zbMATH — the first resource for mathematics

Choosing weights from alternative optimal solutions of dual multiplier models in DEA. (English) Zbl 1114.90401
Summary: We propose a two-step procedure to be used for the selection of the weights that we obtain from the multiplier model in a DEA efficiency analysis. It is well known that optimal solutions of the envelopment formulation for extreme efficient units are often highly degenerate and, consequently, have alternate optima for the weights. Different optimal weights may then be obtained depending, for instance, on the software used. The idea behind the procedure we present is to explore the set of alternate optima in order to help make a choice of optimal weights. The selection of weights for a given extreme efficient point is connected with the dimension of the efficient facets of the frontier. Our approach makes it possible to select the weights associated with the facets of higher dimension that this unit generates and, in particular, it selects those weights associated with a full dimensional efficient facet (FDEF) if any. In this sense the weights provided by our procedure will have the maximum support from the production possibility set. We also look for weights that maximize the relative value of the inputs and outputs included in the efficiency analysis in a sense to be described in this article.

90B50 Management decision making, including multiple objectives
Full Text: DOI
[1] Allen, R.; Athanassopoulos, A.; Dyson, R.G.; Thanassoulis, E., Weights restrictions and value judgements in data envelopment analysis: evolution, development and future directions, Annals of operations research, 73, 13-34, (1997) · Zbl 0890.90002
[2] Bessent, A.; Bessent, W.; Elam, J.; Clark, T., Efficiency frontier determination by constrained facet analysis, Operations research, 36, 5, 785-796, (1988) · Zbl 0655.90045
[3] Chang, K.P.; Guh, Y.Y., Linear production functions and data envelopment analysis, European journal of operational research, 52, 215-223, (1991) · Zbl 0746.90003
[4] Charnes, A.; Cooper, W.W., Management models and industrial applications of linear programming, (1961), John Wiley and Sons New York · Zbl 0107.37004
[5] Charnes, A.; Cooper, W.W., Programming with linear fractional functionals, Naval research logistics quarterly, 9, 181-186, (1962) · Zbl 0127.36901
[6] Charnes, A.; Cooper, W.W.; Rhodes, E., Measuring the efficiency of decision making units, European journal of operational research, 2/6, 429-444, (1978) · Zbl 0416.90080
[7] Charnes, A.; Cooper, W.W.; Thrall, R.M., A structure for classifying and characterizing efficiency and inefficiency in data envelopment analysis, Journal of productivity analysis, 2, 197-237, (1991)
[8] Chen, Y.; Morita, H.; Zhu, J., Multiplier bounds in DEA via strong complementary slackness condition solutions, International journal of production economics, 86, 11-19, (2003)
[9] Cooper, W.W.; Park, K.S.; Pastor, J.T., Marginal rates and elasticities of substitution in DEA, Journal of productivity analysis, 13, 105-123, (2000)
[10] Cooper, W.W.; Seiford, L.M.; Tone, K., Data envelopment analysis: A comprehensive text with models, applications. references and DEA-solver software, (2000), Kluwer Academic Publishers Boston · Zbl 0990.90500
[11] Cooper, W.W.; Deng, H.; Gu, B.; Li, S.; Thrall, R.M., Using DEA to improve the management of congestion in Chinese industries (1981-1997), Socio-economic planning sciences, 35, 227-242, (2001)
[12] Cooper, W.W., Ruiz, J.L., Sirvent, I. submitted for publication. Selecting weights to evaluate the effectiveness of basketball players with DEA. Journal of Productivity Analysis.
[13] Dyson, R.G.; Thanassoulis, E., Reducing weight flexibility in data envelopment analysis, Journal of the operational research society, 39, 563-576, (1988)
[14] Farrell, M.J., The measurement of productive efficiency, Journal of the royal statistical society, series A, 120, 253-290, (1957)
[15] Green, R.H.; Doyle, J.R.; Cook, W.D., Efficiency bounds in data envelopment analysis, European journal of operational research, 89, 482-490, (1996) · Zbl 0915.90037
[16] Olesen, O.; Petersen, N.C., Indicators of ill-conditioned data sets and model misspecification in data envelopment analysis: an extended facet approach, Management science, 42, 205-219, (1996) · Zbl 0881.90003
[17] Olesen, O.; Petersen, N.C., Identification and use of efficient faces and facets in DEA, Journal of productivity analysis, 20, 323-360, (2003)
[18] Thanassoulis, E., Introduction to the theory and application of data envelopment analysis: A foundation text with integrated software, (2001), Kluwer Academic Publishers Boston
[19] Thanassoulis, E.; Allen, R., Simulating weights restrictions in data envelopment analysis by means of unobserved dmus, Management science, 44, 586-594, (1998) · Zbl 1003.90511
[20] Thanassoulis, E.; Dyson, R.G.; Foster, M.J., Relative efficiency assessments using data envelopment analysis: an application to data on rates departments, Journal of the operational research society, 38, 397-411, (1987)
[21] Thompson, R.G.; Singleton, F.D.; Thrall, R.M.; Smith, B.A., Comparative site evaluations for locating a high-energy physics lab in Texas, Interfaces, 16, 35-49, (1986)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.