Exact and heuristic algorithms for solving the generalized vehicle routing problem with flexible fleet size

The generalized vehicle routing problem with flexible fleet size (GVRP‐flex) extends the classical capacitated vehicle routing problem (CVRP) by partitioning the set of required nodes into clusters and has interesting applications such as humanitarian logistics. The problem aims at minimizing the total cost for a set of routes, such that each cluster is visited exactly once and its total demand is delivered to one of its nodes. An exact method based on column generation (CG) and two metaheuristics derived from iterated local search are proposed for the case with flexible fleet size. On five sets of benchmarks, including a new one, the CG approach often provides good upper and lower bounds, whereas the metaheuristics find, in a few seconds, solutions with small optimality gaps.