CHAPTER 3

The Near Optimal Siting of Hazardous Waste (Used Lead Acid Battery (ULAB)) Collection Facilities in The Republic of Mauritius Using the Esmvere Cplex k-median solver algorithm

Abstract/Preface

The k-median algorithm is a well-known combinatorial optimization problem. k-median problem is essentially the p-median problem that has been around for almost 60 years. However, because of its usefulness it has been found relevant in many modern-day applications such as advanced drone technology, self-driving vehicles, image processing and many other avenues that have to do with efficient distribution of resources, were outliers must be eliminated. Research work on this problem is on-going. The level of hardness of this problem, the approximability lower bound of this problem, has not yet been achieved. To the best of our knowledge all known prior algorithms solving the k-median problem used the input of a distance matrix. The study introduces the ESMVERE k-median problem solver, which replaces traditional distance matrices with GPS-based Euclidean distance calculations, simplifying data input and reducing computational complexity. This research examines the challenge of hazardous waste management from Used Lead Acid Batteries (ULABs) in Mauritius, a pressing public health and environmental concern due to the risks of lead exposure. The study’s key contribution is the practical adaptation of theoretical k-median frameworks to address environmental challenges, offering a replicable model for hazardous waste management in other contexts. It highlights the potential for mathematical modelling to drive practical solutions to global environmental challenges