This paper studied an optimal lane reservation problem with time-dependent link travel times. It aims to design time-guaranteed paths by converting some existing general-purpose lanes to reserved lanes with the objective of minimizing the total traffic impact of reserved lanes on general-purpose lanes. The traffic impact is caused by reserved lanes because they can be used by some special road users only and the adjacent general-purpose lanes may be more congested. The considered problem is to NP-hard. We propose a new mixed integer nonlinear programming model and transform it to an equivalent tractable linear model. We propose a cut-and-solve based algorithm in which new strategies are developed for generating piercing cuts. Computational results show that it is much more efficient to solve the proposed new model in the paper than the model in the literature and the overall performance of the proposed algorithm outperforms a direct use of an optimization solver of CPLEX on randomly generated instances.