A complete ranking of decision making units with interval data

Abstract

Interval data envelopment analysis (interval DEA) deals with the problem of efficiency assessment when the inputs and/or outputs of decision making units (DMUs) are given as interval data. This paper focuses on the problem of ranking DMUs with interval data. First, we define extreme efficient units, super efficiency score, the best and the worst efficiency (inefficiency) frontiers in the interval DEA context. Then, we propose a novel method based on the lower and upper super efficiency scores of a unit under evaluation and the distance of that unit to four developed frontiers. Our method ranks all efficient and inefficient units which is one of the main advantages of it. Our method uses several essential criteria simultaneously to rank units with interval data. These criteria increase the discrimination power of our proposed method. Potential application of this method is illustrated with a dataset consisting of 30 branches of the social security insurance organisation in Tehran.