{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,5]],"date-time":"2026-04-05T01:14:53Z","timestamp":1775351693490,"version":"3.50.1"},"reference-count":71,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2017,2,11]],"date-time":"2017-02-11T00:00:00Z","timestamp":1486771200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2019,7]]},"DOI":"10.1007\/s10479-017-2423-5","type":"journal-article","created":{"date-parts":[[2017,2,11]],"date-time":"2017-02-11T17:44:28Z","timestamp":1486835068000},"page":"43-76","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":74,"title":["On selecting directions for directional distance functions in a non-parametric framework: a review"],"prefix":"10.1007","volume":"278","author":[{"given":"Ke","family":"Wang","sequence":"first","affiliation":[]},{"given":"Yujiao","family":"Xian","sequence":"additional","affiliation":[]},{"given":"Chia-Yen","family":"Lee","sequence":"additional","affiliation":[]},{"given":"Yi-Ming","family":"Wei","sequence":"additional","affiliation":[]},{"given":"Zhimin","family":"Huang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,2,11]]},"reference":[{"key":"2423_CR1","doi-asserted-by":"publisher","first-page":"314","DOI":"10.1016\/j.ejor.2015.10.064","volume":"250","author":"N Adler","year":"2016","unstructured":"Adler, N., & Voltab, N. (2016). Accounting for externalities and disposability: A directional economic environmental distance function. European Journal of Operational Research, 250, 314\u2013327.","journal-title":"European Journal of Operational Research"},{"key":"2423_CR2","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/s11123-011-0244-0","volume":"35","author":"MD Agee","year":"2012","unstructured":"Agee, M. D., Atkinson, S. E., & Crocker, T. D. (2012). Child maturation, time-invariant, and time-varying inputs: Their interaction in the production of child human capital. Journal of Productivity Analysis, 35, 29\u201344.","journal-title":"Journal of Productivity Analysis"},{"key":"2423_CR3","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1007\/s11123-007-0039-5","volume":"28","author":"J Aparicio","year":"2007","unstructured":"Aparicio, J., Ruiz, J. L., & Sirvent, I. (2007). Closest targets and minimum distance to the Pareto-efficient frontier in DEA. Journal of Productivity Analysis, 28, 209\u2013218.","journal-title":"Journal of Productivity Analysis"},{"key":"2423_CR4","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1016\/j.enpol.2014.01.016","volume":"68","author":"B Arabi","year":"2014","unstructured":"Arabi, B., Munisamy, S., Emrouznejad, A., & Shadman, F. (2014). Power industry restructuring and eco-efficiency changes: A new slacks-based model in Malmquist\u2013Luenberger Index measurement. Energy Policy, 68, 132\u2013145.","journal-title":"Energy Policy"},{"key":"2423_CR5","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1016\/j.mcm.2008.08.007","volume":"49","author":"C Baek","year":"2009","unstructured":"Baek, C., & Lee, J. (2009). The relevance of DEA benchmarking information and the least-distance measure. Mathematical and Computer Modelling, 49, 265\u2013275.","journal-title":"Mathematical and Computer Modelling"},{"issue":"3","key":"2423_CR6","doi-asserted-by":"publisher","first-page":"374","DOI":"10.1016\/j.strueco.2004.04.008","volume":"16","author":"E Ball","year":"2005","unstructured":"Ball, E., F\u00e4re, R., Grosskopf, S., & Zaim, O. (2005). Accounting for externalities in the measurement of productivity growth: The Malmquist cost productivity measure. Structural Change and Economic Dynamics, 16(3), 374\u2013394.","journal-title":"Structural Change and Economic Dynamics"},{"key":"2423_CR7","doi-asserted-by":"publisher","first-page":"2216","DOI":"10.1016\/j.ecolecon.2009.04.004","volume":"68","author":"MJ Bellenger","year":"2009","unstructured":"Bellenger, M. J., & Herlihy, A. T. (2009). An economic approach to environmental indices. Ecological Economics, 68, 2216\u20132223.","journal-title":"Ecological Economics"},{"key":"2423_CR8","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1006\/jeth.1996.0096","volume":"70","author":"RG Chambers","year":"1996","unstructured":"Chambers, R. G., Chung, Y., & F\u00e4re, R. (1996a). Benefit and distance functions. Journal of Economic Theory, 70, 407\u2013419.","journal-title":"Journal of Economic Theory"},{"key":"2423_CR9","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1111\/j.1468-0106.1996.tb00184.x","volume":"1","author":"R Chambers","year":"1996","unstructured":"Chambers, R., F\u00e4re, R., & Grosskopf, S. (1996b). Productivity growth in APEC countries. Pacific Economic Review, 1, 181\u2013190.","journal-title":"Pacific Economic Review"},{"issue":"5","key":"2423_CR10","doi-asserted-by":"publisher","first-page":"1064","DOI":"10.1287\/opre.1120.1094","volume":"60","author":"C-M Chen","year":"2012","unstructured":"Chen, C.