An extended inequality approach for evaluating decision making units with a single output

In this work, an extended evaluation approach for decision making units (DMUs) with a single output is proposed. Firstly, the input and output data for each DMU are changed in the same proportion until all the outputs are equal, and then the coordinate system is established with input i as the ith coordinate axis. Secondly, in the coordinate system, the production possibility set, which is spanned by all the DMUs without the evaluated DMU, is expressed by inequalities. Moreover, the mathematical expression of the line segment joining the origin to the evaluated DMU is given. Thirdly, the efficiency measure of the evaluated DMU is obtained from the relationship between the production possibility set and the line segment. In order to distinguish the weak efficiency and efficiency, the partially ordered set and minimal element are introduced in the paper. Finally, an example is provided to illustrate the proposed approach.