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Fleets constitute the most important production means in transportation. Their appropriate management is crucial for all companies having transportation duties. The paper is the first one of a series of three papers that the author dedicates to the strategic vehicle fleet management topic. The paper discusses ways of fulfilling company's transportation needs (MAKE-or-BUY problem). It means the choice between using company's own and outside fleet (buying transportation services in a market). The essence of the MAKE-or-BUY problem lies in a time dependency, a seasonal nature of transportation needs. It leads to the MAKE-and-BUY solutions including utilization of both in-house and outside fleets. In the paper an original mathematical model (an optimization method) allowing for the MAKE-and-BUY analysis is proposed. An application of the proposed optimization method in a real-life decision situation (the case study) within the Polish environment and the obtained solution are presented. The solution shows a low economic justification for using the MAKE option in practice. Especially when a fleet composed of brand new vehicles is considered. The paper will be continued in two further papers dedicated to strategic vehicle fleet management problems including fleet sizing/composition and fleet replacement.