Evaluation of productivity, efficiency and ranking of thermal power plants: an approach based on stochastic data envelopment analysis
Subject Areas :
1 - Department of Management, Dehaghan ,Branch, Islamic Azad University, Dehaghan, Iran
Keywords: Stochastic Data envelopment analysis, Undesirable outputs, stochastic cross-efficiency evaluation, expected ranking criterion, stochastic ranking priority,
Abstract :
In data envelopment analysis, different models are developed in different fields with different data for evaluation and ranking of DMUs. While in many applications issues, unit managers are faced with stochastic data, and they need a method to evaluate their supervised units in a way that can evaluate and rank such DMUs. When working with stochastic data, considering the probability of occurrence of unpredictable states (the level of error) provided by managers, the DMUs are evaluated. In this paper using Probability statistics techniques and normal distribution and the BCC model with undesirable outputs and a specific risk ofSpecified,a new stochastic model called Expected Ranking Criterion is introduced. Based on this,the stochastic cross-efficiency evaluation. Given the non-uniqueness of resulting optimal solutions, a model is introduced for rating priorities by which cross-efficiency is performed using aggressive method. The proposed model is implemented for 32 thermal power plants with stochastic inputs and undesirable outputs.
References:
References:
Andersen, P., Petersen, N.C., (1993).A procedure for ranking efficient units in data envelopment analysis. Management Science, 39 (10), 1261-1264.
Amirteimoori, A., Charles, V., & Mehdizadeh, S. (2023). Stochastic data envelopment analysis in the presence of undesirable outputs. Journal of the Operational Research Society, 1-14.
Banker RD, Charnes A and Cooper WW (1984). Some method for estimating technical and scale inefficiencies in data envelopment analysis. Management Science 30(9): 1078–1092.
Bruni ME, Conforti D, Beraldi P and Tundis E (2009). Probabilistically constrained models for efficiency and dominance in DEA. International Journal of Production Economics 117(1): 219–228.
Cooper WW, Huang ZM, Lelas V, Li SX and Olesen OB (1998). Chance constrained programming formulations for stochastic characterizations of efficiency and dominance in DEA. Journal of Productivity Analysis 9(1): 530–579.
Cooper WW, Deng H, Huang Z and Li Susan X (2002). Chance constrained programming approaches to technical efficiencies and inefficiencies in stochastic data envelopment analysis. Journal of the Operational Research Society 53(12): 1347–1356.
Cooper WW, Deng H, Huang ZM and Li SX (2004). Chance constrained programming approaches to congestion in stochastic data envelopment analysis. European Journal of Operational Research 155(2):487–501.
Charnes A, Cooper WW and Rhodes E (1978). Measuring the efficiency of decision making units. European Journal of Operational Research 2 (6): 429–444.
Cook, W., Roll, Y., Kazakov, A.,(1990). DEA model for measuring the relative efficiencies of highway maintenance patrols. INFOR 28 (2), 811-818.
Charnes A and Cooper WW (1959). Chance-constrained programming. Management Science 6 (1): 73–79.
Chen Z, Wanke P, Antunes JJM, Zhang N (2017). Chinese airline efficiency under CO2 emissions and flight delays: A stochastic network DEA model. Energy Economics 68: 89-108.
Charles V, Cornillier F(2017). Value of the stochastic efficiency in data envelopment analysis. Expert Systems with Applications, Volume 81, Pages 349-357.
Chen Z, Wanke P, Antunes JJM, Zhang N (2017). Chinese airline efficiency under CO2 emissions and flight delays: A stochastic network DEA model. Energy Economics 68: 89-108.
Dotoli M, Epicoco N, Falagario M and Sciancalepore F (2016). A Stochastic cross-efficiency data envelopment analysis approach for supplier selection under uncertainty .International Transactions in Operational Research 23, 725-748.
Davtalab-Olyaie M, Asgharian M, Partovi Nia V (2019). Stochastic ranking and dominance in DEA. International Journal of Production Economics, Volume 214, Pages 125-138
De Mello JC, Meza LA, da Silveira JQ, Gomes EG (2013). About negative efficiencies in cross evaluation BCC input oriented models. European Journal of Operational Research 229(3):732-7.
