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A well-defined composite indicator: an application to corporate social responsibility. (English) Zbl 1442.90095
Summary: This paper introduces a model to construct composite indicators for performance evaluation of decision making units, which is based upon the determination of the least distance from each assessed unit to a frontier estimated by data envelopment analysis. This generates less demanding targets from a benchmarking point of view. The model also makes it possible to account for the existence of slacks in all the considered dimensions (sub-indicators), playing with the notion of Pareto efficiency. Additionally, our approach satisfies units invariance, translation invariance and strong monotonicity and ensures that the weights used for the aggregation of the sub-indicators are always strictly positive. All previous approaches based on data envelopment analysis have failed to satisfy at least one of these properties. We also implement a new version of the Russell output measure of technical efficiency working with full-dimensional efficient facets. Finally, the new approach is illustrated by an application to the sphere of corporate social responsibility, showing the main empirical implications of the theoretical properties.
MSC:
90B50 Management decision making, including multiple objectives
90C05 Linear programming
90C11 Mixed integer programming
91B38 Production theory, theory of the firm
62R07 Statistical aspects of big data and data science
Software:
CPLEX
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[1] 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
[2] Banker, RD; Charnes, A.; Cooper, WW, Some models for estimating technical and scale inefficiencies in Data Envelopment Analysis, Manag. Sci., 30, 1078-1092 (1984) · Zbl 0552.90055
[3] Chambers, RG; Chung, Y.; Färe, R., Profit, directional distance functions, and Nerlovian efficiency, J. Optim. Theory Appl., 98, 2, 351-364 (1998) · Zbl 0909.90040
[4] Färe, R.; Grosskopf, S.; Lovell, CAK, The Measurement of Efficiency of Production (1985), Boston: Kluwer Academic Publishers, Boston
[5] Lovell, CAK; Pastor, JT, Units invariant and translation invariant DEA models, Oper. Res. Lett., 18, 3, 147-151 (1995) · Zbl 0855.90004
[6] Aparicio, J.; Pastor, JT; Vidal, F., The weighted additive distance function, Eur. J. Oper. Res., 254, 1, 338-346 (2016) · Zbl 1346.91119
[7] Pastor, JT; Ruiz, JL; Sirvent, I., An enhanced DEA Russell graph efficiency measure, Eur. J. Oper. Res., 115, 596-607 (1999) · Zbl 0946.91030
[8] Tone, K., A slacks-based measure of efficiency in data envelopment analysis, Eur. J. Oper. Res., 130, 3, 498-509 (2001) · Zbl 0990.90523
[9] Aparicio, J.; Ruiz, JL; Sirvent, I., Closest targets and minimum distance to the Pareto-efficient frontier in DEA, J. Prod. Anal., 28, 209-218 (2007)
[10] Aparicio, J.; Mahlberg, B.; Pastor, JT; Sahoo, BK, Decomposing technical inefficiency using the principle of least action, Eur. J. Oper. Res., 239, 3, 776-785 (2014) · Zbl 1339.90164
[11] Cherchye, L.; Lovell, CK; Moesen, W.; Van Puyenbroeck, T., One market, one number? A composite indicator assessment of EU internal market dynamics, Eur. Econ. Rev., 51, 3, 749-779 (2007)
[12] Cherchye, L.; Moesen, W.; Rogge, N.; Van Puyenbroeck, T., An introduction to ‘benefit of the doubt’ composite indicators, Soc. Indic. Res., 82, 111-145 (2007)
[13] Cherchye, L.; Moesen, W.; Van Puyenbroeck, T., Legitimately diverse, yet comparable: on synthesizing social inclusion performance in the EU, J. Common Mark. Stud., 42, 919-955 (2004)
[14] Lovell, CAK, Measuring the macroeconomic performance of the Taiwanese economy, Int. J. Prod. Econ., 39, 165-178 (1995)
[15] Sahoo, BK; Acharya, D., Constructing macroeconomic performance index of Indian states using DEA, J. Econ. Stud., 39, 1, 63-83 (2012)
[16] Shen, Y.; Hermans, E.; Brijs, T.; Wets, G., Data Envelopment Analysis for composite indicators: A multiple layer model, Soc. Indic. Res., 114, 739-756 (2013)
[17] Fusco, E., Enhancing non-compensatory composite indicators: a directional proposal, Eur. J. Oper. Res., 242, 620-630 (2015) · Zbl 1341.91110
[18] Sahoo, BK; Singh, R.; Mishra, B.; Sankaran, K., Research productivity in management schools of India during 1968-2015: a directional Benefit-of Doubt model analysis, Omega, 66, 118-139 (2017)
