Universal efficiency scores in data envelopment analysis based on a robust approach

We propose a novel DEA method for computing efficiency scores. The method is based on a robust optimization viewpoint: the higher scores for those decision making units (DMU's) that remain efficient even for larger simultaneous and independent variations of all data and vice versa. Moreover, the value of each score itself gives the distance to inefficiency (or the distance to efficiency for inefficient units), so it provides a decision maker with an additional useful information on how stable the DMU is. The efficiency scores can be computed by solving generalized linear fractional programming problems, but we also present a tight linear programming approximation that preserves the order of rankings. We show many remarkable properties of our approach: It preserves the order of rankings compared to the classical approach, and it is unit invariant. It is naturally normalized, so it can be used for computing universal scores of DMU's of unrelated models. It gives scores not only for inefficient, but also for efficient decision making units. It can also be easily extended to generalized or alternative models, for instance to deal with interval data. We present several examples confirming the desirable properties of the method. (C) 2019 Elsevier Ltd. All rights reserved.