The logistic network design is an abstract optimization problem that, under
the assumption of minimal cost, seeks the optimal configuration of the supply
chain's infrastructures and facilities based on customer demand. Key economic
decisions are taken about the location, number, and size of manufacturing
facilities and warehouses based on the optimal solution. Therefore,
improvements in the methods to address this question, which is known to be in
the NP-hard complexity class, would have relevant financial consequences. Here,
we implement in the D-Wave quantum annealer a hybrid classical-quantum
annealing algorithm. The cost function with constraints is translated to a spin
Hamiltonian, whose ground state encodes the searched result. As a benchmark, we
measure the accuracy of results for a set of paradigmatic problems against the
optimal published solutions (the error is on average below 1%), and the
performance is compared against the classical algorithm, showing a remarkable
reduction in the number of iterations. This work shows that state-of-the-art
quantum annealers may codify and solve relevant supply-chain problems even
still far from useful quantum supremacy.Comment: 9 pages and 2 figure