In this paper, we consider a new selective routing problem, where a subset of customers should be serviced by a limited fleet of vehicles with the aim of minimizing the total latency. A service level constraint is added to guarantee that a minimum system performance is achieved. Assuming that the travel times are uncertain, we address the problem through a mean-risk approach. The inclusion of risk in the objective function makes the problem computationally challenging. To solve it, we propose an efficient heuristic, relying on a variable neighbourhood search mechanism, able to strike the balance between service level and latency. A detailed discussion of the model, which includes simulation tests and a sensitivity analysis, is carried out to illustrate the applicability of our approach in a post-disaster scenario, taking as a case study the Haiti earthquake in 2010. Additional computational experiments show that the proposed heuristic is effective for this difficult problem and often matches optimal solutions for small and medium-scale benchmark instances
