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An Experimental Study on Changes in DEA Efficiency and Reference Sets by Weight Restrictions and Analysis Sample Size

Oh, Dongil

Published: January 2000 · Vol. 29, No. 4 · pp. 749-768
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Abstract

In the DEA (Data Envelopment Analysis) model, relative weights are endogenously determined so that each decision-making unit (DMU) is evaluated in the most favorable light, thereby eliminating arbitrariness and achieving objectivity in evaluation. This study generated experimental data to analyze how DEA efficiency and reference sets vary substantially depending on weight constraints and sample size, and how relative efficiency has a significant relationship with changes in the reference set. The findings revealed that DEA efficiency depends not only on the true efficiency defined by the Cobb-Douglas function but also on constraints and sample size. It was confirmed that the proportion of overestimation decreases as sample size increases in both constrained and unconstrained cases, with the constrained case exhibiting a greater rate of decrease. Furthermore, analysis of reference set changes using a logit function showed that reference sets are sensitive to sample size and constraints; when constraints are imposed, the number of reference sets is distributed close to the mean, whereas without constraints, the distribution is comparatively wider. Although the DEA model remains useful even when infinite flexibility is granted to weights or when sample size is small, its significance can be further enhanced by introducing subjective values for weights and increasing the sample size.