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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 third one of a series of three papers that the author dedicates to the strategic vehicle fleet management topic. The paper discusses ways of building replacement strategies for companies' fleets of vehicles. It means deciding for how long to exploit particular vehicles in a fleet (the fleet replacement problem-FR). The essence of this problem lies in the minimization of vehicle/fleet exploitation costs by balancing ownership and utilization costs and taking into account budget limitations. In the paper an original mathematical model (an optimization method) allowing for the FR 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 that there exist optimal exploitation periods of particular vehicles in a fleet. However, combination of them gives a replacement plan for an entire fleet violating budget constraints. But it is possible to adjust individual age to replacement of particular vehicles to fulfill budget constraints without losing economical optimality of a developed replacement plan for an entire fleet. The paper is the last one of a series of three papers that the author dedicated to the strategic vehicle fleet management topic including the following managerial decision problems: MAKE-or-BUY, sizing/composition and replacement.