Hosseinzadeh Lotfi F, Nematollahi N, Behzadi MH, Mirbolouki M and Moghaddas Z (2012). Centralized resource allocation with stochastic data. Journal of Computational and Applied Mathematics 236 (7): 1783–1788.
Hosseinzadeh Lotfi, F., RostamyMalkhalifeh, M., Aghayi, N., Ghelej Beigi, Z., Gholami, K., (2013). An improved method for ranking alternatives in multiple criteria decision analysis. Applied Mathematical Modelling, 37, (1-2), 25-33
Hadi-Vencheh A, Esmaeilzadeh A (2013). A new super-efficiency model in the presence of negative data. Journal of the Operational Research Society 64(3):396-401.
Izadikhah, M., Saen, R.F., 2018. Assessing sustainability of supply chains by chance- constrained two-stage DEA model in the presence of undesirable factors.
Jradi S, Ruggiero J (2018). Stochastic data envelopment analysis: A quantile regression approach to estimate the production frontier. European Journal of Operational Research, In press, corrected proof, Available online 9 November 2018.
Jiang, T., Zhang, Y., & Jin, Q. (2021). Sustainability efficiency assessment of listed companies in China: a super-efficiency SBM-DEA model considering undesirable output. Environmental Science and Pollution Research, 28(34), 47588-47604.
Jin J, Zhou D, Zhou P (2014). Measuring environmental performance with stochastic environmental DEA: the case of APEC economies. Economic Modelling 38:80-6.
Khanjani Shiraz, R., Tavana, M., & Fukuyama, H. (2021). A joint chance-constrained data envelopment analysis model with random output data. Operational Research, 21(2), 1255-1277.
Khodabakhshi M (2011). Super-efficiency in stochastic data envelopment analysis: An input relaxation approach. Journal of Computational and Applied Mathematics 235(16): 4576–4588.
Kao Ch, Liu Sh (2019). Stochastic efficiency measures for production units with correlated data. European Journal of Operational Research, Volume 273, Issue 1, 16, Pages 278-287.
Land KC, Lovell CAK and Thore S (1993). Chance constrained data envelopment analysis. Managerial and Decision Economics 14 (6): 541–554.
Liu, J., Fang, M., Jin, F., Wu, C., Chen, H., (2020). Multi-attribute decision making based on stochastic DEA cross-efficiency with ordinal variable and its application to evaluation of banks’ sustainable development. Sustainability 12 (6), 2375.
Liu W, Wang Y, Lyu Sh (2017). The upper and lower bound evaluation based on the quantile efficiency in stochastic data envelopment analysis. Expert Systems with Applications, Volume 85, Pages 14-24.
Lu, C.C., Chiu, Y.H., Shyu, M.K., Lee, J.H (2013). Measuring CO2 emission efficiency in OECD countries: application of the hybrid efficiency model. Economical Modeling 32, 130–135.
Morita H and Seiford LM (1999). Characteristics on stochastic DEA efficiency-Reliability and probability being efficient. Journal of Operational Research Society of Japan 42(4): 389–404.
Mandal, S.K (2010). Do undesirable output and environmental regulation matter in energy efficiency analysis? Evidence from Indian cement industry. Energy Policy 38(10), 6076–6083.
Park S, Ok Ch, Ha Ch (2018). A stochastic simulation-based holistic evaluation approach with DEA for vendor selection. Computers & Operations Research, Volume 100, Pages 368-378.
Takahashi, F. L., & Vasconcelos, M. R. (2023). Bank efficiency and undesirable output: An analysis of non-performing loans in the Brazilian banking sector. Finance Research Letters, 104651.
Ren, J., Gao, B., Zhang, J., Chen, C., 2020. Measuring the energy and carbon emission efficiency of regional transportation systems in China:Chance-constrained DEA models. Math. Probl. Eng. 2020.
Qu, Y., Li, J., & Wang, S. (2022). Green total factor productivity measurement of industrial enterprises in Zhejiang Province, China: A DEA model with undesirable output approach. Energy Reports, 8, 307-317.
Omrani, H., Oveysi, Z., Emrouznejad, A., & Teplova, T. (2023). A mixed-integer network DEA with shared inputs and undesirable outputs for performance evaluation: Efficiency measurement of bank branches. Journal of the Operational Research Society, 74(4), 1150-1165.
