Background: Fleets constitute the most important production means in transportation. Their appropriate management is crucial for all companies having transportation duties. The paper is the second one of a series of three papers that the author dedicates to the strategic vehicle fleet management topic.

Material and methods: The paper discusses ways of building companies' fleets of vehicles. It means deciding on
the number of vehicles in a fleet (the fleet sizing problem - FS) and types of vehicles in a fleet (the fleet composition problem - FC). The essence of both problems lies in balancing transportation supply and demand taking into account different demand types to be fulfilled and different vehicle types that can be put into a fleet. Vehicles, which can substitute each other while fulfilling different demand types. In the paper an original mathematical model
(an optimization method) allowing for the FS/FC analysis is proposed.

Results: 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 some best fitted (optimal) fleet size / composition matching company's transportation requirements. An optimal fleet size / composition allows for a significantly higher fleet utilization (10-15% higher) than any other, including random fleet structure. Moreover, any changes in the optimal fleet size / composition, even small ones, result in a lower utilization of vehicles (lower by a few percent).

Conclusions: The presented in this paper analysis, on the one hand, is consistent with a widespread opinion that the number of vehicle types in a fleet should be limited. In the other words it means that the versatility / interchangeability of vehicles is very important. On the other hand, the analysis proves that even small changes in a fleet size / fleet composition can result in an important changes of the fleet effectiveness (measured for example by the utilization ratio).