-M., & Delmas, M. A. (2012). Measuring eco-inefficiency: A new frontier approach. Operations Research, 60(5), 1064\u20131079.","journal-title":"Operations Research"},{"key":"2423_CR11","doi-asserted-by":"publisher","first-page":"621","DOI":"10.1016\/j.omega.2012.06.006","volume":"41","author":"Y Chen","year":"2013","unstructured":"Chen, Y., Du, J., & Huo, J. Z. (2013). Super-efficiency based on a modified directional distance function. Omega, 41, 621\u2013625.","journal-title":"Omega"},{"key":"2423_CR12","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1006\/jema.1997.0146","volume":"51","author":"Y Chung","year":"1997","unstructured":"Chung, Y., F\u00e4re, R., & Grosskopf, S. (1997). Productivity and undesirable outputs: A directional distance function approach. Journal of Environmental Management, 51, 229\u2013240.","journal-title":"Journal of Environmental Management"},{"key":"2423_CR13","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1006\/jeem.1996.0005","volume":"30","author":"JS Coggins","year":"1996","unstructured":"Coggins, J. S., & Swinton, J. R. (1996). The price of pollution: A dual approach to valuing \n                    \n                      \n                    \n                    $$\\text{ SO }_2$$\n                    \n                      \n                        \n                          \n                          SO\n                          \n                            \n                            2\n                          \n                        \n                      \n                    \n                   allowances. Journal of Environmental Economics and Management, 30, 58\u201372.","journal-title":"Journal of Environmental Economics and Management"},{"issue":"9","key":"2423_CR14","doi-asserted-by":"publisher","first-page":"3921","DOI":"10.1016\/j.energy.2010.06.013","volume":"35","author":"RG Cong","year":"2010","unstructured":"Cong, R. G., & Wei, Y. M. (2010). Potential impact of (CET) carbon emissions trading on China\u2019s power sector: A perspective from different allowance allocation options. Energy, 35(9), 3921\u20133931.","journal-title":"Energy"},{"issue":"6","key":"2423_CR15","doi-asserted-by":"publisher","first-page":"4148","DOI":"10.1016\/j.rser.2012.03.049","volume":"16","author":"RG Cong","year":"2012","unstructured":"Cong, R. G., & Wei, Y. M. (2012). Experimental comparison of impact of auction format on carbon allowance market. Renewable & Sustainable Energy Reviews, 16(6), 4148\u20134156.","journal-title":"Renewable & Sustainable Energy Reviews"},{"key":"2423_CR16","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1023\/A:1007701304281","volume":"11","author":"WW Cooper","year":"1999","unstructured":"Cooper, W. W., Park, K. S., & Pastor, J. T. (1999). RAM: A range adjusted measure of inefficiency for use with additive models, and relations to other models and measures in DEA. Journal of Productivity Analysis, 11, 5\u201342.","journal-title":"Journal of Productivity Analysis"},{"key":"2423_CR17","doi-asserted-by":"publisher","first-page":"585","DOI":"10.1016\/j.ijpe.2009.04.011","volume":"120","author":"B Dervaux","year":"2009","unstructured":"Dervaux, B., Leleu, H., Minvielle, E., Valdmanis, V., Aegerter, P., & Guidet, B. (2009). Performance of French intensive care units: A directional distance function approach at the patient level. International Journal of Production Economics, 120, 585\u2013594.","journal-title":"International Journal of Production Economics"},{"key":"2423_CR18","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1016\/j.reseneeco.2015.11.001","volume":"43","author":"LM Du","year":"2016","unstructured":"Du, L. M., Hanley, A., & Zhang, N. (2016). Environmental technical efficiency, technology gap and shadow price of coal-fuelled power plants in China: A parametric meta-frontier analysis. Resource and Energy Economics, 43, 