Abstract
Recent papers have provided a number of overviews in connection with the fast growing literature on bad outputs in Data Envelopment Analysis (DEA), such as defective products, emissions and waste. However, there does not seem to exist any comprehensive overview of the opposite phenomenon, particularly not regarding DEA, namely of bads as undesirable objects or factors which are desirable input (flow) into transformation processes, e.g. into waste incineration. Moreover, the terms ‘bad input’ and ‘(un-)desirable input/factor’ are not clearly defined. We use a purely preference-based notion for the desirability of inputs and outputs. A systematic literature search reveals only 22 DEA articles which explicitly address the (desirable) input of bads as original undesirable factors, i.e. as input into the first stage of a single- or multi-stage process. Their detailed analysis shows that current approaches are based on two core ideas involving various efficiency measures. Only four papers deal with real applications of original undesirable factors, namely waste water treatment. Moreover, those disposability assumptions for DEA models often critically discussed in relation to bad outputs (e.g. weak disposability) are not used in these papers, presumably because the processes modelled are themselves disposal processes. Finally, we exemplarily demonstrate how DEA models with bads as inputs (and outputs) can be systematically derived from a decision-theoretic generalization of DEA methodology proposed in the literature.








Similar content being viewed by others
References
Abbasali, M., & Ebadi, S. (2012). Determination measure of efficiency using by undesirable inputs of DEA. Life Science Journal-Acta Zhengzhou University Overseas Edition, 9(4), 4714–4718.
Akther, S., Fukuyama, H., & Weber, W. L. (2013). Estimating two-stage network slacks-based inefficiency: An application to Bangladesh banking. Omega, 41(1), 88–96.
Aliakbarpoor, Z., & Izadikhah, M. (2012). Evaluation and ranking DMUs in the presence of both undesirable and ordinal factors in data envelopment analysis. International Journal of Automation and Computing, 9(6), 609–615.
Allen, K. (1999). DEA in the ecological context—an overview. In G. Westermann (Ed.), Data envelopment analysis in the service sector (pp. 203–235). Wiesbaden: Deutscher Universitäts-Verlag.
Amirteimoori, A., Kordrostami, S., & Sarparast, M. (2006). Modeling undesirable factors in data envelopment analysis. Applied Mathematics and Computation, 180(2), 444–452.
Ardabili, J. S., Aghayi, N., & Monzali, A. (2007). New efficiency using undesirable factors of data envelopment analysis. AMO—Advanced Modeling and Optimization, 9(2), 249–255.
Ashrafi, A., & Jaafar, A. B. (2011). Performance measurement of two-stage production systems with undesirable factors by data envelopment analysis. Journal of Applied Sciences, 11(20), 3515–3519.
Baumgärtner, S., Dyckhoff, H., Faber, M., Proops, J., & Schiller, J. (2001). The concept of joint production and ecological economies. Ecological Economics, 36(3), 365–372.
Boggs, R. L. (1997). Hazardous waste treatment facilities: Modeling production with pollution as both an input and an output. Ann Arbor: UMI Company.
Chen, C.-M., Du, J., Huo, J., & Zhu, J. (2012). Undesirable factors in integer-valued DEA: Evaluating the operational efficiencies of city bus systems considering safety records. Decision Support Systems, 54(1), 330–335.
Chen, Y., Cook, W. D., Li, N., & Zhu, J. (2009). Additive efficiency decomposition in two stage DEA. European Journal of Operational Research, 196(3), 1170–1176.
Cheng, G., Zervopoulos, P., & Qian, Z. (2013). A variant of radial measure capable of dealing with negative inputs and outputs in data envelopment analysis. European Journal of Operational Research, 225(1), 100–105.
Chung, Y. H., Färe, R., & Grosskopf, S. (1997). Productivity and undesirable outputs: A directional distance function approach. Journal of Environmental Management, 51(3), 229–240.
Cook, W. D., & Zhu, J. (2014). Data envelopment analysis: A handbook on the modeling of internal structures and networks. New York: Springer.
Cooper, W. W., Seiford, L. M., & Tone, K. (2007). Data envelopment analysis: A comprehensive text with models, applications, references and DEA-solver software (2nd ed.). New York: Springer.
Cooper, W. W., Seiford, L. M., & Zhu, J. (2011). Handbook on data envelopment analysis (2nd ed.). New York: Springer.
