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A fleet sizing problem in a road freight transportation company with heterogeneous fleet and its own technical back-up facilities is considered in the paper. The mathematical model of the decision problem is formulated in terms of multiobjective, non-linear, integer programming. The model is based on queuing theory. Three optimisation criteria that focus on technical and economical aspects of the problem are proposed. The solution procedure is composed of two general steps. In the first step a sample of efficient solutions is generated. In the second step this set is reviewed and evaluated by the Decision Maker. Evaluation of the solutions and selection of the most satisfactory fleet size is carried out with an application of three MCDA methods: LBS, ELECTRE and UTA.