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doi: 10.3934/jimo.2022027
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Development of opened-network data envelopment analysis models under uncertainty

Yazd University, Yazd, Iran

*Corresponding author: Hasan Hosseini-Nasab

Received  April 2021 Revised  November 2021 Early access March 2022

Efficiency evaluation is a very important and key issue in competitive conditions. Organizations and companies face various uncertainties, and this makes it extremely difficult and complex to evaluate their efficiency. In this research, opened-network data envelopment analysis models have been developed in uncertain space for three uncertain states, including: uncertain outputs, uncertain inputs, and simultaneous uncertain inputs and outputs. The proposed models have been used to evaluate the efficiency of 10 two-stage processes, seller and buyer in a supply chain, and the impact of data uncertainty is examined. The results obtained from the developed models have been compared with the results of traditional DEA network models. The validity and accuracy of the developed models have also been examined. The results have shown that the reliability of the proposed models is higher than the traditional DEA network model. Also, by examining the efficiency of decision-making units in different conditions of data uncertainty and deviations, it was determined that the greater the range of this deviation, the lower the efficiency score of different units will be, which is consistent with reality.

Citation: Hasan Hosseini-Nasab, Vahid Ettehadi. Development of opened-network data envelopment analysis models under uncertainty. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022027
References:
[1]

M. J. Farrell, The measurement of productive efficiency, Journal of the Royal Statistical Society, 120 (1957), 253-290. 

[2]

A. CharnesW. W. Cooper and E. Rhodes, measuring the efficiency of decision making units, European Journal of Operational Research, 2 (1978), 429-444.  doi: 10.1016/0377-2217(78)90138-8.

[3]

R. Fare and S. Grosskopf, Network DEA. Socio-Econom-ic Planning Sciences, 32 (2000), 23-40.

[4]

L. Liang and F. Yang, DEA models for supply chain efficiency evaluation, Annals of Operations Research, 145 (2006), 35-49.  doi: 10.1007/s10479-006-0026-7.

[5]

C. Chen and H. Yan, Network DEA model for supply chain performance evaluation, European journal of operational research, 213 (2011), 147-155.  doi: 10.1016/j.ejor.2011.03.010.

[6]

A. Ebrahimnejad, M. Tavana and F. Hoseinzadeye lotfi, A three-stage data envelopment analysis model with application to banking industry, Measurement, 49 (2014), 308-319.

[7]

C. Kao, Efficiency decomposition for general multi-stage systems in data envelopment analysis. European Journal of Operational Research, 232 (2014), 117-124. doi: 10.1016/j.ejor.2013.07.012.

[8]

W.D. Cook, J. Zhou and G. Bi, Network DEA: Additive efficiency decomposition, European journal of operational research, 207 (2010), 1122-1129.

[9]

C. Y. Lee and A. L. Johnson, Two-dimensional efficiency decomposition to measure the demand effect in productivity analysis, European Journal of Operational Research, 216 (2012), 584-593.

[10]

W. W. Cooper, Chance constrained programming approaches to congestion in stochastic data envelopment analysis, European Journal of Operational Research, 155 (2004), 487-501. doi: 10.1016/S0377-2217(02)00901-3.

[11]

Y. M. Wang, R. Greatbanks and J. B. Yang, Interval efficiency assessment using data envelopment analysis, Fuzzy sets and Systems, 153 (2005), 347-370. doi: 10.1016/j.fss.2004.12.011.

[12]

A. Hatami-Marbini, A. Emrouznejad and M. Tavana, A taxonomy and review of the fuzzy data envelopment analysis literature: two decades in the making, European journal of operational research, 214 (2011), 457-472. doi: 10.1016/j.ejor.2011.02.001.

[13]

P. Peykani, E. Mohammadi, A. Emrouznejad, M. S. Pishvaee and M. Rostamy-Malkhalifeh, Fuzzy data envelopment analysis: an adjustable approach, Expert Systems with Applications, 136 (2019), 439-452.

[14]

A. L. Soyster, Convex programming with set-inclusive constraints and applications to inexact linear programming, Operations research, 21 (1973), 1154-1157. doi: 10.1287/opre.22.4.892.