Olesen, OB and Petersen N (2016). Stochastic Data Envelopment Analysis-A review. Europen Journal of Operational Research 251(1):1-13.
Olesen OB (2006). Comparing and combining two approaches for chance constrained DEA. Journal of Productivity Analysis 26(2): 103–119.
Ruiz, J.L., Sirvent, I., (2012). On the DEA total weight flexibility and the aggregation in cross-efficiency evaluations. European Journal of Operational Research 223 (3), 732-738.
Simar L, Keilegom, I and Zelenyuk W (2017). Nonparametric least squares methods for stochastic frontier models. Journal of Productivity Analysis 47(3):189-204
Sueyoshi, T., (1999). DEA nonparametric ranking test and index measurement: slackadjusted DEA and an application to Japanese agriculture cooperatives. Omega Int. J. Management Science 27 (3), 315-326.
Sexton, T.R., Silkman, R.H., Hogan, A.J., (1986). Data envelopment analysis: critique and extensions. In: Silkman, R.H. (Ed.), Measuring Efficiency: an Assessment of Data Envelopment Analysis. Jossey-Bass, San Francisco, CA, 73-105.
Shi, G.M., Bi, J., Wang, J.N (2010). Chinese regional industrial energy efficiency evaluation based on a DEA model of fixing non-energy inputs. Energy Policy 38 (10), 6172–6179.
Sueyoshi, T., Goto, M (2010). Should the US clean air act include CO2 emission control? Examination by data envelopment analysis. Energy Policy 38 (10), 5902–5911.
Wang, Y. M., Chin, K. S, (2010). A neutral DEA model for cross-efficiency54-
evaluation and its extension, Expert Systems with Applications 37, 3666- 3675.
Wanke, P., Y. Tan, J. Antunes, and A. Hadi-Vencheh.( 2020). Business environment drivers and technical efficiency in the Chinese energy industry: A robust Bayesian stochastic frontier analysis. Computers & Industrial Engineering 106487.
Wu, J., Chu, J., Sun, J., Zhu, Q., (2016). DEA cross-efficiency evaluation based on Pareto improvement. European Journal of Operational Research 248 (2), 571-579.
Wu, C., Li, Y., Liu, Q., & Wang, K. (2013). A stochastic DEA model considering undesirable outputs with weak disposability. Mathematical and Computer Modelling, 58(5-6), 980-989.
Yang F, Ang S, Xia Q and Yang C (2012). Ranking DMUs by using interval DEA cross efficiency matrix with acceptability analysis. European Journal of Operational Research 223(2): 483–488.
Zhou Z, Lin L, Xiao H, Ma C and Wu S (2017). Stochastic network DEA model for two-stage systems under the centralized control organization mechanism. Computers & Industrial Engineering 110: 404-412.
References:
Andersen, P., Petersen, N.C., (1993).A procedure for ranking efficient units in data envelopment analysis. Management Science, 39 (10), 1261-1264.
Amirteimoori, A., Charles, V., & Mehdizadeh, S. (2023). Stochastic data envelopment analysis in the presence of undesirable outputs. Journal of the Operational Research Society, 1-14.
Banker RD, Charnes A and Cooper WW (1984). Some method for estimating technical and scale inefficiencies in data envelopment analysis. Management Science 30(9): 1078–1092.
Bruni ME, Conforti D, Beraldi P and Tundis E (2009). Probabilistically constrained models for efficiency and dominance in DEA. International Journal of Production Economics 117(1): 219–228.
Cooper WW, Huang ZM, Lelas V, Li SX and Olesen OB (1998). Chance constrained programming formulations for stochastic characterizations of efficiency and dominance in DEA. Journal of Productivity Analysis 9(1): 530–579.
Cooper WW, Deng H, Huang Z and Li Susan X (2002). Chance constrained programming approaches to technical efficiencies and inefficiencies in stochastic data envelopment analysis. Journal of the Operational Research Society 53(12): 1347–1356.
Cooper WW, Deng H, Huang ZM and Li SX (2004). Chance constrained programming approaches to congestion in stochastic data envelopment analysis. European Journal of Operational Research 155(2):487–501.
Charnes A, Cooper WW and Rhodes E (1978). Measuring the efficiency of decision making units. European Journal of Operational Research 2 (6): 429–444.
