Globally Optimal Facility Locations for Continuous-Space Facility Location Problems

The continuous-space single- and multi-facility location problem has attracted much attention in previous studies. This study focuses on determining the globally optimal facility locations for two- higher-dimensional problems when Manhattan distance is considered. Before we propose exact method, start with single-facility obtain global minimizer using a statistical approach. Then, an method developed to determine solution problem, which different from clustering algorithms. Based newly investigated properties of minimizer, extend it transfer discrete-space problem. To illustrate effectiveness efficiency proposed several instances benchmark are provided compare performances methods, illustrates superiority decision-making problems.