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

Abstract

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.

Optimization of Electric Bus Scheduling Considering Charging Station Resource Constraints

“…Considering a partial charging strategy and the time-of-use price, Li et al ( 36 ) proposed a model of stationary charger deployment and a transit network schedule. Jiang et al ( 37 ) developed a robust scheduling model considering partial recharging and travel time uncertainty. The above works have enriched the research on vehicle scheduling and charging strategies.…”

The Robustness of Battery Electric Bus Transit Networks under Charging Infrastructure Disruptions

“…Liu [24] Zheng [26] Zhou [40] Bie [39] Hu [42] Jiang [41] An [13] Liu [25] Overall, the literature adopts optimization models for BEB relying on a minimization function of the system cost, utility impact, and component sizing. However, a minimization function is not ideal for BEB system configuration, especially when challenged with disruption events (e.g., power outage) [43].…”

“…through the utilization of Robust and Two-stage Stochastic optimization approaches), such as the works of [13,[24][25][26][39][40][41][42]. This approach considers the uncertainty associated with several parameters, as detailed in Table 2.…”

“…The latter is the main aim of the present paper. ✓ Zheng [26] ✓ Zhou [40] ✓ Bie [39] ✓ ✓ Hu [42] ✓ ✓ Jiang [41] ✓ A n [ 1 3 ] ✓ Liu [25] ✓…”

Enhancing Electric Bus Charging Scheduling: An Energy-Integrated Dynamic Bus Replacement Strategy with Time-of-Use Pricing

“…However, due to the limited on-board battery capacity, electric buses (EBs) require one or more charging sessions during daily operation [6][7][8][9]. Conventional diesel bus scheduling timetables are inapplicable to electric buses [10,11].…”