This paper presents a joint optimization of the timetable, bus formation, and vehicle scheduling in a flexible public transport (PT) system that utilizes autonomous modular vehicles (AMVs). In this system, AMVs have the capability to detach or join with each other at intermediate stops along the route to dynamically adjust the bus formation (capacity). To increase vehicle utilization, a flexible scheduling strategy is proposed that allows AMVs to detach from one modular bus and join another modular bus in either direction of a bidirectional line. In particular, the penalty cost for each detachment or joining operation, as well as the limited number of available AMVs is explicitly considered. We formulate a unified model for the integrated optimization of the modular bus service (timetable and bus formation) and vehicle scheduling by introducing two types of decision variables. The objective is to minimize overall system costs, including passenger waiting time cost, operational costs, and detachment/joining penalty costs. The two types of decision variables are coupled by a vehicle resource consistency constraint, ensuring the conformity of the modular bus service and vehicle scheduling decisions. To tackle the complexity of our model, the Alternating Direction Method of Multipliers (ADMM) is employed to decompose it into two subproblems, which can be efficiently solved using a customized forward dynamic programming algorithm and a commercial solver. The model is validated using illustrative examples and a real-world instance from the Beijing Public Transport system, and it is compared with two benchmark models. Our results demonstrate the efficiency of the ADMM-based solution framework for solving the integrated optimization model. Furthermore, our findings indicate that the use of AMVs in PT systems can lead to reduced overall system costs and increased vehicle utilization.

Battery capacity degradation in battery electric buses (BEBs) poses a significant operational challenge for transit agencies. This study presents a sustainable battery scheduling and echelon utilization framework considering battery capacity fading and charging infrastructure integrated with solar photovoltaic (PV) and energy storage systems. The framework aims to minimize the sum of bus charging, battery replacement, and carbon emission costs during the BEB lifespan. We first present a power battery replacement problem for a single bus fleet, then extend it to a joint power battery replacement and fleet-depot matching problem. Finally, we propose a power battery replacement and fleet-depot problem by introducing solar PV and energy storage systems. Dynamic programming, Lagrange relaxation, and a two-step approach are adopted to solve the three problems. A case study involving six bus depots in Beijing demonstrates that optimal battery replacement schedules can significantly lower charging costs. Moreover, integrating solar PV and energy storage is shown to considerably reduce both charging costs and carbon emissions.

Optimizing battery swapping station (BSS) configuration is essential to enhance BSS’s energy savings and economic feasibility, thereby facilitating energy refueling efficiency of electric taxis (ETs). This study proposes a novel modular battery swapping mode (BSM) that allows ET drivers to choose the number of battery blocks to rent according to their driving range requirements and habits, improving BSS’s economic profitability and operational flexibility. We further develop a data-driven approach to optimizing the configuration of modular BSS considering the scheduling of battery charging at the operating stage under a scenario of time-of-use (ToU) price. We use the travel patterns of taxis extracted from the GPS trajectory data on 12,643 actual taxis in Beijing, China. Finally, we test the effectiveness and performance of our data-driven model and modular BSM in a numerical experiment with traditional BSM as the benchmark. Results show that the BSS with modular BSM can save 38% on the investment cost of purchasing ET battery blocks and is better able to respond to the ToU price than to the benchmark. The results of the sensitivity analysis suggest that when the peak electricity price is too high, additional battery blocks must be purchased to avoid charging during those peak periods.