Robust productivity growth and efficiency measurement with undesirable outputs: evidence from the oil industry. (English) Zbl 1502.90090
Summary: This paper aims to contribute to the contemporary and imperative research on the performance and productivity growth of the oil industry. Among cutting edge methods, frontier analysis is a successful approach that has been widely used to assess the efficiency and productivity of entities with multiple resources and multiple outputs. This study first develops a unique framework based upon data envelopment analysis (DEA) to measure efficiency and productivity in the way that it tackles the uncertainty in data and undesirable outputs and, in turn, provides useful information to decision-makers. An adaptive robust optimisation is utilised to combat uncertain data whose distributions are unknown and consider the nexus between the level of conservatism and decision-makers’ risk preference. The key advantage of the proposed robust DEA approach is that the results remain relatively unchanged when uncertain conditions exist in the problem. An empirical study on the oil refinery is presented in situations of data uncertainty along with considering \(CO_2\) emissions as the undesirable output to conduct environmental efficiency and productivity analysis of the \(25\) countries over the period 2000-2018. The empirical results obtained from the proposed approach give some imperative implications. First, results show that the price of robustness does not affect identically for varying technologies when assessing productivity in a global oil market, and the USA oil industry is observed as the highest productivity growth in all cases confirming its efforts for the rapid rise in oil extraction and production at low costs. There may be practical lessons for other nations to learn from the USA oil industry to improve productivity. Findings also support a considerable regress during the 2008 Global Financial Crisis in the oil industry compared to the rest of the periods in question, and due to monetary and fiscal stimulus, there is a sharp productivity growth from 2009 to 2011. The other implication that can be drawn is that the GDP growth rate and technology innovation can more effectively improve the productivity of the oil industry across the globe.
MSC:
| 90B50 | Management decision making, including multiple objectives |
| 91B82 | Statistical methods; economic indices and measures |
| 90C08 | Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) |
| 90C05 | Linear programming |
| 91B06 | Decision theory |
| 90C90 | Applications of mathematical programming |
Keywords:
data envelopment analysis; oil refinery; productivity growth; robust optimisation; undesirable outputReferences:
| [1] | Al-Mana, AA; Nawaz, W.; Kamal, A.; Koҫ, M., Financial and operational efficiencies of national and international oil companies: an empirical investigation, Resour Policy, 68, 101701 (2020) |
| [2] | Aparicio, J.; Pastor, JT; Zofio, JL, On the inconsistency of the Malmquist-Luenberger index, Eur J Oper Res, 229, 3, 738-742 (2013) · Zbl 1317.90186 |
| [3] | Arabmaldar, A.; Jablonsky, J.; Saljooghi, FH, A new robust DEA model and super-efficiency measure, Optimization, 66, 5, 723-736 (2017) · Zbl 1369.90089 |
| [4] | Arabmaldar, A.; Kwasi Mensah, E.; Toloo, M., Robust worst-practice interval DEA with non-discretionary factors, Expert Syst Appl, 182, 115256 (2021) |
| [5] | Atris, AM; Goto, M., Vertical structure and efficiency assessment of the US oil and gas companies, Resour Policy, 63, 101437 (2019) |
| [6] | Atris, AM, Assessment of oil refinery performance: application of data envelopment analysis-discriminant analysis, Resour Policy, 65, 101543 (2020) |