[15]

A. Ben-Tal and A. Nemirovski, Lectures on modern convex optimization: analysis, algorithms, and engineering applications, Georgia Institute of Technology, Atlanta Georgia USA, 2001.

[16]

D. Bertsimas and M. Sim, The price of robustness. Operations research, 52 (2004), 35-53. doi: 10.1287/opre.1030.0065.

[17]

J. Nouri and H. Lotfi, An analysis of the implementation of energy efficiency measures in the vegetable oil industry of Iran: a data envelopment analysis approach, Journal of Cleaner Production, 52 (2013), 84-93.

[18]

M. Tsutsui and M. Goto, A multi-division efficiency evaluation of US electric power companies using a weighted slacks-based measure, Socio-Economic Planning Sciences, 43 (2009), 201-208.

[19]

G. Bi, N. Feng and F. Diang,. Estimating relative efficiency of DMU: Pareto principle and Monte Carlo oriented DEA approach, Information Systems and Operational Research, 50 (2012), 44-57. doi: 10.3138/infor.50.1.044.

[20]

C. Kao, Network data envelopment analysis: A review, European journal of operational research, 239 (2014), 1-16. doi: 10.1016/j.ejor.2014.02.039.

[21]

J. Ruggiero, Data envelopment analysis with stochastic data, Journal of the Operational Research Society, 55 (2004), 1008-1012.

[22]

S. J. Sadjadi, H. Omrani and A. Makouei, An interactive robust data envelopment analysis model for determining alternative targets in Iranian electricity distribution companies, Expert Systems with Applications, 38 (2011), 9830-9839.

[23]

A. H. Shokouhi and M. Tavana, A robust optimization approach for imprecise data envelopment analysis, Computers and Industrial Engineering, 59 (2010), 387-397.

[24]

H. Omrani, F. Adabi and N. Adabi, Designing an efficient supply chain network with uncertain data: a robust optimization-data envelopment analysis approach, Journal of the Operational Research Society, 68 (2017), 816-828.

[25]

T. Zu, M. Wen and R. Kang, An optimal evaluating method for uncertainty metrics in reliability based on uncertain data envelopment analysis, Microelectronics Reliability, 75 (2017), 283-287.

[26]

M. Ehrgott, A. Holder, and O. Nohadani, Uncertain data envelopment analysis, European Journal of Operational Research, 268 (2018), 231-242. doi: 10.1016/j.ejor.2018.01.005.

[27]

W. Lio and B. Liu, Uncertain data envelopment analysis with imprecisely observed inputs and outputs, Fuzzy Optimization and Decision Making, 17 (2018), 357-373. doi: 10.1007/s10700-017-9276-x.

[28]

N. Aghayi and M.A. Raayatpanah, A robust optimization approach to overall profit efficiency with data uncertainty: application on bank industry, Journal of the Chinese Institute of Engineers, 42 (2019), 160-168.

[29]

W. Hu, Y. Guo, J. Tian, and L. Chen, Eco-efficiency of centralized wastewater treatment plants in industrial parks: A slack-based data envelopment analysis, Resources, Conservation and Recycling, 141 (2019). 176-186.

[30]

G. Cavone, N. Epicoco, M. Morelli and M. Dotoli, Design of Modern Supply Chain Networks Using Fuzzy Bargaining Game and Data Envelopment Analysis, IEEE Transactions on Automation Science and Engineering, 45 (2020), 27-45.

[31]

D. De, S. Chowdhury, P. KumarDey and S.Ghosh, Impact of lean and sustainability oriented innovation on sustainability performance of small and medium sized enterprises: a data envelopment analysis-based framework, International Journal of Production Economics, 219 (2020), 416-430. doi: 10.1016/j.ijpe.2018.07.003.

[32]

C. Álvarez-Rodríguez, M. Martín-Gamboa and D. Iribarren, Sustainability-oriented efficiency of retail supply chains: A combination of Life Cycle Assessment and dynamic network Data Envelopment Analysis, Science of the Total Environment, 705 (2020), 135977.

