Interval data

Interval Data Envelopment Analysis (Interval DEA) is a methodology to assess the efficiency of decision-making units (DMUs) in the presence of interval data. Sensitivity analysis and sustainability evaluation of decision- making units are as the most important concerns of Decision Makers (DM). In the past decades, many scholars have been attracted to the sustainability evaluation of DMUs from different perspectives. This study focuses on the sensitivity analysis in DEA and proposes an approach to determine the sustainability radius of the cost efficiency of units with interval data. Potential application of our proposed methods is illustrated by a numerical example from the literature review.

In this paper we extend the concept of "cost minimizing industry structure" and develop two DEA models for dealing with imprecise data. The main aim of this study is to propose an approach to compute the industry cost efficiency measure in the presence of interval data. We will see that the value obtained by the proposed approach is an interval value. The lower bound and upper bound of the interval industry cost efficiency measure are computed and then decomposed into three components to examine the relationship between them and the lower and upper bounds of the individual interval cost efficiency measures. We also define the cost efficient organization of the industry as a set of DMUs, which minimizes the total cost of producing the interval industry output vector. In fact, this paper determines the optimal number of DMUs and the reallocation of the industry observed outputs among them. We hereby determine the effects of the optimal number of DMUs and the reallocation of outputs among them on the interval industry cost efficiency measure. Finally, a numerical example will be presented to illustrate the proposed approach.