Finding all the strong and weak defining hyperplanes of PPS without solving any LPs

Abstract

The production possibility set (PPS) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs. In this paper, we propose an algorithm for finding all the 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. To do so, by finding non-dominated points and some artificial DMUs we generate all hyperplanes passes through them. Then, supporting and interior hyperplanes of PPS are detected - among the generated hyperplanes. After pretermitting interior hyperplanes, we obtain strong 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. Using numerical examples, we will demonstrate how to use the results.