Dealing with missing information in data envelopment analysis by means of low-rank matrix completion

In data envelopment analysis (DEA) it is usually necessary to perform some data preprocessing routines. For example, in many practical situations, it may occur that some of the input and/or output values are not available for all the decision-making units (DMUs). Therefore, in such situations, it becomes necessary to set up a strategy to deal with the missing data. In this context, the present work proposes the application of a recent matrix approximation approach, known as low-rank matrix completion, for preprocessing missing data in DEA. The proposed method is evaluated through a number of numerical experiments carried out on both synthetic and actual data. We compare, for a wide range of missing data proportions, the efficiencies of DMUs obtained after recovering the missing entries to those obtained in an ideal situation, in which all data is known. We also provide comparisons with other approaches that deal with missing data in the context of DEA. The results attest the viability of the application of the proposed low-rank matrix completion strategy to DEA.