[33]

O. B. Olesen and N. C. Petersen, Stochastic data envelopment analysis-A review, European journal of operational research, 251 (2016), 2-21. doi: 10.1016/j.ejor.2015.07.058.

show all references

References:
[1]

M. J. Farrell, The measurement of productive efficiency, Journal of the Royal Statistical Society, 120 (1957), 253-290. 

[2]

A. CharnesW. W. Cooper and E. Rhodes, measuring the efficiency of decision making units, European Journal of Operational Research, 2 (1978), 429-444.  doi: 10.1016/0377-2217(78)90138-8.

[3]

R. Fare and S. Grosskopf, Network DEA. Socio-Econom-ic Planning Sciences, 32 (2000), 23-40.

[4]

L. Liang and F. Yang, DEA models for supply chain efficiency evaluation, Annals of Operations Research, 145 (2006), 35-49.  doi: 10.1007/s10479-006-0026-7.

[5]

C. Chen and H. Yan, Network DEA model for supply chain performance evaluation, European journal of operational research, 213 (2011), 147-155.  doi: 10.1016/j.ejor.2011.03.010.

[6]

A. Ebrahimnejad, M. Tavana and F. Hoseinzadeye lotfi, A three-stage data envelopment analysis model with application to banking industry, Measurement, 49 (2014), 308-319.

[7]

C. Kao, Efficiency decomposition for general multi-stage systems in data envelopment analysis. European Journal of Operational Research, 232 (2014), 117-124. doi: 10.1016/j.ejor.2013.07.012.

[8]

W.D. Cook, J. Zhou and G. Bi, Network DEA: Additive efficiency decomposition, European journal of operational research, 207 (2010), 1122-1129.

[9]

C. Y. Lee and A. L. Johnson, Two-dimensional efficiency decomposition to measure the demand effect in productivity analysis, European Journal of Operational Research, 216 (2012), 584-593.

[10]

W. W. Cooper, Chance constrained programming approaches to congestion in stochastic data envelopment analysis, European Journal of Operational Research, 155 (2004), 487-501. doi: 10.1016/S0377-2217(02)00901-3.

[11]

Y. M. Wang, R. Greatbanks and J. B. Yang, Interval efficiency assessment using data envelopment analysis, Fuzzy sets and Systems, 153 (2005), 347-370. doi: 10.1016/j.fss.2004.12.011.

[12]

A. Hatami-Marbini, A. Emrouznejad and M. Tavana, A taxonomy and review of the fuzzy data envelopment analysis literature: two decades in the making, European journal of operational research, 214 (2011), 457-472. doi: 10.1016/j.ejor.2011.02.001.

[13]

P. Peykani, E. Mohammadi, A. Emrouznejad, M. S. Pishvaee and M. Rostamy-Malkhalifeh, Fuzzy data envelopment analysis: an adjustable approach, Expert Systems with Applications, 136 (2019), 439-452.

[14]

A. L. Soyster, Convex programming with set-inclusive constraints and applications to inexact linear programming, Operations research, 21 (1973), 1154-1157. doi: 10.1287/opre.22.4.892.

[15]

A. Ben-Tal and A. Nemirovski, Lectures on modern convex optimization: analysis, algorithms, and engineering applications, Georgia Institute of Technology, Atlanta Georgia USA, 2001.

[16]

D. Bertsimas and M. Sim, The price of robustness. Operations research, 52 (2004), 35-53. doi: 10.1287/opre.1030.0065.

[17]

J. Nouri and H. Lotfi, An analysis of the implementation of energy efficiency measures in the vegetable oil industry of Iran: a data envelopment analysis approach, Journal of Cleaner Production, 52 (2013), 84-93.

[18]

M. Tsutsui and M. Goto, A multi-division efficiency evaluation of US electric power companies using a weighted slacks-based measure, Socio-Economic Planning Sciences, 43 (2009), 201-208.

[19]

G. Bi, N. Feng and F. Diang,. Estimating relative efficiency of DMU: Pareto principle and Monte Carlo oriented DEA approach, Information Systems and Operational Research, 50 (2012), 44-57. doi: 10.3138/infor.50.1.044.

