A Hybrid Algorithm for the Fleet Size and Mix Vehicle Routing Problem

This paper deals with the Fleet Size and Mix (FSM) Vehicle Routing Problem. The FSM generalizes the classical Vehicle Routing Problem (VRP) by allowing the existence of an unlimited heterogeneous fleet of vehicles. Each type of vehicle is associated with a distance-dependent and/or fixed cost. The objective is to determine the best fleet composition as well as the set of routes that minimize the travel costs. The proposed hybrid algorithm is composed by an Iterated Local Search (ILS) based heuristic and a Set Partitioning (SP) formulation. The SP model is solved by means of a Mixed Integer Programming (MIP) solver that interactively calls the ILS heuristic during its execution. The developed algorithm was tested on benchmark instances involving up to 100 customers. The results obtained are highly competitive since the hybrid approach was always capable to find or improve the best known solutions reported in the literature.