×

zbMATH — the first resource for mathematics

The maximum and minimum number of efficient units in DEA with interval data. (English) Zbl 1116.90380
Summary: In original data envelopment analysis (DEA) models, inputs and outputs are measured by exact values on a ratio scale. Cooper et al. [Manage. Sci. 45, 597 (1999)] recently addressed the problem of imprecise data in DEA, in its general form. In this case, units do not have constant efficiency score and their efficiency score depend on the choice of data of units. Therefore, it is attractive to know upper and lower bounds for the number of efficient units. In this paper, we concentrate on DEA with interval data and describe which data settings of units produce the maximum number of efficient units, then we discuss about the minimum number of efficient units.

MSC:
90C06 Large-scale problems in mathematical programming
62-07 Data analysis (statistics) (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Charnes, A.; Cooper, W.W.; Rhodes, E., Measuring the efficiency of decision making unit, European journal of operational research, 2, 429-444, (1978) · Zbl 0416.90080
[2] Despotis, D.K.; Smirlis, Y.G., Data envelopment analysis with imprecise data, European journal of operational research, 140, 24-36, (2002) · Zbl 1030.90055
[3] 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
[4] Zhu, J., Imprecise data envelopment analysis (IDEA): a review and improvement with an application, European journal of operational research, 144, 513-529, (2003) · Zbl 1012.90013
[5] Tone, K., Measurement and improvement of efficiency by DEA, (1993), Nikkagiren Publishers, (in Japanese)
[6] Cook, W.D.; Doyle, J.; Green, R.; Kress, M., Multiple criteria modeling and ordinal data: evaluation in terms of subset of criteria, European journal of operational research, 98, 602-609, (1997) · Zbl 0917.90007
[7] Cook, W.D.; Kress, M.; Siford, 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
[8] Cook, W.D.; Kress, M.; Siford, L., On the use of ordinal data in data envelopment analysis, Journal of the operational research society, 44, 133-140, (1993) · Zbl 0776.90005
[9] 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
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.