| [7] | Bădin, L.; Daraio, C.; Simar, L., A bootstrap approach for bandwidth selection in estimating conditional efficiency measures, Eur J Oper Res, 277, 2, 784-797 (2019) · Zbl 1430.62255 |
| [8] | Balk, BM, Scale efficiency and productivity change, J Prod Anal, 15, 159-183 (2001) |
| [9] | Balk, BM; Zofio, J., The many decompositions of total factor productivity change, ERIM Rep Ser Res Manag (2018) · doi:10.2139/ssrn.3167686 |
| [10] | Banker, RD; Charnes, A.; Cooper, WW, Some models for estimating technical and scale inefficiencies in data envelopment analysis, Manage Sci, 30, 9, 1078-1092 (1984) · Zbl 0552.90055 |
| [11] | Barros, C.; Antunes, OS, Productivity change in the oil blocks of Angola, Energy Sour Part B, 9, 4, 413-424 (2014) |
| [12] | Barros, CP; Managi, S., Productivity assessment of Angola’s oil blocks, Energy, 34, 11, 2009-2015 (2009) |
| [13] | Ben-Tal, A.; Nemirovski, A., Robust convex optimization, Math Oper Res, 23, 4, 769-805 (1998) · Zbl 0977.90052 |
| [14] | Ben-Tal, A.; Nemirovski, A., Robust solutions of linear programming problems contaminated with uncertain data, Math Program, 88, 3, 411-424 (2000) · Zbl 0964.90025 |
| [15] | Ben-Tal, A.; El Ghaoui, L.; Nemirovski, A., Robust optimization (2009), Princeton University Press · Zbl 1221.90001 |
| [16] | Bertsimas, D.; Sim, M., The price of robustness, Oper Res, 52, 1, 35-53 (2004) · Zbl 1165.90565 |
| [17] | Bevilacqua, M.; Braglia, M., Environmental efficiency analysis for ENI oil refineries, J Clean Prod, 10, 1, 85-92 (2002) |
| [18] | Caves, DW; Christensen, LR; Diewert, WE, The economic theory of index numbers and the measurement of input, output, and productivity, Econometrica, 50, 6, 1393 (1982) · Zbl 0524.90028 |
| [19] | Cazals, C.; Florens, JP; Simar, L., Nonparametric frontier estimation: a robust approach, J Econom, 106, 1, 1-25 (2002) · Zbl 1051.62116 |
| [20] | Charnes, A.; Cooper, WW; Rhodes, E., Measuring the efficiency of decision making units, Eur J Oper Res, 2, 6, 429-444 (1978) · Zbl 0416.90080 |
| [21] | Charnes, A.; Cooper, WW; Golany, B.; Seiford, L.; Stutz, J., Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions, J Econom, 30, 1-2, 91-107 (1985) · Zbl 0582.90007 |
| [22] | Chen, Y.; Ali, AI, DEA malmquist productivity measure: new insights with an application to computer industry, Eur J Oper Res, 159, 1, 239-249 (2004) · Zbl 1065.90512 |
| [23] | Chen, K.; Zhu, J., Computational tractability of chance constrained data envelopment analysis, Eur J Oper Res, 274, 3, 1037-1046 (2019) · Zbl 1430.90441 |
| [24] | Collins G (2016) China’s evolving oil demand: slowing overall growth, gasoline replacing diesel as demand driver, refined product exports rising substantially. Energy Environ Regul Aff |
| [25] | Cooper, WW; Park, KS; Yu, G., IDEA and AR-IDEA: models for dealing with imprecise data in DEA, Manag Sci, 45, 4, 597-607 (1999) · Zbl 1231.90289 |
| [26] | Cooper, WW; Seiford, LM; Tone, K., Data envelopment analysis a comprehensive text with models, applications, references and dea-solver software (2007), Springer · Zbl 1111.90001 |
| [27] | Dalei, NN; Joshi, JM, Estimating technical efficiency of petroleum refineries using DEA and tobit model: an India perspective, Comput Chem Eng, 142, 107047 (2020) |
| [28] | Daouia, A.; Florens, JP; Simar, L., Robust frontier estimation from noisy data: a Tikhonov regularization approach, Econom Stat, 14, 1-23 (2020) |
| [29] | Daraio, C.; Simar, L., Advanced robust and nonparametric methods in efficiency analysis. methodology and applications (2007), Springer · Zbl 1149.91003 |
| [30] | Daraio, C.; Simar, L., Directional distances and their robust versions: computational and testing issues, Eur J Oper Res, 237, 1, 358-369 (2014) |
| [31] | Ehrgott, M.; Holder, A.; Nohadani, O., Uncertain data envelopment analysis, Eur J Oper Res, 268, 231-242 (2018) · Zbl 1403.90508 |
