Abstract
This paper identifies alternative, more easily attainable benchmarks for inefficient decision making units (DMUs). This is done by extending data envelopment analysis (DEA), a popular linear programming method that optimizes the ratio of multiple weighted outputs to multiple weighted inputs, using the resultant ratio as a proxy measure of efficiency of the DMU. DEA identifies peers for an inefficient DMU; DMUs that could serve as benchmarks for the inefficient DMU to improve its current efficiency level. In this paper, we propose a method for computing an alternative benchmark that is based on linear combination of the peer DMUs. The alternative benchmarks are in many instances and in some respects, more easily attainable, and hence provide a more meaningful target for the inefficient DMU. To derive the alternative benchmark, we combine results of the multiplier and the envelopment form of DEA in a logical and intuitive manner. The proposed model is simple and practical, and provides a more meaningful transition path for an inefficient DMU as is empirically demonstrated using the familiar “Hospital” data set.
Similar content being viewed by others
References
Ghalanos, A., Theussl, S.: Rsolnp: general non-linear optimization using augmented lagrange multiplier method. R package version 1.12 (2012)
Allen, R., Athanassopoulos, A., Dyson, R.G., Thanassoulis, E.: Weights restrictions and value judgments in data envelopment analysis: evolution development and future directions. Ann. Oper. Res. 73, 13–34 (1997)
Cooper, W.W., Seiford, L.M., Tone, K.: Data envelopment analysis–a comprehensive text with models, applications, references and DEA-solver software. Springer Science+Business Media, LLC (2007)
Gonçalves, D.A., Soares de Mello, J.C.C.B., Meza, L.A., Lins, M.P.E.: When a value judgement using the technique of unobserved DMUs can be changed by weight restrictions (2004)
Hornik, K., Theussl, S.: Rglpk: R/GNU linear programming kit interface. http://CRAN.R-project.org/package=Rglpk (2012). R package version 0.3-8
Podinovski, V.V., Athanassopoulos, A.: Assessing the relative efficiency of decision making units using DEA models with weight restrictions. J. Oper. Res. Soc. 49, 500–508 (1998)
R Development Core Team: R: A Language and Environment for StatisticalComputing. R Foundation for Statistical Computing, Vienna, Austria, http://www.R-project.org/ (2012). ISBN 3-900051-07-0
Rebba, V., Rizzi, D.: The role of demand and weight restrictions in DEA measurement of hospital efficiency with an application to the hospitals of Veneto region, Italy (2003, preprint). Available at http://www.decon.unipd.it/assets/pdf/dp/0041.pdf; JEL Classification: D24, I12 (2003)
Stewart, T.J.: Goal directed benchmarking for organizational efficiency. Omega 38, 534–539 (2010)
Wong, Y.H.B., Beasley, J.E.: Restricting weight flexibility in data envelopment analysis. J. Oper. Res. Soc. 41, 829–835 (1990)
Ye, Y.: Interior algorithms for linear, quadratic, and linearly constrained non-linear programming. Ph.D. Thesis, Department of EES, Stanford University (1987)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Patel, G.N., Bose, A. Seeking alternative DEA benchmarks. OPSEARCH 51, 23–35 (2014). https://doi.org/10.1007/s12597-013-0130-9
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12597-013-0130-9