Cook, W., Roll, Y., Kazakov, A.,(1990). DEA model for measuring the relative efficiencies of highway maintenance patrols. INFOR 28 (2), 811-818.
Charnes A and Cooper WW (1959). Chance-constrained programming. Management Science 6 (1): 73–79.
Chen Z, Wanke P, Antunes JJM, Zhang N (2017). Chinese airline efficiency under CO2 emissions and flight delays: A stochastic network DEA model. Energy Economics 68: 89-108.
Charles V, Cornillier F(2017). Value of the stochastic efficiency in data envelopment analysis. Expert Systems with Applications, Volume 81, Pages 349-357.
Chen Z, Wanke P, Antunes JJM, Zhang N (2017). Chinese airline efficiency under CO2 emissions and flight delays: A stochastic network DEA model. Energy Economics 68: 89-108.
Dotoli M, Epicoco N, Falagario M and Sciancalepore F (2016). A Stochastic cross-efficiency data envelopment analysis approach for supplier selection under uncertainty .International Transactions in Operational Research 23, 725-748.
Davtalab-Olyaie M, Asgharian M, Partovi Nia V (2019). Stochastic ranking and dominance in DEA. International Journal of Production Economics, Volume 214, Pages 125-138
De Mello JC, Meza LA, da Silveira JQ, Gomes EG (2013). About negative efficiencies in cross evaluation BCC input oriented models. European Journal of Operational Research 229(3):732-7.
Hosseinzadeh Lotfi F, Nematollahi N, Behzadi MH, Mirbolouki M and Moghaddas Z (2012). Centralized resource allocation with stochastic data. Journal of Computational and Applied Mathematics 236 (7): 1783–1788.
Hosseinzadeh Lotfi, F., RostamyMalkhalifeh, M., Aghayi, N., Ghelej Beigi, Z., Gholami, K., (2013). An improved method for ranking alternatives in multiple criteria decision analysis. Applied Mathematical Modelling, 37, (1-2), 25-33
Hadi-Vencheh A, Esmaeilzadeh A (2013). A new super-efficiency model in the presence of negative data. Journal of the Operational Research Society 64(3):396-401.
Izadikhah, M., Saen, R.F., 2018. Assessing sustainability of supply chains by chance- constrained two-stage DEA model in the presence of undesirable factors.
Jradi S, Ruggiero J (2018). Stochastic data envelopment analysis: A quantile regression approach to estimate the production frontier. European Journal of Operational Research, In press, corrected proof, Available online 9 November 2018.
Jiang, T., Zhang, Y., & Jin, Q. (2021). Sustainability efficiency assessment of listed companies in China: a super-efficiency SBM-DEA model considering undesirable output. Environmental Science and Pollution Research, 28(34), 47588-47604.
Jin J, Zhou D, Zhou P (2014). Measuring environmental performance with stochastic environmental DEA: the case of APEC economies. Economic Modelling 38:80-6.
Khanjani Shiraz, R., Tavana, M., & Fukuyama, H. (2021). A joint chance-constrained data envelopment analysis model with random output data. Operational Research, 21(2), 1255-1277.
Khodabakhshi M (2011). Super-efficiency in stochastic data envelopment analysis: An input relaxation approach. Journal of Computational and Applied Mathematics 235(16): 4576–4588.
Kao Ch, Liu Sh (2019). Stochastic efficiency measures for production units with correlated data. European Journal of Operational Research, Volume 273, Issue 1, 16, Pages 278-287.
Land KC, Lovell CAK and Thore S (1993). Chance constrained data envelopment analysis. Managerial and Decision Economics 14 (6): 541–554.
Liu, J., Fang, M., Jin, F., Wu, C., Chen, H., (2020). Multi-attribute decision making based on stochastic DEA cross-efficiency with ordinal variable and its application to evaluation of banks’ sustainable development. Sustainability 12 (6), 2375.
Liu W, Wang Y, Lyu Sh (2017). The upper and lower bound evaluation based on the quantile efficiency in stochastic data envelopment analysis. Expert Systems with Applications, Volume 85, Pages 14-24.
Lu, C.C., Chiu, Y.H., Shyu, M.K., Lee, J.H (2013). Measuring CO2 emission efficiency in OECD countries: application of the hybrid efficiency model. Economical Modeling 32, 130–135.
