A new cut-and-solve and cutting plane combined approach for the capacitated lane reservation problem

• A transportation planning problem via lane reservation is studied.
• An exact approach based on cut-and-solve and cutting plane method is developed.
• Separation algorithms are proposed to find valid inequalities for cutting plane method.
• Computational results show the approach is efficient compared with IP solver CPLEX.

This paper investigates a capacitated lane reservation problem with residual capacity. The focus of the problem is to design time-guaranteed paths for a set of transportation tasks via lane reservation with respect to the residual capacity issue. The lane reservation can ensure the time-guaranteed travel but has negative impact on the normal traffic. Thus, the objective of the problem is to minimize the impact of such lane reservation by optimally selecting lanes in the network to be reserved. For this NP-hard problem, an exact approach based on the cut-and-solve and cutting plane methods is developed. New separation algorithms are proposed to find appropriate valid inequalities according to the characteristic of the problem to accelerate the optimal convergence of the resolution approach. Numerical computational results show that the developed approach is efficient as compared with state-of-the-art algorithms in the literature and the IP solver CPLEX.