Uncertain data envelopment analysis with imprecisely observed inputs and outputs. (English) Zbl 1428.90080
Summary: Data envelopment analysis (DEA) is a powerful analytical tool in operations research and management for measuring and estimating the efficiency of decision-making units. Both the inputs and the outputs are assumed to be known constants in the classical DEA models. However, in many cases, those data (e.g., carbon emissions and social benefit) cannot be measured in a precise way. Therefore, in this article, the inputs and outputs are considered as uncertain variables and a new uncertain DEA model is introduced. The sensitivity and stability of the new model are also analyzed. Finally, a numerical example of the new model is documented.
MSC:
| 90B50 | Management decision making, including multiple objectives |
| 90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |
Keywords:
data envelopment analysis; uncertainty theory; uncertain variable; sensitivity and stability analysisReferences:
| [1] | Banker, RD; Charnes, A; Cooper, WW, Some models for estimating technical and scale efficiencies in data envelopment analysis, Management Science, 30, 1078-1092, (1984) · Zbl 0552.90055 · doi:10.1287/mnsc.30.9.1078 |
| [2] | Charnes, A; Cooper, WW; Rhodes, E, Measuring the efficiency of decision making units, European Journal of Operational Resarch, 2, 429-444, (1978) · Zbl 0416.90080 · doi:10.1016/0377-2217(78)90138-8 |
| [3] | Charnes, A; Cooper, WW; Golany, B; Seiford, L; Stutz, J, Foundations of data envelopment analysis for Pareto-koopmans efficient empirical production functions, Journal of Econometrics, 30, 91-107, (1985) · Zbl 0582.90007 · doi:10.1016/0304-4076(85)90133-2 |
| [4] | Charnes, A; Haag, S; Jaska, P; Semple, J, Sensitivity of efficiency calculations in the additive model of data envelopment analysis, Journal of Systems Science, 23, 789-798, (1992) · Zbl 0749.90002 · doi:10.1080/00207729208949248 |
| [5] | Cooper, WW; Park, KS; Pastor, JT, RAM: A range adjusted measure of inefficiency for use with additive models, and relations to other models and measures in DEA, Journal of Productivity Analysis, 11, 5-24, (1999) · doi:10.1023/A:1007701304281 |
| [6] | Cooper, W. W., Seiford, L. M., & Tone, K. (2000). Data envelopment analysis: A comprehensive text with models, applications, references, and DEA-Solver software. Boston: Kluwer Academic. · Zbl 0990.90500 |
| [7] | Guo, P; Tanaka, H; Inuiguchi, M, Self-organizing fuzzy aggregation models to rank the objects with multiple attributes, IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 30, 573-580, (2000) |
| [8] | Kahneman, D; Tversky, A, Prospect theory: an analysis of decision under risk, Econometrica, 47, 263-292, (1979) · Zbl 0411.90012 · doi:10.2307/1914185 |
| [9] | Lertworasirikul, S; Fang, SC; Joines, JA; Nuttle, HLW, Fuzzy data envelopment analysis (DEA): A possibility approach, Fuzzy Sets and Systems, 139, 379-394, (2003) · Zbl 1047.90080 · doi:10.1016/S0165-0114(02)00484-0 |
| [10] | Lertworasirikul, S; Fang, SC; Joines, JA; Nuttle, HLW; Verdegay, JL (ed.), Fuzzy data envelopment analysis: A credibility approach, 141-158, (2003), Berlin · Zbl 1051.90040 · doi:10.1007/978-3-540-36461-0_10 |
| [11] | Liu, B. (2007). Uncertainty theory (2nd ed.). Berlin: Springer. · Zbl 1141.28001 |
| [12] | Liu, B. (2009a). Theory and practice of uncertain programming (2nd ed.). Berlin: Springer. · Zbl 1158.90010 · doi:10.1007/978-3-540-89484-1 |
| [13] | Liu, B, Some research problems in uncertain theory, Journal of Uncertain Systems, 3, 3-10, (2009) |
| [14] | Liu, B. (2010). Uncertainty theory: A branch of mathematics for modeling human uncertainty. Berlin: Springer. · doi:10.1007/978-3-642-13959-8 |
| [15] | Liu, B, Why is there a need for uncertainty theory, Journal of Uncertain Systems, 6, 3-10, (2012) |
| [16] | Liu, B; Chen, XW, Uncertain multiobjective programming and uncertain goal programming, Journal of Uncertainty Analysis and Applications, 3, 10, (2015) · doi:10.1186/s40467-015-0036-6 |
| [17] | Liu, B; Yao, K, Uncertain multilevel programming: algorithm and applications, Computers and Industrial Engineering, 89, 235-240, (2015) · doi:10.1016/j.cie.2014.09.029 |
| [18] | Liu, YH; Ha, MH, Expected value of function of uncertain variables, Journal of Uncertain Systems, 4, 181-186, (2009) |
| [19] | Sengupta, JK, A fuzzy systems approach in data envelopment analysis, Computers and Industrial Engineering, 24, 259-266, (1992) · Zbl 0765.90004 |
| [20] | Sengupta, JK, Measuring efficiency by a fuzzy statistical approach, Fuzzy Sets and Systems, 46, 73-80, (1992) · doi:10.1016/0165-0114(92)90268-9 |
| [21] | Triantis, KP; Girod, O, A mathematical programming approach for measuring technical efficiency in a fuzzy environment, Journal of Productivity Analysis, 10, 85-102, (1998) · doi:10.1023/A:1018350516517 |
| [22] | Wen, M. L. (2015). Uncertain data envelopment analysis. Berlin: Springer. · Zbl 1311.90002 · doi:10.1007/978-3-662-43802-2 |
| [23] | Wen, ML; Kang, R, Data envelopment analysis (DEA) with uncertain inputs and outputs, Journal of Applied Mathematics, 2, 1-7, (2014) |
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.
