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Multi-valued indicators in DEA in the presence of undesirable outputs: A goal-directed approach

  • School of Management, University of Science and Technology of China, Hefei 230026, China

Cite this:
https://doi.org/10.52396/JUST-2021-0092
  • Received Date: 11 April 2021
  • Rev Recd Date: 10 May 2021
  • Publish Date: 31 July 2021
    Abstract

  • Abstract

    The data envelopment analysis (DEA) is an important data-driven method for the performance evaluation and performance improvement of a set of peer decision making units (DMUs), involving multiple inputs and multiple outputs which are identified as performance indicators. However, some performance indicators, unlike conventional DEA models with one single value, may have more than one value because of different definitions or measurement standards referring to multi-valued indicators. In addition, the performance indicators reflect the current status of DMUs, which ignore the goals of decision-makers. We first propose two modified slacks-based DEA models to deal with multi-valued indicators and provide the Pareto-optimal solution in two common decision-making scenarios, namely the decentralized and centralized decision-making cases. Furthermore, we extend the models by incorporating with the goals of decision-makers to help the DMUs improve their performance and get close to the goals of decision-makers as much as possible. The slacks-based approaches and integration of goals enhance the discriminability of the models to DMUs and provide more practical improvement for some indicators. A case study of 22 cities in the Yangtze River delta region in China is used to illustrate the effectiveness and practicality of our proposed models.

    Abstract

    The data envelopment analysis (DEA) is an important data-driven method for the performance evaluation and performance improvement of a set of peer decision making units (DMUs), involving multiple inputs and multiple outputs which are identified as performance indicators. However, some performance indicators, unlike conventional DEA models with one single value, may have more than one value because of different definitions or measurement standards referring to multi-valued indicators. In addition, the performance indicators reflect the current status of DMUs, which ignore the goals of decision-makers. We first propose two modified slacks-based DEA models to deal with multi-valued indicators and provide the Pareto-optimal solution in two common decision-making scenarios, namely the decentralized and centralized decision-making cases. Furthermore, we extend the models by incorporating with the goals of decision-makers to help the DMUs improve their performance and get close to the goals of decision-makers as much as possible. The slacks-based approaches and integration of goals enhance the discriminability of the models to DMUs and provide more practical improvement for some indicators. A case study of 22 cities in the Yangtze River delta region in China is used to illustrate the effectiveness and practicality of our proposed models.
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    • References(43)
  • [1]
    Charnes A, Cooper W W, Rhodes E. Measuring the efficiency of decision making units. European Journal of Operational Research, 1978, 2(6): 429-444.
    [2]
    Ruiz J L, Sirvent I. Common benchmarking and ranking of units with DEA. Omega, 2016, 65: 1-9.
    [3]
    Cook W D, Ramón N, Ruiz J L, et al. DEA-based benchmarking for performance evaluation in pay-for-performance incentive plans. Omega, 2019, 84: 45-54.
    [4]
    Liu J S, Lu L Y, Lu W M.Research fronts in data envelopment analysis. Omega, 2016, 58: 33-45.
    [5]
    Emrouznejad A, Yang G L. A survey and analysis of the first 40 years of scholarly literature in DEA: 1978–2016. Socio-Economic Planning Sciences, 2018, 61: 4-8.
    [6]
    Sueyoshi T, Yuan Y, Goto M. A literature study for DEA applied to energy and environment. Energy Economics, 2017, 62: 104-124.
    [7]
    Zhou P, Ang B W, Poh K L. A survey of data envelopment analysis in energy and environmental studies. European Journal of Operational Research, 2008, 189(1): 1-18.
    [8]
    Lozano S. Slacks-based inefficiency approach for general networks with bad outputs: An application to the banking sector. Omega, 2016, 60: 73-84.
    [9]
    Cook W D, Zhu J. Classifying inputs and outputs in data envelopment analysis. European Journal of Operational Research, 2007, 180(2): 692-699.
    [10]
    Adler N, Golany B. Including principal component weights to improve discrimination in data envelopment analysis. Journal of the Operational Research Society, 2002, 53(9): 985-991.
    [11]
    Amirteimoori A, Despotis D K, Kordrostami S. Variables reduction in data envelopment analysis. Optimization, 2014, 63(5): 735-745.
    [12]
    Toloo M, Hančlová J. Multi-valued measures in DEA in the presence of undesirable outputs. Omega, 2020, 94: 102041.
    [13]
    Cook W D, Bala K. Performance measurement and classification data in DEA: input-oriented model. Omega, 2007, 35(1): 39-52.
