A round-trip bus evacuation model with scheduling and routing planning

As emergencies occur more frequently, such as natural disasters and industrial accidents, evacuation planning attracts more and more attention. Bus is often used to evacuate car-free people due to its large capacity and manageability. To improve the efficiency and practicality of public transport evacuation plans, this paper presents a round-trip bus evacuation model based on unfixed routes with simultaneous optimization of bus scheduling and routing planning. With constraints of bus capacity, evacuee demand at pick-up points, time windows and flow balance, the proposed model aims to reduce the total evacuee time cost, including in-bus travel time and waiting time. Moreover, a two-layer algorithm, integrating the insertion algorithm and the edge-exchange algorithm, is devised to obtain the model sub-optimal solution. To verify the effectiveness of the proposed model and solution, two cases are presented in this paper. In the first case, the proposed model and algorithm manage to solve bus evacuation problems effectively. Furthermore, sensitivity analyses are conducted to show the impact factors on the objective function. Based on the realistic topology and size network of Ningbo in China, the second case illustrates the practical value of the model and solution in large-scale evacuation, and demonstrates the superiority over the conventional solution.