Covering problems are well-studied in the domain of Operations Research, and, in particular, Location Science. When the location space is a network, the most frequent assumption is to consider the candidate facility locations, the points to be covered, or both, to be discrete sets. In this talk, we study the set-covering location problem when both demand points and candidate locations are continuous sets on a network, and we propose several Mixed-Integer Linear Programming Formulations. CFLG.jl is an open-source software written in the Julia programming language for the continuous set cover problem, and these MILP formulations are implemented in CFLG.jl. CFLG.jl can be extended to model other covering problems on networks, such as discrete cover problems. We conduct the numerical experiment of CFLG.jl on several benchmarks and compare the performance of different MILP formulations. The results show that our formulations are more scalable than the existing formulation. slides
This talk is presented at session MILP approaches for location and routing problems, in 32st European Conference on Operational Research (EURO2022).