Additive integer-valued data envelopment analysis with missing data: A multi-criteria evaluation approach.

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.