A note and new extensions on “interval efficiency measures in data envelopment analysis with imprecise data”

This paper deals with imprecise data in data envelopment analysis (DEA). We construct a new pair of mathematical programming models by using the concepts of ‘inf’ and ‘sup’ to calculate the exact values of the lower- and upper-bound efficiency scores in the presence of interval and ordinal data. The...

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Bibliographic Details
Published in:Operational research 2021-12, Vol.21 (4), p.2719-2737
Main Authors: Ebrahimi, Bohlool, Tavana, Madjid, Charles, Vincent
Format: Article
Language:English
Subjects:
Business and Management
Computational efficiency
Computational Intelligence
Data analysis
Data envelopment analysis
Efficiency
Linear programming
Lower bounds
Management Science
Mathematical analysis
Mathematical models
Mathematical programming
Operations Research
Operations Research/Decision Theory
Original Paper
Upper bounds
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Summary:This paper deals with imprecise data in data envelopment analysis (DEA). We construct a new pair of mathematical programming models by using the concepts of ‘inf’ and ‘sup’ to calculate the exact values of the lower- and upper-bound efficiency scores in the presence of interval and ordinal data. The method proposed in this study is motivated by the approach introduced by Kao (Eur J Oper Res 174(2):1087–1099, 2006) where a pair of two-level mathematical DEA models are converted into linear programming (LP) models to calculate the lower- and upper-bound efficiency scores in the presence of pure ordinal data. We show that the LP model proposed by Kao (2006) for finding the lower-bound efficiency score yields the upper-bound efficiency score. We propose an improved model that overcomes this drawback and successfully calculates the lower- and upper-bound efficiency scores. We demonstrate the applicability of our models with a numerical example and exhibit its efficacy through comparison with Kao’s (2006) approach.
ISSN:1109-2858
1866-1505
DOI:10.1007/s12351-019-00524-x