Extension Of Interval DEA Theory And Its Application

So far, there are some research achievements in establishing DEA model and method with interval data, but the follow-up work is still insufficient. Therefore, this study tries to fill in the blank after obtaining the interval efficiency and its classification, the main framework and the innovation are as follows:(1) For the inefficient DMUs, the interval efficiency is improved by increasing outputs, decreasing inputs or adjusting inputs and outputs simultaneously, thus the lower bound of interval efficiency increase as much as possible, the upper bound arrive at the production frontier. The target point is obtained by applying interval ideal point and establishing corresponding models. The adjusted level can be calculated by comparing the original point and the target point. In this paper, IDMUs B, C, D, F, H are all inefficient DMUs. Take IDMU B for example, the first output is [1.8,2.2], the adjusted output is [4.16,4.652], thus the adjusted efficiency turns [0.4222,0.6226] into [0.8759,1] and is improved. Likewise, set the weight is (0.8,0.2), then the input change1into0.5556, the first output becomes [2.1564,2.2002] and the efficiency improves at [0.8333,1]。(2) Sensitivity analysis with interval data in DEA is discussed. On one hand, the data change form can be divided into absolute data change and percentage data change. On the other hand, for absolute data change, the sensitivity analysis can be discussed under VRS situation and the analysis can be discussed under CRS situation for percentage data change. For each kind of data change, this part not only restrict attention to inputs and outputs data change simultaneously in the decision making units under evaluation, but also considers different subsets in various inputs and ouputs where I={1,2,…,m}, O={1,2,…,s} for all other DMUs.(3) Two non-radial DEA approaches based upon the slacks-based measurement for dealing with interval data are formulated. One is used to obtain efficiencies whereas the other is used to identify specific inefficiencies for the DMU under evaluation. The uncertain models can be transformed into certain model to otain interval efficiency and its classification by applying Pareto optimal methods. The results show its advantage such as unit variation, superior discrimination and always have a solution under CRS and VRS situation.