The selective minimum latency problem under travel time variability: An application to post-disaster assessment operations

•A new selective vehicle routing problem is defined, where a service level is enforced.•We address the problem under risk, presenting a mean-risk approach.•We develop a heuristic approach to solve the proposed problem.•We present a case study related to the rapid assessment routing problem in the aftermath of a dramatic disaster.•We conduct extensive computational experiments for the case study as well as for a set of benchmark instances.•The computational results show the effectiveness of the proposed approach which yields near-optimal solutions in a limited amount of time. 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.