Dakpo, K. H., Jeanneaux, P., & Latruffe, L. (2016). Modelling pollution-generating technologies in performance benchmarking: Recent developments, limits and future prospects in the nonparametric framework. European Journal of Operational Research, 250(2), 347–359.
Daly, H. E. (2005). Economics in a full world. Scientific American, 293(3), 100–107.
Diabat, A., Shetty, U., & Pakkala, T. P. M. (2015). Improved efficiency measures through directional distance formulation of data envelopment analysis. Annals of Operations Research, 229(1), 325–346.
Dyckhoff, H. (1992). Betriebliche Produktion: Theoretische grundlagen einer umweltorientierten Produktionswirtschaft. Berlin: Springer.
Dyckhoff, H. (2000). The natural environment—towards an essential factor of the future. International Journal of Production Research, 38(12), 2583–2590.
Dyckhoff, H. (2016). Sustainability performance measurement with data envelopment analysis: A combined production- and decision-theoretic approach. Available at SSRN: https://ssrn.com/abstract=2868027.
Dyckhoff, H., & Allen, K. (2001). Measuring ecological efficiency with data envelopment analysis (DEA). European Journal of Operational Research, 132(2), 312–325.
Ethridge, D. (1973). The inclusion of wastes in the theory of the firm. Journal of Political Economy, 81(6), 1430–1441.
Emrouznejad, A., Anouze, A. L., & Thanassoulis, E. (2010). A semi-oriented radial measure for measuring the efficiency of decision making units with negative data, using DEA. European Journal of Operational Research, 200(1), 297–304.
Färe, R., & Grosskopf, S. (1983). Measuring output efficiency. European Journal of Operational Research, 13(2), 173–179.
Färe, R., Grosskopf, S., Lovell, C. A. K., & Pasurka, C. (1989). Multilateral productivity comparisons when some outputs are undesirable: A nonparametric approach. The Review of Economics and Statistics, 71(1), 90–98.
Färe, R., Grosskopf, S., & Pasurka, C. (1986). Effects on relative efficiency in electric power generation due to environmental controls. Resources and Energy, 8(2), 173–179.
Färe, R., Grosskopf, S., & Pasurka, C. (2007). Environmental production functions and environmental directional distance functions. Energy, 32(7), 1055–1066.
Georgescu-Roegen, N. (1975). Energy and economic myths. Southern Economic Journal, 41(3), 347–381.
Harzing, A. W. (2013). Journal quality list, 50th version (5th July 2013). Demand (14th October 2013) at: http://www.harzing.com/jql.htm.
Huang, R., & Li, Y. (2013). Undesirable input–output two-phase DEA model in an environmental performance audit. Mathematical and Computer Modelling, 58(5–6), 971–979.
Jahanshahloo, G. R., Vencheh, A. H., Foroughi, A. A., & Matin, R. K. (2004). Inputs/outputs estimation in DEA when some factors are undesirable. Applied Mathematics and Computation, 156(1), 19–32.
Jahanshahloo, G. R., Lotfi, F. H., Shoja, N., Tohidi, G., & Razavyan, S. (2005). Undesirable inputs and outputs in DEA models. Applied Mathematics and Computation, 169(2), 917–925.
Koopmans, T. C. (1951). Analysis of production as an efficient combination of activities. In T. C. Koopmans (Ed.), Activity analysis of production and allocation (pp. 33–97). New York: Wiley.
Kordrostami, S., & Amirteimoori, A. (2005). Un-desirable factors in multi-component performance measurement. Applied Mathematics and Computation, 171(2), 721–729.
Lampe, H. W., & Hilgers, D. (2015). Trajectories of efficiency measurement: A bibliometric analysis of DEA and SFA. European Journal of Operational Research, 240(1), 1–21.
Lewis, H. F., & Sexton, T. R. (2004). Data envelopment analysis with reverse inputs and outputs. Journal of Productivity Analysis, 21(2), 113–132.
Liu, J. S., Lu, L. Y. Y., Lu, W.-M., & Lin, B. J. Y. (2013a). Data envelopment analysis 1978–2010: A citation-based literature survey. Omega, 41(1), 3–15.
Liu, J. S., Lu, L. Y. Y., Lu, W.-M., & Lin, B. J. Y. (2013b). A survey on of DEA applications. Omega, 41(5), 893–902.
Liu, W., Meng, W., Li, X. X., & Zhang, D. Q. (2010). DEA models with undesirable inputs and outputs. Annals of Operations Research, 173(1), 177–194.