14\u201332.","journal-title":"Resource and Energy Economics"},{"issue":"3","key":"2423_CR19","doi-asserted-by":"publisher","first-page":"253","DOI":"10.2307\/2343100","volume":"120","author":"M Farrell","year":"1957","unstructured":"Farrell, M. (1957). The measurement of productive efficiency. Journal of the Royal Statistical Society Series A (General) Part O, 120(3), 253\u2013281.","journal-title":"Journal of the Royal Statistical Society Series A (General) Part O"},{"key":"2423_CR20","volume-title":"New directions: Efficiency and productivity","author":"R F\u00e4re","year":"2004","unstructured":"F\u00e4re, R., & Grosskopf, S. (2004). New directions: Efficiency and productivity. Boston: Kluwer Academic Publishers."},{"key":"2423_CR21","doi-asserted-by":"publisher","first-page":"320","DOI":"10.1016\/j.ejor.2009.01.031","volume":"200","author":"R F\u00e4re","year":"2010","unstructured":"F\u00e4re, R., & Grosskopf, S. (2010). Directional distance functions and slacks-based measures of efficiency. European Journal of Operational Research, 200, 320\u2013322.","journal-title":"European Journal of Operational Research"},{"issue":"1","key":"2423_CR22","doi-asserted-by":"publisher","first-page":"90","DOI":"10.2307\/1928055","volume":"71","author":"R F\u00e4re","year":"1989","unstructured":"F\u00e4re, R., Grosskopf, S., Lovell, C. A. K., & Pasurka, C. (1989). Multilateral productivity comparisons when some outputs are undesirable: A nonparametric approach. Review of Economics and Statistics, 71(1), 90\u201398.","journal-title":"Review of Economics and Statistics"},{"key":"2423_CR23","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1016\/j.jeconom.2004.05.010","volume":"126","author":"R F\u00e4re","year":"2005","unstructured":"F\u00e4re, R., Grosskopf, S., Noh, D. W., & Weber, W. (2005). Characteristics of a polluting technology: Theory and practice. Journal of Econometrics, 126, 469\u2013492.","journal-title":"Journal of Econometrics"},{"key":"2423_CR24","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1016\/0165-0572(86)90016-2","volume":"8","author":"R F\u00e4re","year":"1986","unstructured":"F\u00e4re, R., Grosskopf, S., & Pasurka, C. (1986). Effects on relative efficiency in electric power generation due to environmental controls. Resources and Energy, 8, 167\u2013184.","journal-title":"Resources and Energy"},{"key":"2423_CR25","doi-asserted-by":"publisher","first-page":"715","DOI":"10.1016\/j.ejor.2015.07.040","volume":"248","author":"R F\u00e4re","year":"2016","unstructured":"F\u00e4re, R., Grosskopf, S., & Pasurka, C. (2016). Technical change and pollution abatement cost. European Journal of Operational Research, 248, 715\u2013724.","journal-title":"European Journal of Operational Research"},{"key":"2423_CR26","doi-asserted-by":"publisher","first-page":"1055","DOI":"10.1016\/j.energy.2006.09.005","volume":"32","author":"R F\u00e4re","year":"2007","unstructured":"F\u00e4re, R., Grosskopf, S., & Pasurka, C. A. (2007). Environmental production functions and environmental directional distance functions. Energy, 32, 1055\u20131066.","journal-title":"Energy"},{"key":"2423_CR27","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1080\/00036846.2010.498368","volume":"44","author":"R F\u00e4re","year":"2012","unstructured":"F\u00e4re, R., Grosskopf, S., Pasurka, C. A., & Weber, W. (2012). Substitutability among undesirable outputs. Applied Economics, 44, 39\u201347.","journal-title":"Applied Economics"},{"key":"2423_CR28","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1016\/j.ecolecon.2004.12.022","volume":"56","author":"R F\u00e4re","year":"2006","unstructured":"F\u00e4re, R., Grosskopf, S., & Weber, W. L. (2006). Shadow prices and pollution costs in U.S. agriculture. Ecological Economics, 56, 89\u2013103.","journal-title":"Ecological Economics"},{"key":"2423_CR29","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1007\/s11123-012-0333-8","volume":"40","author":"R F\u00e4re","year":"2013","unstructured":"F\u00e4re, R., Grosskopf, S., & Wittaker, G. (2013). Directional output distance functions: Endogenous constraints based on exogenous normalization constraints. Journal of Productivity Analysis, 40, 267\u2013269.","journal-title":"Journal of Productivity Analysis"},{"issue":"2","key":"2423_CR30","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1016\/0925-5273(92)90009-V","volume":"27","author":"R F\u00e4re","year":"1992","unstructured":"F\u00e4re, R., & Logan, J. (1992). The rate of return regulated version of Farrell efficiency. International Journal of Production Economics, 27(2), 161\u2013165.","journal-title":"International Journal of Production Economics"},{"key":"2423_CR31","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-0651-1","volume-title":"Multi-output production and duality: Theory and applications","author":"R F\u00e4re","year":"1995","unstructured":"F\u00e4re, R., & Primont, D. (1995). Multi-output production and duality: Theory and applications. Boston: Kluwer Academic Publishers."