A box-uncertainty in DEA: A robust performance measurement framework

Abstract

The problem of assessment of Decision Making Units (DMUs) by using Data Envelopment Analysis (DEA) may not be straightforward due to the data uncertainty. Several studies have been developed to incorporate uncertainty into input/output values in the DEA literature. On the other hand, while traditional DEA models focus more on crisp data, there exist many applications in which data is reported in form of intervals. This paper considers the box-uncertainty in data which means that each input/output value is selected from a symmetric box. This specific type of uncertainty has been addressed as Interval DEA approaches. Our proposed model deals with efficiency evaluation of DMUs with imprecise data in a robust optimization. We assume that inputs and outputs are reported in the form of intervals and propose the robust counterpart problem for the envelopment form of the DEA model. Further, we also develop two ranking methods which have more benefits compared to some existing approaches. An illustrative example is provided to show how the proposed approaches work. An application on hospital efficiency in East Virginia is used to show the usefulness of the proposed approaches.