[19] Zanella, A.; Camanho, AS; Dias, TG, Undesirable outputs and weighting schemes in composite indicators based on data envelopment analysis, Eur. J. Oper. Res., 245, 517-530 (2015) · Zbl 1346.90453
[20] Vidoli, F.; Fusco, E.; Mazziotta, C., Non-compensability in composite indicators: a robust directional frontier method, Soc. Indic. Res., 122, 635-652 (2015)
[21] Cherchye, L.; Moesen, W.; Rogge, N.; Van Puenbroeck, T., Constructing composite indicators with imprecise data: a proposal, Expert Syst. Appl., 38, 10940-10949 (2011)
[22] Fusco, E.; Vidoli, F.; Sahoo, BK, Spatial heterogeneity in composite indicator: a methodological proposal, Omega, 77, 1-14 (2018)
[23] Fusco, E.; Vidoli, F.; Rogge, N., Spatial directional robust Benefit of the Doubt approach in presence of undesirable output: an application to Italian waste sector, Omega, 94, 102053 (2020)
[24] Aparicio, J.; Kapelko, M., Enhancing the measurement of composite indicators of corporate social performance, Soc. Indic. Res., 114, 2, 807-826 (2019)
[25] Cooper, WW; Park, KS; Pastor, J., RAM: a range adjusted measure of inefficiency for use with additive models, and relations to other models and measures in DEA, J. Prod. Anal., 11, 5-42 (1999)
[26] Färe, R.; Lovell, CAK, Measuring the technical efficiency of production, J. Econ. Theory, 19, 150-162 (1978) · Zbl 0398.90012
[27] Coelli, T., A multi-stage methodology for the solution of orientated DEA models, Oper. Res. Lett., 23, 3-5, 143-149 (1998) · Zbl 0963.91032
[28] Briec, W., Hölder distance functions and measurement of technical efficiency, J. Prod. Anal., 11, 111-131 (1998)
[29] Frei, FX; Harker, PT, Projections onto efficient frontiers: theoretical and computational extensions to DEA, J. Prod. Anal., 11, 3, 275-300 (1999)
[30] Cherchye, L.; Van Puyenbroeck, T., A comment on multi-stage DEA methodology, Oper. Res. Lett., 28, 2, 93-98 (2001) · Zbl 1016.91022
[31] González, E.; Álvarez, A., From efficiency measurement to efficiency improvement: the choice of a relevant benchmark, Eur. J. Oper. Res., 133, 3, 512-520 (2001) · Zbl 1002.90530
[32] Portela, MCAS; Borges, PC; Thanassoulis, E., Finding closest targets in non-oriented DEA models: the case of convex and non-convex technologies, J. Prod. Anal., 19, 251-269 (2003)
[33] Pastor, JT; Aparicio, J., The relevance of DEA benchmarking information and the least-distance measure: comment, Math. Comput. Model., 52, 1-2, 397-399 (2010) · Zbl 1201.65001
[34] Aparicio, J.; Pastor, JT, A well-defined efficiency measure for dealing with closest targets in DEA, Appl. Math. Comput., 219, 17, 9142-9154 (2013) · Zbl 1288.90083
[35] Aparicio, J.; Pastor, JT, Closest targets and strong monotonicity on the strongly efficient frontier in DEA, Omega, 44, 51-57 (2014)
[36] Fukuyama, H.; Leth Hougaard, J.; Sekitani, K.; Shi, J., Efficiency measurement with a non-convex free disposal hull technology, J. Oper. Res. Soc., 67, 1, 9-19 (2016)
[37] Aparicio, J., A survey on measuring efficiency through the determination of the least distance in data envelopment analysis, J. Cent. Cathedra, 9, 2, 143-167 (2016)
[38] Ando, K.; Kai, A.; Maeda, Y.; Sekitani, K., Least distance based inefficiency measures on the Pareto-efficient frontier in DEA, J. Oper. Res. Soc. Jpn., 55, 1, 73-91 (2012) · Zbl 1278.90257
[39] Fukuyama, H.; Maeda, Y.; Sekitani, K.; Shi, J., Input-output substitutability and strongly monotonic p-norm least distance DEA measures, Eur. J. Oper. Res., 237, 3, 997-1007 (2014) · Zbl 1338.90252
[40] Bessent, A.; Bessent, W.; Elam, J.; Clark, T., Efficiency frontier determination by constrained facet analysis, Oper. Res., 36, 785-796 (1988) · Zbl 0655.90045
[41] Green, RH; Doyle, JR; Cook, WD, Efficiency bounds in Data Envelopment Analysis, Eur. J. Oper. Res., 89, 482-490 (1996) · Zbl 0915.90037
[42] Olesen, OB; Petersen, NC, Indicators of ill-conditioned data sets and model misspecification in Data Envelopment Analysis: an extended facet approach, Manag. Sci., 42, 205-219 (1996) · Zbl 0881.90003
[43] Räty, T., Efficient facet based efficiency index: a variable returns to scale specification, J. Prod. Anal., 17, 65-82 (2002)
