A cross evaluation-based measure of super efficiency in DEA with interval data

The traditional data envelopment analysis (DEA) model as a non-parametric technique can measure the relative efficiencies of a decision-making units (DMUs) set with exact values of inputs and outputs, but it cannot handle the imprecise data. The purpose of this paper is to establish a super efficiency interval data envelopment analysis (IDEA) model, an IDEA model based on cross-evaluation and a cross evaluation-based measure of super efficiency IDEA model. And the authors apply the proposed approach to data on the 29 public secondary schools in Greece, and further demonstrate the feasibility of the proposed approach.

In this paper, based on the IDEA model, the authors propose an improved version of establishing a super efficiency IDEA model, an IDEA model based on cross-evaluation, and then present a cross evaluation-based measure of super efficiency IDEA model by combining the super efficiency method with cross-evaluation. The proposed model cannot only discriminate the performance of efficient DMUs from inefficient ones, but also can distinguish between the efficient DMUs. By using the proposed approach, the overall performance of all DMUs with interval data can be fully ranked.

A numerical example is presented to illustrate the application of the proposed methodology. The result shows that the proposed approach is an effective and practical method to measure the efficiency of the DMUs with imprecise data.

The proposed model can avoid the fact that the original DEA model can only distinguish the performance of efficient DMUs from inefficient ones, but cannot discriminate between the efficient DMUs.

This paper introduces the effective method to obtain the complete rank of all DMUs with interval data.