This paper investigates a capacitated lane reservation problem in a transportation network. The problem is to decide the task paths and select lanes to be reserved in a capacitated network to ensure that each commodity can be transported from its source to destination within a given travel time, meanwhile the lane's capacity is not violated. Its objective is to minimize the total impact of all reserved lanes on other normal lanes. To solve this problem, two integer linear programming models are formulated. The complexity of the problem is proved to be NP-hard. Then an algorithm based on a cut-and-solve idea is proposed to obtain optimal solutions. To evaluate the performance of our proposed algorithm, numerical experiments of randomly generated instances are conducted. Computational results show our algorithm significantly outperforms a well-known optimization software package CPLEX.