Improvement of efficiency intervals based on DEA by adjusting inputs and outputs

We improve the efficiency interval of a DMU by adjusting its given inputs and outputs. The Interval DEA model has been formulated to obtain an efficiency interval consisting of evaluations from both the optimistic and pessimistic viewpoints. DMUs which are not rated as efficient in the conventional sense are improved so that their lower bounds become as large as possible under the condition that their upper bounds attain the maximum value one. The adjusted inputs and outputs keep each other balanced by improving the lower bound of efficiency interval, since the lower bound becomes small if all the inputs and outputs are not proportioned. In order to improve the lower bound of efficiency interval, different target points are defined for different DMUs. The target point can be regarded as a kind of benchmark for the DMU. First, a new approach to improvement by adjusting only outputs or inputs is proposed. Then, the combined approach to improvement by adjusting both inputs and outputs simultaneously is proposed. Lastly, numerical examples are shown to illustrate our proposed approaches.