Integrated dynamic interval data envelopment analysis in the presence of integer and negative data

Abstract

<p style='text-indent:20px;'>The conventional data envelopment analysis (DEA) models presume that the values of input-output variables of the decision-making units (DMUs) are precisely known. However, some real-life situations can authoritatively mandate the data to vary in concrete fine-tuned ranges, which can include negative values and measures that are allowed to take integer values only. Our study proposes an integrated dynamic DEA model to accommodate interval-valued and integer-valued features that can take negative values. The proposed one-step model follows the directional distance function approach to determine the efficiency of DMUs over time in the presence of carryovers connecting the consecutive periods. We use the pessimistic and optimistic standpoints to evaluate the respective lower and upper bounds of the interval efficiency scores of the DMUs. We compare our proposed approach with a few relevant studies in the literature. We also validate our model on a synthetically generated dataset. Furthermore, we showcase the proposed procedure's applicability on a real dataset from 2014 to 2018 of airlines operating in India.</p>