Abstract
Our paper focuses on a robustness analysis of efficiency scores in the context of Data Envelopment Analysis (DEA) assuming interval scale data, as defined in A. Dehnokhalaji, P. J. Korhonen, M. Köksalan, N. Nasrabadi and J. Wallenius, “Efficiency Analysis to incorporate interval scale data”, European Journal of Operational Research 207 (2), 2010, pp. 1116–1121. We first show that the definition of the efficiency score used in our paper is a well-defined measure according to Aparicio and Pastor (J. Aparicio and J. T. Pastor, “A well-defined efficiency measure for dealing with closest targets in DEA”, Applied Mathematics and Computation 219 (17), 2013, pp. 9142–9154.). Next, we characterize how robust the efficiency scores are with respect to improvements and deteriorations of inputs and outputs. We illustrate our analysis with two examples: a simple numerical example and a more complex example using real-world data.
Highlights
The concept of robustness or sensitivity has been widely studied in Data Envelopment Analysis literature
For Decision Making Unit (DMU) 21, the efficiency scores obtained by model (9) in Dehnokhalaji et al (2010) was reported to be equal to 0.231, while the indicator constraints resulted in the efficiency score of 0.269 as you can see from Table (3)
We first showed that our interval scale efficiency measure is well-defined
Summary
The concept of robustness (stability) or sensitivity has been widely studied in Data Envelopment Analysis literature. Zhu (1996) proposed a method for sensitivity analysis in DEA by solving linear programming problems whose optimal values yield particular regions of stability They provided necessary and sufficient conditions for upward variations of inputs and for downward variations of outputs of an (extremely) efficient DMU, which keeps its efficiency score unchanged. Dehnokhalaji, Korhonen, Koksalan, Nasrabadi, & Wallenius (2010) proposed an efficiency analysis for interval scale data. We formulate two multi-objective mixed integer programming models separately to measure the robustness of improvements and deteriorations and provide an interval for each input and output value, resulting in an unchanged efficiency score for all efficient and inefficient DMUs. We show that the modelling can be done via linear programming formulations in case that changes occur just for one input or output, and the stability region reduces to an interval for each individual input and output. A real application is provided in Section 5 and Section 6 concludes the paper
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