The Vehicle Routing Problem (VRP) is a classical combinatorial optimization problem that was
proposed in the late 1950’s and it is still one of the most studied in the field of Operations
Research. The great interest in the VRP is due to its practical importance, as well as the
difficulty in solving it. This work deals with heuristic, exact and hybrid approaches for solving
different variants of the VRP, namely: Capacitated VRP (CVRP), Open VRP (OVRP),
Asymmetric CVRP (ACVRP), VRP with Simultaneous Pickup and Delivery (VRPSPD), VRP
with Mixed Pickup and Delivery (VRPMPD), TSP with Mixed Pickup and Delivery
(TSPMPD), Multi-Depot VRP (MDVRP), Multi-Depot Vehicle Routing Problem with Mixed
Pickup and Delivery (MDVRPMPD) and Heterogeneous Fleet VRP (HFVRP). An extensive
literature review is performed for all these variants, focusing on the main contributions of each
work. Commodity flow formulations for the VRPSPD/VRPMPD are theoretically examined and
their practical performance are measured by a Branch-and-Cut (BC) algorithm. Another BC
algorithm, based on a formulation defined only over the edge variables, is proposed for the
VRPSPD, VRPMPD and MDVRPMPD, where the constraints the ensure that the capacity of
the vehicle is not exceeded in the middle of the route and those that ensure that a route starts and
ends at the same depot are treated in a lazy fashion. The third and last exact approach is a
Branch-cut-and-price algorithm that is also designed to solve the VRPSPD/VRPMPD. These
three exact approaches are tested in benchmark instances involving up to 200 customers and
new optimal solutions are found for 63 open problems. A heuristic algorithm is proposed for
solving the VRPs considered here. The algorithm, called ILS-RVND, is based on the Iterated
Local Search (ILS) metaheuristic and it makes use of a Variable Neighborhood Descent with
Random neighborhood ordering (RVND) in the local search phase. Finally, a hybrid algorithm
that incorporates a Set Partitioning approach into the ILS-RVND heuristic is presented for
solving 8 of the VRPs treated in this work. The developed heuristic and hybrid algorithms are
tested in hundreds of benchmark instances and the results obtained are, on average, highly
competitive.