},{"key":"2423_CR32","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1023\/A:1007746205433","volume":"11","author":"FX Frei","year":"1999","unstructured":"Frei, F. X., & Harker, P. T. (1999). Projections onto efficient frontiers: Theoretical and computational extensions to DEA. Journal of Productivity Analysis, 11, 275\u2013300.","journal-title":"Journal of Productivity Analysis"},{"key":"2423_CR33","doi-asserted-by":"publisher","first-page":"274","DOI":"10.1016\/j.seps.2008.12.001","volume":"43","author":"H Fukuyama","year":"2009","unstructured":"Fukuyama, H., & Weber, W. L. (2009). A directional slacks-based measure of technical inefficiency. Socio-Economic Planning Sciences, 43, 274\u2013287.","journal-title":"Socio-Economic Planning Sciences"},{"key":"2423_CR34","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1007\/s11123-012-0301-3","volume":"39","author":"G Granderson","year":"2013","unstructured":"Granderson, G., & Prior, D. (2013). Environmental externalities and regulation constrained cost productivity growth in the US electric utility industry. Journal of Productivity Analysis, 39, 243\u2013257.","journal-title":"Journal of Productivity Analysis"},{"key":"2423_CR35","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1016\/j.ejor.2012.12.009","volume":"227","author":"GE Halkos","year":"2013","unstructured":"Halkos, G. E., & Tzeremes, N. G. (2013). A conditional directional distance function approach for measuring regional environmental efficiency: Evidence from UK regions. European Journal of Operational Research, 227, 182\u2013189.","journal-title":"European Journal of Operational Research"},{"key":"2423_CR36","doi-asserted-by":"publisher","first-page":"920","DOI":"10.1093\/ajae\/aau035","volume":"97","author":"B Hampf","year":"2014","unstructured":"Hampf, B., & Kr\u00fcger, J. J. (2014a). Optimal directions for directional distance functions: An exploration of potential reductions of greenhouse gases. American Journal of Agricultural Economics, 97, 920\u2013938.","journal-title":"American Journal of Agricultural Economics"},{"key":"2423_CR37","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/j.trd.2014.08.020","volume":"33","author":"B Hampf","year":"2014","unstructured":"Hampf, B., & Kruger, J. J. (2014b). Technical efficiency of automobiles\u2014A nonparametric approach incorporating carbon dioxide emissions. Transportation Research Part D, 33, 47\u201362.","journal-title":"Transportation Research Part D"},{"issue":"2","key":"2423_CR38","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1007\/s11123-011-0255-x","volume":"38","author":"A Hailu","year":"2012","unstructured":"Hailu, A., & Chambers, R. G. (2012). A Luenberger soil quality indicator. Journal of Productivity Analysis, 38(2), 145\u2013154.","journal-title":"Journal of Productivity Analysis"},{"key":"2423_CR39","doi-asserted-by":"publisher","first-page":"280","DOI":"10.1016\/j.ecolecon.2005.02.004","volume":"56","author":"S Kumar","year":"2006","unstructured":"Kumar, S. (2006). Environmentally sensitive productivity growth: A global analysis using Malmquist-Luenberger index. Ecological Economics, 56, 280\u2013293.","journal-title":"Ecological Economics"},{"issue":"4","key":"2423_CR40","doi-asserted-by":"publisher","first-page":"1077","DOI":"10.1111\/j.1467-8276.2005.00788.x","volume":"87","author":"T Kuosmanen","year":"2005","unstructured":"Kuosmanen, T. (2005). Weak disposability in nonparametric productivity analysis with undesirable outputs. American Journal of Agricultural Economics, 87(4), 1077\u20131082.","journal-title":"American Journal of Agricultural Economics"},{"key":"2423_CR41","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1016\/j.ejor.2014.01.026","volume":"237","author":"C-Y Lee","year":"2014","unstructured":"Lee, C.