear deterministic equivalent to this stochastic model. It is shown that under fairly general conditions this non-linear model can be replaced by an ordinary deterministic DEA model. The model is illustrated using a real data set.
MSC:
| 90C15 | Stochastic programming |
| 90B50 | Management decision making, including multiple objectives |
| 90C08 | Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) |
| 90C31 | Sensitivity, stability, parametric optimization |
References:
| [1] | Charnes, A.; Cooper, W. W.; Rhodes, E., Measuring the efficiency of decision making units, Eur. J. Operat. Res., 2, 6, 429-444 (1978) · Zbl 0416.90080 |
| [2] | Charnes, A.; Zlobec, S., Stability of efficiency evaluations in data envelopment analysis, Z. Operat. Res., 33, 3, 167-179 (1989) · Zbl 0671.90080 |
| [3] | A. Charnes, W.W Cooper, M. Sears, S. Zlobec, Efficiency evaluations in perturbed data envelopment analysis. Parametric optimization and related topics, II (Eisenach, 1989), 38-49, Math. Res., 62, Akademie-Verlag, Berlin, 1991, 1989.; A. Charnes, W.W Cooper, M. Sears, S. Zlobec, Efficiency evaluations in perturbed data envelopment analysis. Parametric optimization and related topics, II (Eisenach, 1989), 38-49, Math. Res., 62, Akademie-Verlag, Berlin, 1991, 1989. · Zbl 0741.90072 |
| [4] | Cooper, W. W.; Thompson, R. G.; Thrall, R. M., Extensions and new developments in DEA, Ann. Operat. Res., 66, 47-89 (1996) · Zbl 0863.90003 |
| [5] | Cooper, W. W.; Deng, Hanghui; Gu, Bisheng; Li, Shanling; Thrall, R. M., Using DEA to improve the management of congestion in chinese industries (1981-1997), Socio-Econ. Plan. Sci., 35, 227-242 (2001) |
| [6] | Jahanshahloo, G. R.; Khodabakhshi, M., Suitable combination of inputs for improving outputs in DEA with determining input congestion, Appl. Math. Comput., 151, 1, 263-273 (2004) · Zbl 1043.90538 |
| [7] | Jahanshahloo, G. R.; Khodabakhshi, M., Determining assurance interval for non-Archimedean element in the improving outputs model in DEA, Appl. Math. Comput., 151, 2, 501-506 (2004) · Zbl 1049.90030 |
| [8] | Khodabakhshi, M., A super-efficiency model based on improved outputs in data envelopment analysis, Appl. Math. Comput., 184, 2, 695-703 (2007) · Zbl 1149.90077 |
| [9] | Cooper, W. W.; Huang, Z. M.; Li, S. X., Satisfying DEA models under chance constraints, Ann. Operat. Res., 66, 3-45 (1996) · Zbl 0863.90003 |
| [10] | Cooper, W. W.; Huang, Z. M.; Lelas, V.; Li, S. X.; Olesen, O. B., Chance constrained programming formulations for stochastic characterizations of efficiency and dominance in DEA, J. Product. Anal., 9, 53079 (1998) |
| [11] | Li, S. X., Stochastic models and variable returns to scales in data envelopment analysis, Eur. J. Operat. Res., 104, 532-548 (1998) · Zbl 0960.90508 |
| [12] | Morita, Hiroshi; Seiford, L. M., Characteristics on stochastic DEA efficiency, J. Operat. Res. Soc. Jpn., 42, 4, 389-404 (1999) · Zbl 0998.90059 |
| [13] | Jess, A.; Jongen, H. Th.; Neralić, L.; Stein, O. A., Semi-infinite programming model in data envelopment analysis, Optimization, 49, 4, 369-385 (2001) · Zbl 0988.90044 |
| [14] | Sengupta, J. K., Data envelopment analysis for efficiency measurement in the stochastic case, Comput. Operat. Res., 14, 117-129 (1987) · Zbl 0617.90051 |
| [15] | Banker, R. D.; Charnes, A.; Cooper, W. W., Some models for estimating technical and scale inefficiencies in data envelopment analysis, Manage. Sci., 30, 1078-1092 (1984) · Zbl 0552.90055 |
| [16] | Ali, A. I.; Seiford, L. M., Computational accuracy and Infinitesimals in data envelopment analysis, INFOR, 31, 4, 290-297 (1993) · Zbl 0800.90086 |
| [17] | Mehrabian, S.; Jahanshahloo, G. R.; Alirezaee, M. R., An assurance interval for the non-Archimedean epsilon in DEA models, Operat. Res., 48, 2, 344-347 (1999) |
| [18] | Huang, Z.; Li, S. X., Dominance stochastic models in data envelopment analysis, Eur. J. Operat. Res., 95, 390-403 (1996) · Zbl 0943.90587 |
| [19] | Cooper, W. W.; Deng, H.; Huang, Zhimin; Li, Susan X., Chance constrained programming approaches to congestion in stochastic data envelopment analysis, Eur. J. Operat. Res., 155, 2, 487-501 (2004) · Zbl 1043.90038 |
| [20] | Lahdelma, R.; Salminen, P., Stochastic multicriteria acceptability analysis using the data envelopment model, Eur. J. Operat. Res., 170, 241-252 (2006) · Zbl 1079.90556 |
| [21] | Charnes, A.; Gallegos, A.; Hungyu, L., Robustly efficient parametric frontiers via multiplicative DEA for domestic and international operations of the Latin American airline industry, Eur. J. Operat. Res., 88, 3, 525-536 (1996) · Zbl 0913.90026 |
| [22] | Seiford, J. K.; Zhu, J., Sensitivity analysis of DEA models for simultaneous changes in all the data, J. Operat. Res. Soc., 10, 1060-1071 (1998) · Zbl 1140.90433 |
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