finding all the strong and weak defining hyperplanes of pps without solving any lps

The production possibility set (pps) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs. the frontier the production possibility set can be partitioned to strong defining hyperplanes and weak defining hyperplanes. these hyperplanes are useful in sensitivity and stability analysis, identifying the status of returns to scale of a dmu, incorporating performance into the efficient frontier analysis, and so on. in this paper, by using the basic concepts of linear algebra, we propose an algorithm for finding all strong and weak defining hyperplanes of pps without solving any linear programming problems. the proposed method is applicable to both, pps under constant and variable returns-to-scale assumptions. two numerical examples are presented to explain the usage and effectiveness of the proposed algorithm. our method can be easily implemented using existing packages for mathematical algorithm, such as python.