-Y. (2014). Meta-data envelopment analysis: Finding a direction towards marginal profit maximization. European Journal of Operational Research, 237, 207\u2013216.","journal-title":"European Journal of Operational Research"},{"key":"2423_CR42","doi-asserted-by":"publisher","first-page":"659","DOI":"10.1016\/j.ejor.2016.05.051","volume":"255","author":"C-Y Lee","year":"2016","unstructured":"Lee, C.-Y. (2016). Nash-profit efficiency: A measure of changes in market structures. European Journal of Operational Research, 255, 659\u2013663.","journal-title":"European Journal of Operational Research"},{"issue":"2","key":"2423_CR43","doi-asserted-by":"publisher","first-page":"702","DOI":"10.1007\/s10957-014-0557-z","volume":"164","author":"C-Y Lee","year":"2015","unstructured":"Lee, C.-Y., & Johnson, A. L. (2015). Measuring efficiency in imperfectly competitive markets: An example of rational inefficiency. Journal of Optimization Theory and Applications, 164(2), 702\u2013722.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"2423_CR44","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1006\/jema.2001.0480","volume":"64","author":"J Lee","year":"2002","unstructured":"Lee, J., Park, J., & Kim, T. (2002). Estimation of the shadow prices of pollutants with production\/environment inefficiency taken into account: A nonparametric directional distance function approach. Journal of Environmental Management, 64, 365\u2013375.","journal-title":"Journal of Environmental Management"},{"key":"2423_CR45","doi-asserted-by":"publisher","first-page":"474","DOI":"10.1016\/j.ejor.2013.05.028","volume":"231","author":"H Leleu","year":"2013","unstructured":"Leleu, H. (2013). Shadow pricing of undesirable outputs in nonparametric analysis. European Journal of Operational Research, 231, 474\u2013480.","journal-title":"European Journal of Operational Research"},{"issue":"2","key":"2423_CR46","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1007\/BF00941466","volume":"75","author":"DG Luenberger","year":"1992","unstructured":"Luenberger, D. G. (1992). New optimality principle for economic efficiency and equilibrium. Journal of Optimization Theory and Applications, 75(2), 221\u2013264.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"2423_CR47","doi-asserted-by":"publisher","first-page":"1918","DOI":"10.1016\/j.ecolecon.2010.04.012","volume":"69","author":"AJ Macpherson","year":"2010","unstructured":"Macpherson, A. J., Principe, P. P., & Smith, E. R. (2010). A directional distance function approach to regional environmental-economic assessments. Ecological Economics, 69, 1918\u20131925.","journal-title":"Ecological Economics"},{"key":"2423_CR48","doi-asserted-by":"publisher","first-page":"1124","DOI":"10.1016\/j.eneco.2011.09.011","volume":"34","author":"K Matsushita","year":"2012","unstructured":"Matsushita, K., & Yamane, F. (2012). Pollution from the electric power sector in Japan and efficient pollution reduction. Energy Economics, 34, 1124\u20131130.","journal-title":"Energy Economics"},{"key":"2423_CR49","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1016\/j.jeem.2012.02.005","volume":"64","author":"S Murty","year":"2012","unstructured":"Murty, S., Russell, R. R., & Levkoff, S. B. (2012). On modeling pollution-generating technologies. Journal of Environmental Economics and Management, 64, 117\u2013135.","journal-title":"Journal of Environmental Economics and Management"},{"key":"2423_CR50","unstructured":"Njuki, E., & Bravo-Ureta, B. E. (2015). The economic costs of environmental regulation in U.S. dairy farming: A directional distance function approach. American Journal of Agricultural Economics, 97(4), 1087\u20131106."},{"key":"2423_CR51","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1007\/s11123-010-0178-y","volume":"34","author":"D Oh","year":"2010","unstructured":"Oh, D. (2010). A global Malmquist\u2013Luenberger productivity index. Journal of Productivity Analysis, 34, 183\u2013197.","journal-title":"Journal of Productivity Analysis"},{"key":"2423_CR52","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1016\/j.tre.2013.01.003","volume":"57","author":"TH Oum","year":"2013","unstructured":"Oum, T. H., Pathomsiri, S., & Yoshida, S. (2013). Limitations of DEA-based approach and alternative methods in the measurement and comparison of social efficiency across firms in different transport