[20]

C. Kao, Network data envelopment analysis: A review, European journal of operational research, 239 (2014), 1-16. doi: 10.1016/j.ejor.2014.02.039.

[21]

J. Ruggiero, Data envelopment analysis with stochastic data, Journal of the Operational Research Society, 55 (2004), 1008-1012.

[22]

S. J. Sadjadi, H. Omrani and A. Makouei, An interactive robust data envelopment analysis model for determining alternative targets in Iranian electricity distribution companies, Expert Systems with Applications, 38 (2011), 9830-9839.

[23]

A. H. Shokouhi and M. Tavana, A robust optimization approach for imprecise data envelopment analysis, Computers and Industrial Engineering, 59 (2010), 387-397.

[24]

H. Omrani, F. Adabi and N. Adabi, Designing an efficient supply chain network with uncertain data: a robust optimization-data envelopment analysis approach, Journal of the Operational Research Society, 68 (2017), 816-828.

[25]

T. Zu, M. Wen and R. Kang, An optimal evaluating method for uncertainty metrics in reliability based on uncertain data envelopment analysis, Microelectronics Reliability, 75 (2017), 283-287.

[26]

M. Ehrgott, A. Holder, and O. Nohadani, Uncertain data envelopment analysis, European Journal of Operational Research, 268 (2018), 231-242. doi: 10.1016/j.ejor.2018.01.005.

[27]

W. Lio and B. Liu, Uncertain data envelopment analysis with imprecisely observed inputs and outputs, Fuzzy Optimization and Decision Making, 17 (2018), 357-373. doi: 10.1007/s10700-017-9276-x.

[28]

N. Aghayi and M.A. Raayatpanah, A robust optimization approach to overall profit efficiency with data uncertainty: application on bank industry, Journal of the Chinese Institute of Engineers, 42 (2019), 160-168.

[29]

W. Hu, Y. Guo, J. Tian, and L. Chen, Eco-efficiency of centralized wastewater treatment plants in industrial parks: A slack-based data envelopment analysis, Resources, Conservation and Recycling, 141 (2019). 176-186.

[30]

G. Cavone, N. Epicoco, M. Morelli and M. Dotoli, Design of Modern Supply Chain Networks Using Fuzzy Bargaining Game and Data Envelopment Analysis, IEEE Transactions on Automation Science and Engineering, 45 (2020), 27-45.

[31]

D. De, S. Chowdhury, P. KumarDey and S.Ghosh, Impact of lean and sustainability oriented innovation on sustainability performance of small and medium sized enterprises: a data envelopment analysis-based framework, International Journal of Production Economics, 219 (2020), 416-430. doi: 10.1016/j.ijpe.2018.07.003.

[32]

C. Álvarez-Rodríguez, M. Martín-Gamboa and D. Iribarren, Sustainability-oriented efficiency of retail supply chains: A combination of Life Cycle Assessment and dynamic network Data Envelopment Analysis, Science of the Total Environment, 705 (2020), 135977.

[33]

O. B. Olesen and N. C. Petersen, Stochastic data envelopment analysis-A review, European journal of operational research, 251 (2016), 2-21. doi: 10.1016/j.ejor.2015.07.058.

Figure 1.  Series Structure
Figure 2.  Series Opened-network Mode
Figure 3.  The Structure of the Network under Study
Figure 4.  Efficiency of Different Decision Units
Table 1.  Summary of the Subject Literature
Table 2.  Input and Output Data in Data Envelopment Analysis Model
Table 3.  Results of a Robust Model of Open Network Data Envelopment Analysis($ \hat \alpha $ = 0.05)
Table 4.  Results of a Robust Model of Open Network Data Envelopment Analysis ($ \hat \alpha $ = 0.1)
Table 5.  Results of Robust Model of Open Network Data Envelopment Analysis and Traditional Model
Table 6.  Pearson Correlation Coefficient for Different Models
Table 7.  Information of Decision Units in Terms of Deviation of the Second Stage Outputs
Table 8.  Results with a Deviation Percentage of 10%
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