| [32] | Eller, SL; Hartley, PR; Medlock, KB, Empirical evidence on the operational efficiency of national oil companies, Empir Econom, 40, 3, 623-643 (2011) |
| [33] | Emrouznejad, A.; Rostamy-Malkhalifeh, M.; Hatami-Marbini, A.; Tavana, M.; Aghayi, N., An overall profit Malmquist productivity index with fuzzy and interval data, Math Comput Model, 54, 11-12, 2827-2838 (2011) · Zbl 1235.90085 |
| [34] | Färe, R.; Grosskopf, Sh, Network DEA, Socioecon Plann Sci, 34, 1, 35-49 (2000) |
| [35] | Färe, R.; Grosskopf, Sh; Lovell, CAK; Pasurka, C., Multilateral productivity comparisons when some outputs are undesirable: a nonparametric approach, Rev Econ Stat, 71, 1, 90-98 (1989) |
| [36] | Färe, R.; Grosskopf, SH; Lindgren, B.; Roos, P., Productivity developments in swedish hospitals: a malmquist output index approach, Data Envel Anal Theory Methodol Appl (1994) · Zbl 0862.90094 · doi:10.1007/978-94-011-0637-5_13 |
| [37] | Färe, R.; Grosskopf, SH; Norris, M.; Zhang, Z., Productivity growth, technical progress, and efficiency change in industrialized countries, Am Econom Rev, 84, 66-83 (1994) |
| [38] | Färe R Grosskopf SH, Russell RR (1998) Index numbers: essays in honour of sten malmquist. In: Färe R, Grosskopf S, Russell RR (ed), 1st edn. Springer, Netherlands |
| [39] | Fare, R.; Grosskopf, Sh, Malmquist productivity indexes and fisher ideal indexes, Econ J, 102, 410, 158 (1992) |
| [40] | Farrell, MJ, The measurement of productive efficiency, J. R Stat Soc, 120, 3, 253-290 (1957) |
| [41] | Forman, GS; Divita, VB; Han, J.; Cai, H.; Elgowainy, A.; Wang, M., US refinery efficiency: impacts analysis and implications for fuel carbon policy implementation, Environ Sci Technol, 48, 13, 7625-7633 (2014) |
| [42] | Grifell-Tatjé, E.; Lovell, CAK, A generalized malmquist productivity index, TOP, 7, 1, 81-101 (1999) · Zbl 1115.91358 |
| [43] | Hatami-Marbini, A.; Arabmaldar, A., Robustness of farrell cost efficiency measurement under data perturbations: Evidence from a US manufacturing application, Eur J Oper Res, 295, 2, 604-620 (2021) · Zbl 1487.90372 |
| [44] | Hatami-Marbini, A.; Saati, S., Efficiency evaluation in two-stage data envelopment analysis under a fuzzy environment: a common-weights approach, Appl Soft Comput, 72, 156-165 (2018) |
| [45] | Hatami-Marbini, A.; Emrouznejad, A.; Tavana, M., A taxonomy and review of the fuzzy data envelopment analysis literature: two decades in the making, Eur J Oper Res, 214, 3, 457-472 (2011) · Zbl 1219.90199 |
| [46] | Hatami-Marbini, A.; Tavana, M.; Emrouznejad, A., Productivity growth and efficiency measurements in fuzzy environments with an application to health care, Int J Fuzzy Syst Appl, 2, 2, 1-35 (2012) |
| [47] | Hatami-Marbini, A.; Emrouznejad, A.; Agrell, PJ, Interval data without sign restrictions in DEA, Appl Math Model, 38, 7-8, 2028-2036 (2014) · Zbl 1427.90176 |
| [48] | Hatami-Marbini, A.; Agrell, PJ; Fukuyama, H.; Gholami, K.; Khoshnevis, P., The role of multiplier bounds in fuzzy data envelopment analysis, Ann Oper Res, 250, 1, 249-276 (2017) · Zbl 1361.90027 |
| [49] | Hatami-Marbini, A.; Ghelej Beigi, Z.; Hougaard, JL; Gholami, K., Measurement of returns-to-scale using interval data envelopment analysis models, Comput Ind Eng, 117, 94-107 (2018) |
| [50] | Hosseini, K.; Stefaniec, A., Efficiency assessment of Iran’s petroleum refining industry in the presence of unprofitable output: a dynamic two-stage slacks-based measure, Energy, 189, 116112 (2019) |
| [51] | Ike, CB; Lee, H., Measurement of the efficiency and productivity of national oil companies and its determinants, Geosyst Eng, 17, 1, 1-10 (2014) |
| [52] | Kao, C., Measurement and decomposition of the malmquist productivity index for parallel production systems, Omega, 67, 54-59 (2017) |
