This paper studies a relatively new variant of the classical Vehicle Routing Problem (VRP) - the Fleet Size and Mix Vehicle Routing Problem with Backhauls (FSMVRPB). In this variant a fleet of heterogeneous vehicles is optimized to minimise fixed and operational costs to serve two groups of customers, i.e., deliveries (linehauls) and pickups (backhauls). A reactive tabu search algorithm is developed to solve the FSMVRPB. Some new best known results are obtained for the FSMVRPB data instances.