[44] Koopmans, TC; Koopmans, TC, Analysis of production as an efficient combination of activities, Activity Analysis of Production and Allocation (1951), New York: Wiley, New York · Zbl 0045.09506
[45] Nemhauser, GL; Wolsey, LA, Integer and Combinatorial Optimization (1999), New York: Wiley, New York
[46] Cooper, WW; Pastor, JT; Borras, F.; Aparicio, J.; Pastor, D., BAM: a bounded adjusted measure of efficiency for use with bounded additive models, J. Prod. Anal., 35, 2, 85-94 (2011)
[47] Singer, I., Duality for Nonconvex Approximation and Optimization (2007), Boston, MA: Springer, Boston, MA
[48] Wu, DD, Bilevel programming Data Envelopment Analysis with constrained resource, Eur. J. Oper. Res., 207, 856-864 (2010) · Zbl 1205.90165
[49] Whittaker, G.; Färe, R.; Grosskopf, S.; Barnhart, B.; Bostian, M.; Mueller-Warrant, G.; Griffith, S., Spatial targeting of agri-environmental policy using bilevel evolutionary optimization, Omega, 66, 15-27 (2017)
[50] Shi, C.; Lu, J.; Zhang, G., An extended Kuhn-Tucker approach for linear bilevel programming, Appl. Math. Comput., 162, 1, 51-63 (2005) · Zbl 1090.90175
[51] Beale, E.M.L., Tomlin, J.A.: Special facilities in a general mathematical programming system for non-convex problems using ordered sets of variables. In: Lawrence, J. (ed.) Proceedings of the Fifth International Conference on Operational Research, pp. 447-454. Tavistock Publications, London (1970)
[52] Cooper, WW; Ruiz, JL; Sirvent, I., Choosing weights from alternative optimal solutions of dual multiplier models in DEA, Eur. J. Oper. Res., 180, 1, 443-458 (2007) · Zbl 1114.90401
[53] Mehdiloozad, M.; Mirdehghan, SM; Sahoo, BK; Roshdi, I., On the identification of the global reference set in Data Envelopment Analysis, Eur. J. Oper. Res., 245, 3, 779-788 (2015) · Zbl 1346.90594
[54] Mehdiloozad, M.; Zhu, J.; Sahoo, BK, Identification of congestion in Data Envelopment Analysis under the occurrence of multiple projections: a reliable method capable of dealing with negative data, Eur. J. Oper. Res., 265, 2, 644-654 (2018) · Zbl 1374.90290
[55] Engida, TG; Rao, X.; Berentsen, PBM; Oude Lansink, A., Measuring corporate sustainability performance—the case of European food and beverage companies, J. Clean. Prod., 195, 734-743 (2018)
[56] Auer, BR, Do socially responsible investment policies add or destroy European stock portfolio value?, J. Bus. Ethics, 135, 381-397 (2016)
[57] Surroca, J.; Tribó, JA; Waddock, S., Corporate responsibility and financial performance: the role of intangible resources, Strateg. Manag. J., 31, 463-490 (2010)
[58] Maloni, MJ; Brown, ME, Corporate social responsibility in the supply chain: an application in the food industry, J. Bus. Ethics, 68, 35-52 (2006)
[59] Golany, B.; Roll, Y., An application procedure for DEA, Omega, 17, 237-250 (1989)
[60] Nunamaker, TR, Using data envelopment analysis to measure the efficiency of non-profit organizations: a critical evaluation, Manag. Decis. Econ., 6, 50-58 (1985)
[61] Raab, RL; Lichty, RW, Identifying subareas that comprise a greater metropolitan area: the criterion of county relative efficiency, J. Reg. Sci., 42, 579-594 (2002)
[62] Dyson, RG; Allen, R.; Camanho, AS; Podinovski, VV; Sarrico, CS; Shale, EA, Pitfalls and protocols in DEA, Eur. J. Oper. Res., 132, 245-259 (2001) · Zbl 0980.90038
[63] Cooper, WW; Seiford, LM; Tone, K., Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software (2007), New York: Springer, New York · Zbl 1111.90001
[64] Wilson, P., Dimension reduction in nonparametric models of production, Eur. J. Oper. Res., 267, 349-367 (2018) · Zbl 1403.90442
[65] CPLEX Optimizer User Manual (2013). IBM ILOG. https://www.ibm.com/products/ilog-cplex-optimization-studio. Accessed 30 May 2020
[66] Lozano, S.; Villa, G., Gradual technical and scale efficiency improvement in DEA, Ann. Oper. Res., 173, 123-136 (2010) · Zbl 1186.90076
[67] Nguyen, P-A; Kecskés, A.; Mansi, S., Does corporate social responsibility create shareholder value? The importance of long-term investors, J. Bank. Finance, 112, 105217 (2020)
[68] Gleick, P.H., Allen, L., Christian-Smith, J., Cohen, M.J., Cooley, H., Heberger, M., Morrison, J., Palaniappan, M., Schulte, P.: The World’s Water Volume 7: The Biennial Report on Freshwater Resources. Island Press, Washington (2011)
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