| [53] | Kapustin, NO; Grushevenko, DA, Exploring the implications of Russian energy strategy project for oil refining sector, Energy Policy, 117, 198-207 (2018) |
| [54] | Karagiannis, G.; Knox Lovell, CA, Productivity measurement in radial DEA models with a single constant input, Eur J Oper Res, 251, 1, 323-328 (2016) · Zbl 1346.90591 |
| [55] | Kasperski, A.; Zieliński, P., Soft robust solutions to possibilistic optimization problems, Fuzzy Sets Syst, 422, 130-148 (2021) · Zbl 1522.90282 |
| [56] | Kevork, IS; Pange, J.; Tzeremes, P.; Tzeremes, NG, Estimating malmquist productivity indexes using probabilistic directional distances: an application to the European banking sector, Eur J Oper Res, 261, 3, 1125-1140 (2017) · Zbl 1403.91380 |
| [57] | Klopp GA (1985) The analysis of the efficiency of production system with multiple inputs and outputs. PhD dissertation, University of Illinois, Industrial and System Engineering College, Chicago |
| [58] | Korhonen, PJ; Luptacik, M., Eco-efficiency analysis of power plants: an extension of data envelopment analysis, Eur J Oper Res, 154, 2, 437-446 (2004) · Zbl 1146.91327 |
| [59] | Kuosmanen, T., Weak disposability in nonparametric production analysis with undesirable outputs, Am J Agric Econ, 87, 4, 1077-1082 (2005) |
| [60] | Landete, M.; Monge, JF; Ruiz, JL, Robust DEA efficiency scores: a probabilistic/combinatorial approach, Expert Syst Appl, 86, 145-154 (2017) |
| [61] | Lu, C., Robust data envelopment analysis approaches for evaluating algorithmic performance, Comput Ind Eng, 81, 78-89 (2015) |
| [62] | Malmquist, S., Index numbers and indifference surfaces, Trabajos De Estadistica, 4, 2, 209-242 (1953) · Zbl 0052.15903 |
| [63] | Managi, S.; Opaluch, JJ; Jin, D.; Grigalunas, TA, Technological change and depletion in offshore oil and gas, J Environ Econ Manag, 47, 2, 388-409 (2004) · Zbl 1076.91530 |
| [64] | Maniadakis, N.; Thanassoulis, E., A cost malmquist productivity index, Eur J Oper Res, 154, 2, 396-409 (2004) · Zbl 1146.90450 |
| [65] | Mardani, A.; Zavadskas, EK; Streimikiene, D.; Jusoh, A.; Khoshnoudi, M., A comprehensive review of data envelopment analysis (DEA) approach in energy efficiency, Renew Sustain Energy Rev, 70, 1298-1322 (2017) |
| [66] | Mayer, A.; Zelenyuk, V., Aggregation of malmquist productivity indexes allowing for reallocation of resources, Eur J Oper Res, 238, 3, 774-785 (2014) · Zbl 1338.91085 |
| [67] | Mekaroonreung, M.; Johnson, AL, Estimating the efficiency of American petroleum refineries under varying assumptions of the disposability of bad outputs, Int J Energy Sect Manag, 4, 3, 356-398 (2010) |
| [68] | Mulvey, JM; Vanderbei, RJ; Zenios, SA, Robust optimization of large-scale systems, Oper Res, 43, 2, 264-281 (1995) · Zbl 0832.90084 |
| [69] | Nemati, M.; Kazemi Matin, R.; Toloo, M., A two-stage DEA model with partial impacts between inputs and outputs: application in refinery industries, Ann Oper Res, 295, 1, 285-312 (2020) · Zbl 1456.90103 |
| [70] | Olesen, OB; Petersen, NC, Chance constrained efficiency evaluation, Manag Sci, 41, 3, 442-457 (1995) · Zbl 0833.90004 |
| [71] | Olesen, OB; Petersen, NC, Stochastic data envelopment analysis - a review, Eur J Oper Res, 251, 1, 2-21 (2016) · Zbl 1346.90595 |
| [72] | Omrani, H., Common weights data envelopment analysis with uncertain data: a robust optimization approach, Comput Ind Eng, 66, 4, 1163-1170 (2013) |
| [73] | Pastor, JT; Lovell, CAK, A global malmquist productivity index, Econ Lett, 88, 2, 266-271 (2005) · Zbl 1254.91615 |
| [74] | Pastor, JT; Asmild, M.; Lovell, CAK, The biennial malmquist productivity change index, Socioecon Plann Sci, 45, 1, 10-15 (2011) |
