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The vehicle fleet mix (VFM) problem is the vehicle routing problem with additional practical extensions. The VFM problem involves a heterogeneous fleet of vehicles with their associated variable running and fixed purchasing/renting costs. The objective is to find the optimal fleet composition of vehicles and a set of feasible routes that minimize the total costs. In this paper, two techniques are proposed: a constructive heuristic and a tabu search metaheuristic. The constructive heuristic is an enhanced modification of the Salhi and Rand route perturbation procedure. The tabu metaheuristic is new and it uses a compound-moves neighbourhood with a special data structure. Computational results are reported on a set of 20 test problems from the literature. The proposed methods obtain new results that improve upon the best published results.