A systematic review of the Esmvere algorithms, which are contributions in the field of uncapacitated facility location problems and k-median problems

The objective of the present paper is to review my personal contributions in the field of Uncapacitated Facility Location Problems. This paper is an analysis of scientific contributions, mainly the relevance, originality and significance of three published articles, around location science. The published journal articles are derived from a single source as novel solutions to a real-world case study. They contrast and revolutionize over 60 years of solutions to the UFL problem and k-median problem. The research introduces a new data analysis method, a Hamming distance-based k-median clustering algorithm based on the R Language. The research also introduces novel reformulations of the UFL and k-median problems which replace traditional distance matrices with Global Position System (GPS) based Euclidean Distance calculations, simplifying data input and reducing computational complexity. The reformulations are based on the CPLEX Opl language. The novel software inventions are all used to solve a real-world problem which involves the near optimal siting of Hazardous Waste Used Lead Acid Battery (ULAB) collection facilities in the republic of Mauritius. The thrust of this review is to analyze the novelty, compare, contrast and discuss all the remarks made by various reviewers. Hence this review combines and summarizes the three papers and explains the contribution of the three novel software inventions developed to solve a real-world problem.