| [75] | Pastor, JT; Lovell, CAK; Aparicio, J., Defining a new graph inefficiency measure for the proportional directional distance function and introducing a new Malmquist productivity index, Eur J Oper Res, 281, 1, 222-230 (2020) · Zbl 1431.91295 |
| [76] | Ramanathan, R., A multi-factor efficiency perspective to the relationships among world GDP, energy consumption and carbon dioxide emissions, Technol Forecast Soc Change, 73, 5, 483-494 (2006) |
| [77] | Ray, SC; Desli, E., Productivity growth, technical progress, and efficiency change in industrialized countries: comment, Am Econ Rev, 87, 1033-1039 (1997) |
| [78] | Sadjadi, SJ; Omrani, H., Data envelopment analysis with uncertain data: an application for Iranian electricity distribution companies, Energy Policy, 36, 11, 4247-4254 (2008) |
| [79] | Sadjadi, SJ; Omrani, H.; Abdollahzadeh, S.; Alinaghian, M.; Mohammadi, H., A robust super-efficiency data envelopment analysis model for ranking of provincial gas companies in Iran, Expert Syst Appl, 38, 9, 10875-10881 (2011) |
| [80] | Seiford, LM; Zhu, J., Modeling undesirable factors in efficiency evaluation, Eur J Oper Res, 142, 16-20 (2002) · Zbl 1079.90565 |
| [81] | Sengupta, JK, A fuzzy systems approach in data envelopment analysis, Comput Math Appl, 24, 8-9, 259-266 (1992) · Zbl 0765.90004 |
| [82] | Sheng, Y.; Wu, Y.; Shi, X.; Zhang, D., Energy trade efficiency and its determinants: a malmquist index approach, Energy Econom, 50, 306-314 (2015) |
| [83] | Shestalova, V., Sequential malmquist indices of productivity growth: an application to OECD industrial activities, J Prod Anal, 19, 2-3, 211-226 (2003) |
| [84] | Shokouhi, AH; Hatami-Marbini, A.; Tavana, M.; Saati, S., A robust optimization approach for imprecise data envelopment analysis, Comput Ind Eng, 59, 3, 387-397 (2010) |
| [85] | Shokouhi, AH; Shahriari, H.; Agrell, PJ; Hatami-Marbini, A., Consistent and robust ranking in imprecise data envelopment analysis under perturbations of random subsets of data, OR Spectrum, 36, 1, 133-160 (2014) · Zbl 1290.90053 |
| [86] | Simar, L.; Wilson, PW, Sensitivity analysis of efficiency scores: how to bootstrap in nonparametric frontier models, Manag Sci, 44, 1, 49-61 (1998) · Zbl 1012.62501 |
| [87] | Simar, L.; Wilson, PW, Estimating and bootstrapping malmquist indices, Eur J Oper Res, 115, 3, 459-471 (1999) · Zbl 0959.91053 |
| [88] | Soyster, AL, Convex programming with set-inclusive constraints and applications to inexact linear programming, Oper Res, 21, 5, 1154-1157 (1973) · Zbl 0266.90046 |
| [89] | Sueyoshi, T., Stochastic DEA for restructure strategy: an application to a japanese petroleum company, Omega, 28, 4, 385-398 (2000) |
| [90] | Sueyoshi, T.; Goto, M., Data envelopment analysis for environmental assessment: comparison between public and private ownership in petroleum industry, Eur J Oper Res, 216, 3, 668-678 (2012) · Zbl 1237.90151 |
| [91] | Sueyoshi, T.; Goto, M., Returns to scale and damages to scale under natural and managerial disposability: Strategy, efficiency and competitiveness of petroleum firms, Energy Econom, 34, 3, 645-662 (2012) |
| [92] | Sueyoshi, T.; Goto, M., DEA environmental assessment in time horizon: radial approach for malmquist index measurement on petroleum companies, Energy Econom, 51, 329-345 (2015) |
| [93] | Sueyoshi, T.; Wang, D., Sustainability development for supply chain management in U.S. petroleum industry by DEA environmental assessment, Energy Econom, 46, 360-374 (2014) |
| [94] | Sueyoshi, T.; Wang, D., DEA environmental assessment on US petroleum industry: non-radial approach with translation invariance in time horizon, Energy Econom, 72, 276-289 (2018) |
| [95] | Sueyoshi, T.; Yuan, Y.; Goto, M., A literature study for DEA applied to energy and environment, Energy Econom, 62, 104-124 (2017) |
