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Data envelopment analysis with imprecise data. (English) Zbl 1030.90055
Summary: In original Data Envelopment Analysis (DEA) models, inputs and outputs are measured by exact values on a ratio scale. W. W. Cooper, K. S. Park, and G. Yu [Manag. Sci. 45, 597-607 (1999)] recently addressed the problem of imprecise data in DEA, in its general form. We develop in this paper an alternative approach for dealing with imprecise data in DEA. Our approach is to transform a nonlinear DEA model to a linear programming equivalent, on the basis of the original data set, by applying transformations only on the variables. Upper and lower bounds for the efficiency scores of the units are then defined as natural outcomes of our formulations. It is our specific formulation that enables us to proceed further in discriminating among the efficient units by means of a post-DEA model and the endurance indices. We then proceed still further in formulating another post-DEA model for determining input thresholds that turn an inefficient unit to an efficient one.

MSC:
90C08 Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.)
90C31 Sensitivity, stability, parametric optimization
90B50 Management decision making, including multiple objectives
Software:
DEA
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References:
[1] Ali, A.I.; Cook, W.D.; Seiford, L.M., Strict vs. weak ordinal relations for multipliers in data envelopment analysis, Management science, 37, 733-738, (1991) · Zbl 0743.90004
[2] Charnes, A.; Cooper, W.W.; Lewin, A.Y.; Seiford, L.M., Data envelopment analysis: theory, methodology and applications, (1994), Kluwer Academic Publishers Norwell, MA · Zbl 0858.00049
[3] Cook, W.D.; Doyle, J.; Green, R.; Kress, M., Multiple criteria modeling and ordinal data: evaluation in terms of subsets of criteria, European journal of operational research, 98, 602-609, (1997) · Zbl 0917.90007
[4] Cook, W.D.; Kress, M.; Seiford, L., On the use of ordinal data in data envelopment analysis, Journal of the operational research society, 44, 133-140, (1993) · Zbl 0776.90005
[5] Cook, W.D.; Kress, M.; Seiford, L., Data envelopment analysis in the presence of both quantitative and qualitative factors, Journal of the operational research society, 47, 945-953, (1996) · Zbl 0863.90002
[6] Cooper, W.W.; Park, K.S.; Yu, G., IDEA and AR-IDEA: models for dealing with imprecise data in DEA, Management science, 45, 597-607, (1999) · Zbl 1231.90289
[7] Despotis, D.K., Fractional minmax goal programming: A unified approach to priority estimation and preference analysis in MCDM, Journal of the operational research society, 47, 989-999, (1996) · Zbl 0864.90109
[8] Doyle, J.; Green, R., Efficiency and cross-efficiency in DEA: derivations, meanings and uses, Journal of the operational research society, 43, 567-578, (1994) · Zbl 0807.90016
[9] Dyson, R.G.; Thanassoulis, E., Reducing weight flexibility in data envelopment analysis, Journal of the operational research society, 39, 563-576, (1988)
[10] Golany, B., A note on including ordinal relations among multipliers in data envelopment analysis, Management science, 34, 1029-1033, (1988) · Zbl 0645.90043
[11] Roll, Y.; Cook, W.D.; Golany, B., Controlling factor weights in data envelopment analysis, IIE transactions, 23, 2-9, (1991)
[12] Sarkis, J.; Talluri, S., A decision model for evaluation of flexible manufacturing systems in the presence of both cardinal and ordinal factors, International journal of production research, 37, 2927-2938, (1999) · Zbl 0949.90584
[13] Sexton, T.R.; Silkman, R.H.; Hogan, A.J., Data envelopment analysis: critique and extensions, (), 73-105
[14] Thompson, R.G.; Langemeier, L.N.; Lee, C.T.; Thrall, R.M., The role of multiplier bounds in efficiency analysis with application to kansas farming, Journal of econometrics, 46, 93-108, (1990)
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