Abstract
Traditional data envelopment analysis (DEA) models assume that all the inputs and outputs data are available. However, missing data is a common problem in data analysis. Although several scholars have developed techniques to conduct DEA with missing data, these techniques have some disadvantages. A multi-criteria evaluation approach is proposed to measure the efficiency of decision making units (DMUs) with missing data. In this approach, analysts first estimate the upper and lower bounds of DMUs’ efficiency using the proposed I-addIDEA-U models (interval additive integer-valued DEA models with undesirable outputs) that can be applied to address integer-valued variables and undesirable outputs. Then, DMUs’ “relative” efficiency is evaluated using the proposed “Halo + Hot deck” DEA method (if there is no correlation between variables) or regression DEA techniques (if there is a correlation between variables). Finally, the multi-index comprehensive evaluation method is applied to determine which scenario (the lower bound of efficiency, the “relative” efficiency, or the upper bound of efficiency) should be selected. With a case study, it is shown that the proposed multi-criteria evaluation approach is more effective than traditional approaches such as the mean imputation DEA method, the deletion DEA method, and the dummy entries DEA method.
Highlights
Traditional data envelopment analysis (DEA) models assume that all the inputs and outputs data are available [1, 2]
If the data related to some vital variables of decision making units (DMUs) are missing, traditional DEA models cannot be applied to measure the performance of these DMUs [3, 4]
It is worth noting that the outliers have been removed from the diagrams and the results show that there is no relationship between the annual pallet loss rate and the other variables
Summary
Traditional data envelopment analysis (DEA) models assume that all the inputs and outputs data are available [1, 2]. They use simple imputation methods or deletion methods to handle missing data, which may lead to erroneous results While they modify basic radial DEA models to measure the efficiency of DMUs with missing data, they are unable to deal with integer-valued variables or undesirable variables. To handle missing data in DEA a multi-criteria evaluation approach is proposed based on the Hot deck imputation, regression imputation, Halo effect, interval DEA, integer DEA, additive DEA, DEA with undesirable outputs, and multi-index comprehensive.
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