    [14]
    Shimshak D G, Lenard M L, Klimberg R K. Incorporating quality into data envelopment analysis of nursing home performance: A case study. Omega, 2009, 37(3): 672-685.
    [15]
    Chen M H, Ang S, Jiang L J, et al. Centralized resource allocation based on cross-evaluation considering organizational objective and individual preferences. OR Spectrum, 2020, 42: 529-565.
    [16]
    Lozano S, Hinojosa M, Mármol A. Extending the bargaining approach to DEA target setting. Omega, 2019, 85: 94-102.
    [17]
    Stewart T J. Goal directed benchmarking for organizational efficiency. Omega, 2010, 38(6): 534-539.
    [18]
    Azadi M, Mirhedayatian S M, Saen R F. A new fuzzy goal directed benchmarking for supplier selection. International Journal of Services and Operations Management, 2013, 14(3): 321-335.
    [19]
    Ruiz J L, Sirvent I. Performance evaluation through DEA benchmarking adjusted to goals. Omega, 2019, 87: 150-157.
    [20]
    Zhou X Y, Luo R., An Q X, et al. Water resource environmental carrying capacity-based reward and penalty mechanism: A DEA benchmarking approach. Journal of Cleaner Production, 2019, 229: 1294-1306.
    [21]
    Podinovski V V. Bridging the gap between the constant and variable returns-to-scale models: Selective proportionality in data envelopment analysis. Journal of the Operational Research Society, 2004, 55(3): 265-276.
    [22]
    Färe R, Grosskopf S, Lovell C K, et al. Multilateral productivity comparisons when some outputs are undesirable: A nonparametric approach. The Review of Economics and Statistics, 1989, 71(1): 90-98.
    [23]
    Kuosmanen T. Weak disposability in nonparametric production analysis with undesirable outputs. American Journal of Agricultural Economics, 2005, 87(4): 1077-1082.
    [24]
    Yang H, Pollitt M. The necessity of distinguishing weak and strong disposability among undesirable outputs in DEA: Environmental performance of Chinese coal-fired power plants. Energy Policy, 2010, 38(8): 4440-4444.
    [25]
    Tone K. A slacks-based measure of efficiency in data envelopment analysis. European Journal of Operational Research, 2001, 130(3): 498-509.
    [26]
    Du J, Liang L, Zhu J. A slacks-based measure of super-efficiency in data envelopment analysis: A comment. European Journal of Operational Research, 2010, 204(3): 694-697.
    [27]
    Ripoll-Zarraga A E, Lozano S. A centralised DEA approach to resource reallocation in Spanish airports. Annals of Operations Research, 2020, 288(2): 701-732.
    [28]
    Charnes A, Cooper W W, Golany B, et al. Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions. Journal of Econometrics, 1985, 30(1-2): 91-107.
    [29]
    Scheel H. Undesirable outputs in efficiency valuations. European Journal of Operational Research, 2001, 132(2): 400-410.
    [30]
    Halme M, Joro T, Korhonen P, et al. A value efficiency approach to incorporating preference information in data envelopment analysis. Management Science, 1999, 45(1): 103-115.
    [31]
    Azadi M, Saen R F, Zoroufchi K H. A new goal-directed benchmarking for supplier selection in the presence of undesirable outputs. Benchmarking: An International Journal, 2014, 21(3): 314-328.
    [32]
    Khoveyni M, Eslami R. Managerial goals directed benchmarking for organised efficiency in data envelopment analysis. International Journal of Information and Decision Sciences, 2016, 8(1): 1-23.
    [33]
    Tao Y, Zhang S L. Environmental efficiency of electric power industry in the Yangtze River delta. Mathematical and Computer Modelling, 2013, 58(5-6): 927-935.
    [34]
    Reinhard S, Lovell C K, Thijssen G J. Environmental efficiency with multiple environmentally detrimental variables; estimated with SFA and DEA. European Journal of Operational Research, 2000, 121(2): 287-303.
    [35]
    Wu J, Li M J, Zhu Q Y, et al. Energy and environmental efficiency measurement of China's industrial sectors: A DEA model with non-homogeneous inputs and outputs. Energy Economics, 2019, 78: 468-480.
    [36]
    Chu J F, Wu J, Song M L. An SBM-DEA model with parallel computing design for environmental efficiency evaluation in the big data context: A transportation system application. Annals of Operations Research, 2018, 270(1-2): 105-124.
    [37]
    Wu J, Xia P P, Zhu Q Y, et al. Measuring environmental efficiency of thermoelectric power plants: A common equilibrium efficient frontier DEA approach with fixed-sum undesirable output. Annals of Operations Research, 2019, 275(2): 731-749.