modes: An empirical study in Japan. Transportation Research Part E, 57, 16\u201326.","journal-title":"Transportation Research Part E"},{"key":"2423_CR53","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1016\/j.tre.2007.07.002","volume":"44","author":"S Pathomsiri","year":"2008","unstructured":"Pathomsiri, S., Haghani, A., Dresner, M., & Windle, R. J. (2008). Impact of undesirable outputs on the productivity of US airports. Transportation Research Part E, 44, 235\u2013259.","journal-title":"Transportation Research Part E"},{"key":"2423_CR54","doi-asserted-by":"publisher","first-page":"798","DOI":"10.1016\/j.ejor.2012.02.025","volume":"220","author":"AJ Picazo-Tadeo","year":"2012","unstructured":"Picazo-Tadeo, A. J., Beltr\u00e1n-Esteve, M., & G\u00f3mez-Lim\u00f3n, J. A. (2012). Assessing eco-efficiency with directional distance functions. European Journal of Operational Research, 220, 798\u2013809.","journal-title":"European Journal of Operational Research"},{"key":"2423_CR55","doi-asserted-by":"publisher","first-page":"3332","DOI":"10.1016\/j.jenvman.2009.05.015","volume":"90","author":"AJ Picazo-Tadeo","year":"2009","unstructured":"Picazo-Tadeo, A. J., & Prior, D. (2009). Environmental externalities and efficiency measurement. Journal of Environmental Management, 90, 3332\u20133339.","journal-title":"Journal of Environmental Management"},{"key":"2423_CR56","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1016\/j.reseneeco.2004.07.001","volume":"27","author":"AJ Picazo-Tadeo","year":"2005","unstructured":"Picazo-Tadeo, A. J., Reig-Mart\u00ednez, E., & Hern\u00e1ndez-Sancho, F. (2005). Directional distance functions and environmental regulation. Resource Energy Economics, 27, 131\u2013142.","journal-title":"Resource Energy Economics"},{"issue":"6","key":"2423_CR57","doi-asserted-by":"publisher","first-page":"1743","DOI":"10.1287\/opre.1090.0794","volume":"58","author":"VV Podinovski","year":"2010","unstructured":"Podinovski, V. V., & F\u00f8rsund, F. R. (2010). Differential characteristics of efficient frontiers in data envelopment analysis. Operations Research, 58(6), 1743\u20131754.","journal-title":"Operations Research"},{"key":"2423_CR58","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1023\/A:1022813702387","volume":"19","author":"M Portela","year":"2003","unstructured":"Portela, M., Borges, P. C., & Thanassoulis, E. (2003). Finding closest targets in non-oriented DEA models: The case of convex and non-convex technologies. Journal of Productivity Analysis, 19, 251\u2013269.","journal-title":"Journal of Productivity Analysis"},{"key":"2423_CR59","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1016\/j.ijpe.2008.09.005","volume":"116","author":"SC Ray","year":"2008","unstructured":"Ray, S. C., Chen, L., & Mukherjee, K. (2008). Input price variation across locations and a generalized measure of cost efficiency. International Journal of Production Economics, 116, 208\u2013218.","journal-title":"International Journal of Production Economics"},{"key":"2423_CR60","first-page":"133","volume":"35","author":"SC Ray","year":"2000","unstructured":"Ray, S. C., & Mukherjee, K. (2000). Decomposition of cost competitiveness in US manufacturing: Some state by state comparisons. Indian Economic Review, 35, 133\u2013153.","journal-title":"Indian Economic Review"},{"key":"2423_CR61","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1016\/j.eneco.2006.01.005","volume":"29","author":"JP Rezek","year":"2007","unstructured":"Rezek, J. P., & Campbell, R. C. (2007). Cost estimates for multiple pollutants: A maximum entropy approach. Energy Economics, 29, 503\u2013519.","journal-title":"Energy Economics"},{"key":"2423_CR62","volume-title":"Theory of cost and production functions","author":"RW Shephard","year":"1970","unstructured":"Shephard, R. W. (1970). Theory of cost and production functions. Princeton, NJ: Princeton University Press."