Morita H and Seiford LM (1999). Characteristics on stochastic DEA efficiency-Reliability and probability being efficient. Journal of Operational Research Society of Japan 42(4): 389–404.
Mandal, S.K (2010). Do undesirable output and environmental regulation matter in energy efficiency analysis? Evidence from Indian cement industry. Energy Policy 38(10), 6076–6083.
Park S, Ok Ch, Ha Ch (2018). A stochastic simulation-based holistic evaluation approach with DEA for vendor selection. Computers & Operations Research, Volume 100, Pages 368-378.
Takahashi, F. L., & Vasconcelos, M. R. (2023). Bank efficiency and undesirable output: An analysis of non-performing loans in the Brazilian banking sector. Finance Research Letters, 104651.
Ren, J., Gao, B., Zhang, J., Chen, C., 2020. Measuring the energy and carbon emission efficiency of regional transportation systems in China:Chance-constrained DEA models. Math. Probl. Eng. 2020.
Qu, Y., Li, J., & Wang, S. (2022). Green total factor productivity measurement of industrial enterprises in Zhejiang Province, China: A DEA model with undesirable output approach. Energy Reports, 8, 307-317.
Omrani, H., Oveysi, Z., Emrouznejad, A., & Teplova, T. (2023). A mixed-integer network DEA with shared inputs and undesirable outputs for performance evaluation: Efficiency measurement of bank branches. Journal of the Operational Research Society, 74(4), 1150-1165.
Olesen, OB and Petersen N (2016). Stochastic Data Envelopment Analysis-A review. Europen Journal of Operational Research 251(1):1-13.
Olesen OB (2006). Comparing and combining two approaches for chance constrained DEA. Journal of Productivity Analysis 26(2): 103–119.
Ruiz, J.L., Sirvent, I., (2012). On the DEA total weight flexibility and the aggregation in cross-efficiency evaluations. European Journal of Operational Research 223 (3), 732-738.
Simar L, Keilegom, I and Zelenyuk W (2017). Nonparametric least squares methods for stochastic frontier models. Journal of Productivity Analysis 47(3):189-204
Sueyoshi, T., (1999). DEA nonparametric ranking test and index measurement: slackadjusted DEA and an application to Japanese agriculture cooperatives. Omega Int. J. Management Science 27 (3), 315-326.
Sexton, T.R., Silkman, R.H., Hogan, A.J., (1986). Data envelopment analysis: critique and extensions. In: Silkman, R.H. (Ed.), Measuring Efficiency: an Assessment of Data Envelopment Analysis. Jossey-Bass, San Francisco, CA, 73-105.
Shi, G.M., Bi, J., Wang, J.N (2010). Chinese regional industrial energy efficiency evaluation based on a DEA model of fixing non-energy inputs. Energy Policy 38 (10), 6172–6179.
Sueyoshi, T., Goto, M (2010). Should the US clean air act include CO2 emission control? Examination by data envelopment analysis. Energy Policy 38 (10), 5902–5911.
Wang, Y. M., Chin, K. S, (2010). A neutral DEA model for cross-efficiency54-
evaluation and its extension, Expert Systems with Applications 37, 3666- 3675.
Wanke, P., Y. Tan, J. Antunes, and A. Hadi-Vencheh.( 2020). Business environment drivers and technical efficiency in the Chinese energy industry: A robust Bayesian stochastic frontier analysis. Computers & Industrial Engineering 106487.
Wu, J., Chu, J., Sun, J., Zhu, Q., (2016). DEA cross-efficiency evaluation based on Pareto improvement. European Journal of Operational Research 248 (2), 571-579.
Wu, C., Li, Y., Liu, Q., & Wang, K. (2013). A stochastic DEA model considering undesirable outputs with weak disposability. Mathematical and Computer Modelling, 58(5-6), 980-989.
Yang F, Ang S, Xia Q and Yang C (2012). Ranking DMUs by using interval DEA cross efficiency matrix with acceptability analysis. European Journal of Operational Research 223(2): 483–488.
Zhou Z, Lin L, Xiao H, Ma C and Wu S (2017). Stochastic network DEA model for two-stage systems under the centralized control organization mechanism. Computers & Industrial Engineering 110: 404-412.