    [38]
    Zhou P, Poh K L, Ang B W. A non-radial DEA approach to measuring environmental performance. European Journal of Operational Research, 2007, 178(1): 1-9.
    [39]
    Yang H, Pollitt M. Incorporating both undesirable outputs and uncontrollable variables into DEA: The performance of Chinese coal-fired power plants. European Journal of Operational Research, 2009, 197(3): 1095-1105.
    [40]
    Chen L, Wang Y M, Lai F J. Semi-disposability of undesirable outputs in data envelopment analysis for environmental assessments. European Journal of Operational Research, 2017, 260(2): 655-664.
    [41]
    Wu X, Tan L, Guo J, et al. A study of allocative efficiency of PM 2.5 emission rights based on a zero sum gains data envelopment model. Journal of Cleaner Production, 2016, 113: 1024-1031.
    [42]
    Chen N, Xu L, Chen Z.Environmental efficiency analysis of the Yangtze River economic zone using super efficiency data envelopment analysis (SEDEA) and tobit models. Energy, 2017, 134: 659-671.
    [43]
    Ruiz F, Cabello J M, Luque M. An application of reference point techniques to the calculation of synthetic sustainability indicators. Journal of the Operational Research Society, 2017, 62(1): 189-197.
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    [1]
    Charnes A, Cooper W W, Rhodes E. Measuring the efficiency of decision making units. European Journal of Operational Research, 1978, 2(6): 429-444.
    [2]
    Ruiz J L, Sirvent I. Common benchmarking and ranking of units with DEA. Omega, 2016, 65: 1-9.
    [3]
    Cook W D, Ramón N, Ruiz J L, et al. DEA-based benchmarking for performance evaluation in pay-for-performance incentive plans. Omega, 2019, 84: 45-54.
    [4]
    Liu J S, Lu L Y, Lu W M.Research fronts in data envelopment analysis. Omega, 2016, 58: 33-45.
    [5]
    Emrouznejad A, Yang G L. A survey and analysis of the first 40 years of scholarly literature in DEA: 1978–2016. Socio-Economic Planning Sciences, 2018, 61: 4-8.
    [6]
    Sueyoshi T, Yuan Y, Goto M. A literature study for DEA applied to energy and environment. Energy Economics, 2017, 62: 104-124.
    [7]
    Zhou P, Ang B W, Poh K L. A survey of data envelopment analysis in energy and environmental studies. European Journal of Operational Research, 2008, 189(1): 1-18.
    [8]
    Lozano S. Slacks-based inefficiency approach for general networks with bad outputs: An application to the banking sector. Omega, 2016, 60: 73-84.
    [9]
    Cook W D, Zhu J. Classifying inputs and outputs in data envelopment analysis. European Journal of Operational Research, 2007, 180(2): 692-699.
    [10]
    Adler N, Golany B. Including principal component weights to improve discrimination in data envelopment analysis. Journal of the Operational Research Society, 2002, 53(9): 985-991.
    [11]
    Amirteimoori A, Despotis D K, Kordrostami S. Variables reduction in data envelopment analysis. Optimization, 2014, 63(5): 735-745.
    [12]
    Toloo M, Hančlová J. Multi-valued measures in DEA in the presence of undesirable outputs. Omega, 2020, 94: 102041.
    [13]
    Cook W D, Bala K. Performance measurement and classification data in DEA: input-oriented model. Omega, 2007, 35(1): 39-52.
    [14]
    Shimshak D G, Lenard M L, Klimberg R K. Incorporating quality into data envelopment analysis of nursing home performance: A case study. Omega, 2009, 37(3): 672-685.
    [15]
    Chen M H, Ang S, Jiang L J, et al. Centralized resource allocation based on cross-evaluation considering organizational objective and individual preferences. OR Spectrum, 2020, 42: 529-565.
    [16]
    Lozano S, Hinojosa M, Mármol A. Extending the bargaining approach to DEA target setting. Omega, 2019, 85: 94-102.
    [17]
    Stewart T J. Goal directed benchmarking for organizational efficiency. Omega, 2010, 38(6): 534-539.
    [18]
    Azadi M, Mirhedayatian S M, Saen R F. A new fuzzy goal directed benchmarking for supplier selection. International Journal of Services and Operations Management, 2013, 14(3): 321-335.
    [19]
    Ruiz J L, Sirvent I. Performance evaluation through DEA benchmarking adjusted to goals. Omega, 2019, 87: 150-157.
    [20]
    Zhou X Y, Luo R., An Q X, et al. Water resource environmental carrying capacity-based reward and penalty mechanism: A DEA benchmarking approach. Journal of Cleaner Production, 2019, 229: 1294-1306.