},{"key":"2423_CR63","doi-asserted-by":"publisher","first-page":"853","DOI":"10.1016\/j.ejor.2012.02.030","volume":"220","author":"L Simar","year":"2012","unstructured":"Simar, L., Vanhems, A., & Wilson, P. W. (2012). Statistical inference for DEA estimators of directional distances. European Journal of Operational Research, 220, 853\u2013864.","journal-title":"European Journal of Operational Research"},{"key":"2423_CR64","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/j.jenvman.2005.09.005","volume":"80","author":"M Vardanyan","year":"2006","unstructured":"Vardanyan, M., & Noh, D. W. (2006). Approximating pollution abatement costs via alternative specifications of a multi-output production technology: A case of the U.S. electric utility industry. Journal of Environmental Management, 80, 177\u2013190.","journal-title":"Journal of Environmental Management"},{"key":"2423_CR65","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1016\/j.eneco.2015.11.013","volume":"54","author":"K Wang","year":"2016","unstructured":"Wang, K., & Wei, Y. M. (2016). Sources of energy productivity change in China during 1997\u20132012: A decomposition analysis based on the Luenberger productivity indicator. Energy Economics, 54, 50\u201359.","journal-title":"Energy Economics"},{"key":"2423_CR66","doi-asserted-by":"publisher","first-page":"574","DOI":"10.1016\/j.enpol.2012.04.038","volume":"46","author":"K Wang","year":"2012","unstructured":"Wang, K., Wei, Y. M., & Zhang, X. (2012). A comparative analysis of China\u2019s regional energy and emission performance: Which is the better way to deal with undesirable outputs? Energy Policy, 46, 574\u2013584.","journal-title":"Energy Policy"},{"key":"2423_CR67","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1016\/j.apenergy.2012.11.039","volume":"104","author":"K Wang","year":"2013","unstructured":"Wang, K., Wei, Y. M., & Zhang, X. (2013). Energy and emissions efficiency patterns of Chinese regions: A multi-directional efficiency analysis. Applied Energy, 104, 105\u2013116.","journal-title":"Applied Energy"},{"key":"2423_CR68","doi-asserted-by":"publisher","first-page":"545","DOI":"10.1016\/j.ecolind.2016.02.034","volume":"66","author":"K Wang","year":"2016","unstructured":"Wang, K., Xian, Y., Wei, Y. M., & Huang, Z. (2016). Sources of carbon productivity change: A decomposition and disaggregation analysis based on global Luenberger productivity indicator and endogenous directional distance function. Ecological Indicators, 66, 545\u2013555.","journal-title":"Ecological Indicators"},{"key":"2423_CR69","doi-asserted-by":"publisher","first-page":"6323","DOI":"10.1016\/j.enpol.2007.07.013","volume":"35","author":"M Watanabe","year":"2007","unstructured":"Watanabe, M., & Tanaka, K. (2007). Efficiency analysis of Chinese industry: A directional distance function approach. Energy Policy, 35, 6323\u20136331.","journal-title":"Energy Policy"},{"key":"2423_CR70","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1016\/j.ejor.2012.04.022","volume":"221","author":"P Zhou","year":"2012","unstructured":"Zhou, P., Ang, B. W., & Wang, H. (2012). Energy and CO\n                    \n                      \n                    \n                    $$_2$$\n                    \n                      \n                        \n                          \n                          2\n                        \n                      \n                    \n                   emission performance in electricity generation: A non-radial directional distance function approach. European Journal of Operational Research, 221, 625\u2013635.","journal-title":"European Journal of Operational Research"},{"issue":"3","key":"2423_CR71","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1007\/s11123-012-0292-0","volume":"40","author":"JL Zofio","year":"2013","unstructured":"Zofio, J. L., Paster, J. T., & Aparicio, J. (2013). The directional profit efficiency measure: On why profit efficiency is either technical or allocative. Journal of Productivity Analysis, 40(3), 257\u2013266.","journal-title":"Journal of Productivity Analysis"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-017-2423-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10479-017-2423-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-017-2423-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,18]],"date-time":"2019-07-18T09:42:46Z","timestamp":1563442966000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10479-017-2423-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,11]]},"references-count":71,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2019,7]]}},"alternative-id":["2423"],"URL":"https:\/\/doi.org\/10.1007\/s10479-017-2423-5","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,2,11]]},"assertion":[{"value":"11 February 2017","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}