Determination of the Efficient Frontier of Weak and Strong Production Possibility Set using Genetic Algorithms

Abstract

This article uses genetic algorithms and geometric properties of production plants and a constructive way to determine strong and weak hyperplanes in the Efficient Border collection. Normal vectors in a constructive hyperplane are obtained by mapping the space of hyperplanes based on the real set. The production possibility set (PPS) of an input-based system is determined by utilizing the axiom. By using the genetic algorithm (GA) and the geometric properties of the PPS, this paper presents a solution to choose the strong and weak definitions of the hyperplanes of the so-called "efficient frontier". The generated hyperplanes are crucial for determining the returns to scale and modifying the DMU ranking methods. The hyperplane equation can enable a simple and more accurate analysis of the sensitivity of DEA methods. A numerical example is used to show how the algorithm is used in this paper and how the results are compared.