Abstract
The two-stage network DEA models based on the framework that the efficiency of the whole stage is equal to the product of the efficiencies of two sub-stages can not only turn the ‘black box’ into the ‘glass box’ to identify the root causes of the inefficiency of the network system, but also consider the relationship between the two sub-stages within the whole stage. Nowadays, the two-stage network DEA models have been widely applied in the field of economy and management, such as green supply chain and reverse supply chain. Due to the novelty of evaluation indexes, these emerging research objects with network structure, such as green supply chain, involve not only traditional evaluation indexes such as cost and time, but also some novel evaluation indexes such as customer satisfaction and flexibility. However, these new evaluation indexes are difficult to quantify accurately, which will lead to the failure of the traditional two-stage network DEA models. Therefore, this paper attempts to extend the traditional two-stage network DEA models to the uncertain two-stage network DEA models with the application of uncertainty theory. In the new models, inputs, intermediates and outputs are considered to be uncertain variables to deal with the problem of inaccurate data. Finally, a numerical example of the uncertain two-stage network DEA models will be presented for illustration.
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References
Banker RD (1993) Maximum likelihood, consistency and DEA: statistical foundations. Manag Sci 39(10):1265–1273
Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Oper Res 2(6):429–444
Chen C (2009) A network-DEA model with new efficiency measures to incorporate the dynamic effect in production networks. Eur J Oper Res 194(3):687–699
Chen Y, Zhu J (2004) Measuring information technology’s indirect impact on firm performance. Inf Technol Manag J 5(1–2):9–22
Cook WD, Zhu J (2010) Network DEA: additive efficiency decomposition. Eur J Oper Res 207(2):1122–1129
Cook WD, Tone K, Zhu J (2014) Data envelopment analysis: prior to choosing a model. Omega 44:1–4
Dyckhoff H, Allen K (2001) Measuring ecological efficiency with data envelopment analysis (DEA). Eur J Oper Res 132(2):312–325
Esmaeilzadeh A, Matin RK (2019) Multi-period efficiency measurement of network production systems. Measurement 134:835–844
Fa̋re R, Grosskopf S (2000) Network DEA. Soc Econ Plan Sci 34(1):35–49
Hatami-Marbini A, Saati S (2018) Efficiency evaluation in two-stage data envelopment analysis under a fuzzy environment: a common-weights approach. Appl Soft Comput 72:156–165
Jiang B, Lio W, Li X (2019) An uncertain DEA model for scale efficiency evaluation. IEEE Trans Fuzzy Syst 27(8):1616–1624
Jiang B, Zou Z, Lio W, Li J (2020) The uncertain DEA models for specific scale efficiency identification. J Intell Fuzzy Syst 38:3403–3417
Kao C (2011) Efficiencies of two-stage systems with fuzzy data. Fuzzy Sets Syst 176(1):20–35
Kao C (2014) Network data envelopment analysis: a review. Eur J Oper Res 239(1):1–16
Kao C (2016) Efficiency decomposition and aggregation in network data envelopment analysis. Eur J Oper Res 255(3):778–786
Kao C, Hwang S (2008) Efficiency decomposition in two-stage data envelopment analysis: an application to non-life insurance companies in Taiwan. Eur J Oper Res 185(1):418–429
Lio W, Liu B (2018) Uncertain data envelopment analysis with imprecisely observed inputs and outputs. Fuzzy Optim Decis Mak 17:357–373
Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin
Liu B (2009) Theory and practice of uncertain programming, 2nd edn. Springer, Berlin
Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10
Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, Berlin
Liu B (2012) Why is there a need for uncertainty theory. J Uncertain Syst 6:3–10
Liu B, Chen X (2015) Uncertain multiobjective programming and uncertain goal programming. J Uncertain Anal Appl 3:10
Liu Y, Ha M (2010) Expected value of function of uncertain variables. J Uncertain Syst 4(3):181–186
Liu B, Yao K (2015) Uncertain multilevel programming: algorithm and application. Comput Ind Eng 89:235–240
Olesen OB, Petersen NC (2016) Stochastic data envelopment analysis-a review. Eur J Oper Res 251(1):2–21
Sadjadi SJ, Omrani H (2008) Data envelopment analysis with uncertain data: an application for iranian electricity distribution companies. Energy Policy 36(11):4247–4254
Seiford LM, Zhu J (1999) Profitability and marketability of the top 55 US commercial banks. Manag Sci 45(9):1270–1288
Sengupta JK (1982) Efficiency measurement in stochastic input-output systems. Int J Syst Sci 13(3):273–287
Sexton TR, Lewis HF (2003) Two-stage DEA: an application to major league baseball. J Prod Anal 19(2–3):227–249
Sueyoshi T (2000) Stochastic DEA for restructure strategy: an application to a Japanese petroleum company. Omega 28(4):385–398
Tavana M (2018) Efficiency decomposition and measurement in two-stage fuzzy DEA models using a bargaining game approach. Comput Ind Eng 118:394–408
Wanke P, Kalam Azad A, Emrouznejad A (2018) Efficiency in BRICS banking under data vagueness: a two-stage fuzzy approach. Glob Financ J 35:58–71
Wen M, Guo L, Kang R, Yang Y (2014) Data envelopment analysis with uncertain inputs and outputs. J Appl Math 2:1–7
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This work was supported by National Natural Science Foundation of China Grant No. 61873329 and supported by the Fundamental Research Funds for the Central Universities No. 201713011.
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Jiang, B., Chen, H., Li, J. et al. The uncertain two-stage network DEA models. Soft Comput 25, 421–429 (2021). https://doi.org/10.1007/s00500-020-05157-3
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DOI: https://doi.org/10.1007/s00500-020-05157-3