Optimal Electric Bus Scheduling under Travel Time Uncertainty: A Robust Model and Solution Method

With the increasing adoption of electric buses (e-buses), e-bus scheduling problem has become an essential part of transit operation planning. As e-buses have a limited battery capacity, e-bus scheduling problem aims to assign vehicles to timetabled service trips on the bus routes considering their charging demand. Affected by the dynamic operation environment, the travel time and energy consumption of the e-buses often display considerable randomness, resulting in unexpected trip start delays and battery energy shortages. In this paper, we addressed the e-bus scheduling problem under travel time uncertainty by robust optimization approaches. We consider the cardinality constrained uncertainty set to formulate a robust multidepot EVSP model considering trip time uncertainty and partial recharging. The model is developed based on the dynamic programming equations that we formulated for trip chain robustness checking. A branch-and-price (BP) algorithm is devised to generate provably high-quality solutions for large-scale instances. In the BP algorithm, an efficient label setting algorithm is developed to solve the robust resource-constrained shortest path subproblem. Comprehensive numerical experiments are conducted based on the bus routes in Shenzhen to demonstrate the effectiveness of the suggested methodology. The robustness of the schedules was evaluated through Monte Carlo simulation. The results show that the trip start delay and battery energy shortage caused by the travel time uncertainty can be effectively reduced at the expense of an increase in the operational cost. A trade-off should be made between the reduction in infeasibility rate and increase in operational cost to choose a proper uncertainty budget.

A Data-Based Bi-Objective Approach to Explore the Accessibility of Multimodal Public Transport Networks

One of the top concerns for travelers when choosing public transportation is whether they can reach their destination in limited time and monetary cost on the basis of ensured reliability. However, the existing literature shows no studies on how to evaluate bi-objective multimodal accessibility under travel time uncertainty. In order to fill this research gap, this paper creates a multimodal super network based on smart card data in which the transfers among taxi, bus, and subway modes are developed and applied. Next, we propose a two-stage opportunity accessibility model to calculate bi-objective multimodal accessibility under travel time uncertainty. Then we propose a multimodal reliability path finding model and a reliability boundary convergence algorithm to solve this problem. Finally, we conduct a large-scale real-world case study. It is found that the impedance heterogeneity between different modes is significant, and multimodal travel has better accessibility than a unimodal one. Although multimodal accessibility decreases as the reliability increases, the advantage of multimodal over unimodal accessibility increases with reliability, and it can be improved up to 14.61% by multimodal transfers. This model can effectively guide traffic management departments to improve traffic accessibility in terms of time and cost and advise commuters to choose living places.

The Electric Vehicle Routing Problem with Time Windows under Travel Time Uncertainty

Due to environmental friendliness, electric vehicles have become more and more popular nowadays in the transportation system. For many express companies, it is more and more important to meet the predetermined time window of customers. The uncertainty in travel times often causes uncertain energy consumption and uncertain recharging time, thus electric vehicles may miss the time windows of customers. Therefore, this paper addresses the electric vehicle routing problem with time windows under travel time uncertainty, which aims to determine the optimal delivery strategy under travel time uncertainty. To solve this problem, a robust optimization model is built based on the route-dependent uncertainty sets. However, considering the complexity of the problem, the robust model can only solve few instances including the small number of customers. Thus, a hybrid metaheuristic consisting of the adaptive large neighborhood search algorithm and the local search algorithm is proposed. The results show that the algorithm can obtain the optimal solution for the small-sized instances and the large-sized instances.