Characterizing a Subset of the PPS with Radial Projection Point on a Prespecified Hyperplane

In an approach proposed, Nasrabadi et al. (2014) characterized a subset of production points, the radial projection of which is located on the same facet of the production possibility set (PPS). They obtained the radial projection points by using CCR and BCC models. Some results were posited, which can help one obtain such a subset of the PPS. The sensitivity analysis of inefficient units is also provided. An interval has been achieved over which an individual input/output can be varied and, even then, its corresponding hyperplane does not change. In their proposed approach, two nonlinear programming problems need to be solved to estimate the above mentioned interval. These are, however, difficult to solve. In this paper, some new theorems have been proved so as to obtain a new formula to determine a subset of production points, the projection of which lies on the same hyperplane of the PPS. This new formula leads to the determination of the input preservation region and the output preservation region by solving two linear programming problems that have priority in calculation over the existing methods. To delineate our new approach, two numerical examples are provided at the end.