Liu, W., Sharp, J., & Wu, Z. (2006). Preference, production and performance in data envelopment analysis. Annals of Operations Research, 145(1), 105–127.
Liu, W., Zhou, Z., Ma, C. X., Liu, D., & Shen, W. (2015). Two-stage DEA models with undesirable input-intermediate-outputs. Omega, 56, 74–87.
Lovell, C. A. K., & Pastor, J. T. (1995). Units invariant and translation invariant DEA models. Operations Research Letters, 18(3), 147–151.
Molinos-Senante, M., Hernández-Sancho, F., Mocholí-Arce, M., & Sala-Garrido, R. (2015). Productivity growth of wastewater treatment plants—accounting for environmental impacts: A Malmquist-Luenberger index approach. Urban Water Journal, 13(5), 476–485.
Müser, M., & Dyckhoff, H. (2017). Quality splitting in waste incineration due to non-convex production possibilities. Journal of Business Economics, 87(1), 73–96.
Pastor, J. T. (1996). Translation invariance in data envelopment analysis: A generalization. Annals of Operations Research, 66(2), 93–102.
Pittman, R. W. (1983). Multilateral productivity comparisons with undesirable outputs. The Economic Journal, 93(372), 883–891.
Portela, M. C. A. S., Thanassoulis, E., & Simpson, G. (2004). Negative data in DEA: A directional distance approach applied to bank branches. Journal of the Operational Research Society, 55(10), 1111–1121.
Rees, W. E., & Wackernagel, M. (2013). The shoe fits, but the footprint is larger than earth. PLOS Biology, 11(11), 1–3.
Sahoo, B. K., Luptacik, M., & Mahlberg, B. (2011). Alternative measures of environmental technology structure in DEA: An application. European Journal of Operational Research, 215(3), 750–762.
Seiford, L. M., & Zhu, J. (2002). Modeling undesirable factors in efficiency evaluation. European Journal of Operational Research, 142(1), 16–20.
Sharp, J. A., Meng, W., & Liu, W. (2007). A modified slacks-based measure model for data envelopment analysis with ‘Natural’ negative outputs and inputs. Journal of the Operational Research Society, 58(12), 1672–1677.
Shephard, R. W. (1970). Theory of cost and production functions. Princeton: Princeton University Press.
Song, M., An, Q., Zhang, W., Wang, Z., & Wu, J. (2012). Environmental efficiency evaluation based on data envelopment analysis: A review. Renewable and Sustainable Energy Reviews, 16(7), 4465–4469.
Tone, K. (2001). A slacks-based measure of efficiency in data envelopment analysis. European Journal of Operational Research, 130(3), 498–509.
Tyteca, D. (1996). On the measurement of the environmental performance of firms: Literature review and a productive efficiency perspective. Journal of Environmental Management, 46(3), 281–308.
Vencheh, A. H., Matin, R. K., & Kajani, M. T. (2005). Undesirable factors in efficiency measurement. Applied Mathematics and Computation, 163(2), 547–552.
Wojcik, V., Dyckhoff, H., Gutgesell, S., Müser, M. (2015). Übelinputs in der Data Envelopment Analysis. Unpublished working paper, RWTH Aachen University, Aachen. Demand (1st July 2016) at: http://www.lut.rwth-aachen.de/index.php/forschung/arbeitsberichte.
Worthington, A. C. (2014). A review of frontier approaches to efficiency and productivity measurement in Urban water utilities. Urban Water Journal, 1(11), 55–73.
Yaisawarng, S., & Klein, J. D. (1994). The effects of sulfur dioxide controls on productivity change in the U.S. electric power industry. Review of Economics and Statistics, 76(3), 447–460.
Zhang, N., & Choi, Y. (2014). A note on evolution of directional distance function and its development in energy and environment studies 1997–2013. Renewable and Sustainable Energy Reviews, 33, 50–59.
Zhou, Z., & Liu, W. (2015). DEA models with undesirable inputs, intermediates, and outputs. In J. Zhu (Ed.), Data envelopment analysis: A handbook of models and methods (pp. 415–446). New York: Springer.
Acknowledgements
We are most grateful to two anonymous reviewers who helped to improve a former version of this paper a lot.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wojcik, V., Dyckhoff, H. & Gutgesell, S. The desirable input of undesirable factors in data envelopment analysis. Ann Oper Res 259, 461–484 (2017). https://doi.org/10.1007/s10479-017-2523-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-017-2523-2