| [96] | Tachega, MA; Yao, X.; Liu, Y.; Ahmed, D.; Li, H.; Mintah, C., Energy efficiency evaluation of oil producing economies in Africa: DEA, malmquist and multiple regression approaches, Clean Environ Syst, 2, 100025 (2021) |
| [97] | Tavana, M.; Khanjani Shiraz, R.; Hatami-Marbini, A., A new chance-constrained DEA model with birandom input and output data, J Oper Res Soc, 65, 12, 1824-1839 (2014) |
| [98] | Tavana, M.; Khalili-Damghani, K.; Santos Arteaga, FJ; Hosseini, A., A fuzzy multi-objective multi-period network DEA model for efficiency measurement in oil refineries, Comput Ind Eng, 135, 143-155 (2019) |
| [99] | Tavana, M.; Khalili-Damghani, K.; Santos Arteaga, FJ; Hashemi, A., A Malmquist productivity index for network production systems in the energy sector, Ann Oper Res, 284, 1, 415-445 (2020) |
| [100] | Tavana, M.; Toloo, M.; Aghayi, N.; Arabmaldar, A., A robust cross-efficiency data envelopment analysis model with undesirable outputs, Expert Syst Appl, 167, 114117 (2021) |
| [101] | Thanassoulis, E.; Shiraz, RK; Maniadakis, N., A cost malmquist productivity index capturing group performance, Eur J Oper Res, 241, 3, 796-805 (2015) · Zbl 1339.91093 |
| [102] | Thompson, RG; Dharmapala, PS; Rothenberg, LJ; Thrall, RM, DEA ARs and CRs applied to worldwide major oil companies, J Prod Anal, 5, 2, 181-203 (1994) |
| [103] | Thompson, RG; Lee, E.; Thrall, R., Dea/AR-efficiency of US independent oil/gas producers over time, Comput Oper Res, 19, 5, 377-391 (1992) |
| [104] | Thrall, RM, Measures in DEA with an application to the malmquist index, J Prod Anal, 13, 2, 125-137 (2000) |
| [105] | Tohidi, G.; Razavyan, S.; Tohidnia, S., A global cost malmquist productivity index using data envelopment analysis, J Oper Res Soc, 63, 1, 72-78 (2012) |
| [106] | Toloo, M.; Keshavarz, E.; Hatami-Marbini, A., An interval efficiency analysis with dual-role factors, Or Spectrum, 43, 255-287 (2021) · Zbl 1476.90161 |
| [107] | Tone, K., A slacks-based measure of efficiency in data envelopment analysis, Eur J Oper Res, 130, 3, 498-509 (2001) · Zbl 0990.90523 |
| [108] | Tone, K., A slacks-based measure of super-efficiency in data envelopment analysis, Eur J Oper Res, 143, 1, 32-41 (2002) · Zbl 1073.90520 |
| [109] | Tone, K.; Cooper, WW; Seiford, LM; Zhu, J., Malmquist productivity index, Handbook on data envelopment analysis (2004), Boston: Springer, Boston |
| [110] | Vikas, V.; Bansal, R., Efficiency evaluation of Indian oil and gas sector: data envelopment analysis, Int J Emerg Mark, 14, 2, 362-378 (2019) |
| [111] | Walheer, B., Disaggregation of the cost malmquist productivity index with joint and output-specific inputs, Omega, 75, 1-12 (2018) |
| [112] | Wang, Y.; Zhu, Z.; Liu, Z., Evaluation of technological innovation efficiency of petroleum companies based on BCC-malmquist index model, J Pet Explor Prod Technol, 9, 2405-2416 (2019) |
| [113] | Wegener, M.; Amin, GR, Minimizing greenhouse gas emissions using inverse DEA with an application in oil and gas, Expert Syst Appl, 122, 369-375 (2019) |
| [114] | Yu, D.; He, X., A bibliometric study for DEA applied to energy efficiency: trends and future challenges, Appl Energy, 268, 115048 (2020) |
| [115] | Zelenyuk, V., Aggregation of malmquist productivity indexes, Eur J Oper Res, 174, 2, 1076-1086 (2006) · Zbl 1103.90366 |
| [116] | Zhou-Kangas, Y.; Miettinen, K., Decision making in multiobjective optimization problems under uncertainty: balancing between robustness and quality, Or Spectrum, 41, 391-413 (2019) · Zbl 1428.90093 |
| [117] | Zhu, W.; Zhu, Y.; Yu, Y., China’s regional environmental efficiency evaluation: a dynamic analysis with biennial malmquist productivity index based on common weights, Environ Sci Pollut Res, 27, 32, 39726-39741 (2020) |
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.
