Quantum annealing for the two-level facility location problem

This study explores the effectiveness of quantum approaches in addressing combinatorial optimization problems, arising in the logistics domain. In particular, we concentrate on the two-level Facility Location Problem, which is known to be NP-hard and therefore unable to be solved in a polynomial amount of time. Due to the difficulties in addressing these problems, we explore the potential of quantum annealing techniques to solve the Quantum Unconstrained Binary Optimization formulation, using the D-Wave solver. Furthermore, given that this formulation is still underperforming for large instances, we propose a method to preprocess the logistic network. This method has been developed with the intention of reducing the size of the logistic network, thus allowing for improved system performance as the size of the instances increases. We demonstrate the efficacy of our proposed solution approach through the execution of computational experiments. The objective of these experiments is to validate the performance of quantum annealing with our preprocessing network techniques.