This paper presents an mixed integer nonlinear programming formulation for the lane reservation problem with time-dependent travel times. It aims to design time-guaranteed paths for some transportation tasks via lane reservation strategy, which is to optimally select and reserve some lanes for the use of the tasks with the objective of minimizing the total traffic impact caused by the reserved lanes. The considered problem is NP-hard. The original nonlinear model is transformed into an mixed integer linear program and a cut-and-solve based algorithm is proposed to obtain optimal solutions. Experimental tests on randomly generated instances show that the overall performance of the proposed algorithm outperforms a direct use of an optimization solver of CPLEX.