Mixed-integer Programming for a New Bus-lane Reservation Problem

In this paper, we investigate a new bus-lane reservation problem in transportation network, which aims to optimally decide which lanes to be reserved for the exclusive use of buses and design bus transit paths for bus lines to achieve time-efficient bus transit with stop time window constraints. However, an exclusive bus-lane may cause negative impact on non-bus vehicles running on its adjacent non-reserved lanes as it reduces their available lanes. The objective of the problem is to minimize the total negative impact caused by reserved lanes. To address this problem, we first formulate a mixed-integer non-linear program and its complexity is proved to be NP-hard. Then, the nonlinear model is equivalently transformed into an linear one. Furthermore, properties of the problem are analyzed to reduce the search space for optimal solutions and tighten the proposed linear model. Finally, it is solved using commercial optimization software CPLEX. Computational results on randomly generated instances show the effectiveness of the proposed approach.