    [21]
    Podinovski V V. Bridging the gap between the constant and variable returns-to-scale models: Selective proportionality in data envelopment analysis. Journal of the Operational Research Society, 2004, 55(3): 265-276.
    [22]
    Färe R, Grosskopf S, Lovell C K, et al. Multilateral productivity comparisons when some outputs are undesirable: A nonparametric approach. The Review of Economics and Statistics, 1989, 71(1): 90-98.
    [23]
    Kuosmanen T. Weak disposability in nonparametric production analysis with undesirable outputs. American Journal of Agricultural Economics, 2005, 87(4): 1077-1082.
    [24]
    Yang H, Pollitt M. The necessity of distinguishing weak and strong disposability among undesirable outputs in DEA: Environmental performance of Chinese coal-fired power plants. Energy Policy, 2010, 38(8): 4440-4444.
    [25]
    Tone K. A slacks-based measure of efficiency in data envelopment analysis. European Journal of Operational Research, 2001, 130(3): 498-509.
    [26]
    Du J, Liang L, Zhu J. A slacks-based measure of super-efficiency in data envelopment analysis: A comment. European Journal of Operational Research, 2010, 204(3): 694-697.
    [27]
    Ripoll-Zarraga A E, Lozano S. A centralised DEA approach to resource reallocation in Spanish airports. Annals of Operations Research, 2020, 288(2): 701-732.
    [28]
    Charnes A, Cooper W W, Golany B, et al. Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions. Journal of Econometrics, 1985, 30(1-2): 91-107.
    [29]
    Scheel H. Undesirable outputs in efficiency valuations. European Journal of Operational Research, 2001, 132(2): 400-410.
    [30]
    Halme M, Joro T, Korhonen P, et al. A value efficiency approach to incorporating preference information in data envelopment analysis. Management Science, 1999, 45(1): 103-115.
    [31]
    Azadi M, Saen R F, Zoroufchi K H. A new goal-directed benchmarking for supplier selection in the presence of undesirable outputs. Benchmarking: An International Journal, 2014, 21(3): 314-328.
    [32]
    Khoveyni M, Eslami R. Managerial goals directed benchmarking for organised efficiency in data envelopment analysis. International Journal of Information and Decision Sciences, 2016, 8(1): 1-23.
    [33]
    Tao Y, Zhang S L. Environmental efficiency of electric power industry in the Yangtze River delta. Mathematical and Computer Modelling, 2013, 58(5-6): 927-935.
    [34]
    Reinhard S, Lovell C K, Thijssen G J. Environmental efficiency with multiple environmentally detrimental variables; estimated with SFA and DEA. European Journal of Operational Research, 2000, 121(2): 287-303.
    [35]
    Wu J, Li M J, Zhu Q Y, et al. Energy and environmental efficiency measurement of China's industrial sectors: A DEA model with non-homogeneous inputs and outputs. Energy Economics, 2019, 78: 468-480.
    [36]
    Chu J F, Wu J, Song M L. An SBM-DEA model with parallel computing design for environmental efficiency evaluation in the big data context: A transportation system application. Annals of Operations Research, 2018, 270(1-2): 105-124.
    [37]
    Wu J, Xia P P, Zhu Q Y, et al. Measuring environmental efficiency of thermoelectric power plants: A common equilibrium efficient frontier DEA approach with fixed-sum undesirable output. Annals of Operations Research, 2019, 275(2): 731-749.
    [38]
    Zhou P, Poh K L, Ang B W. A non-radial DEA approach to measuring environmental performance. European Journal of Operational Research, 2007, 178(1): 1-9.
    [39]
    Yang H, Pollitt M. Incorporating both undesirable outputs and uncontrollable variables into DEA: The performance of Chinese coal-fired power plants. European Journal of Operational Research, 2009, 197(3): 1095-1105.
    [40]
    Chen L, Wang Y M, Lai F J. Semi-disposability of undesirable outputs in data envelopment analysis for environmental assessments. European Journal of Operational Research, 2017, 260(2): 655-664.
    [41]
    Wu X, Tan L, Guo J, et al. A study of allocative efficiency of PM 2.5 emission rights based on a zero sum gains data envelopment model. Journal of Cleaner Production, 2016, 113: 1024-1031.
    [42]
    Chen N, Xu L, Chen Z.Environmental efficiency analysis of the Yangtze River economic zone using super efficiency data envelopment analysis (SEDEA) and tobit models. Energy, 2017, 134: 659-671.
    [43]
    Ruiz F, Cabello J M, Luque M. An application of reference point techniques to the calculation of synthetic sustainability indicators. Journal of the Operational Research Society, 2017, 62(1): 189-197.
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