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The paper is the second one from the series of three papers that the Authors dedicate to the freight fleet management topic. The paper presents five quantitative (optimization) methods of solving selected fleet management problems. All the selected management problems are carefully defined and dedicated to them solution methods are roughly characterized, as well. Mathematical models of the selected problems are presented in details, including: the linear model of a Make or Buy problem, the non-linear model of a fleet sizing / composition problem, the linear model of a replacement problem including discounting aspect, the linear model of an assignment of drivers / vehicles to transportation tusks, and the linear, graph theory based model of a VRP problem. The paper will be continued in a next one dedicated to fleet management case studies.