As a researcher in urban transportation systems, I explore the integration of relay and ridesplitting strategies in shared autonomous electric vehicle (SAEV) operations to enhance efficiency and profitability. The rapid growth of the electric vehicle market, particularly in China EV sectors, underscores the importance of optimizing these systems. Traditional ride-hailing models often underutilize vehicles, leading to low order fulfillment rates and economic inefficiencies. By incorporating ridesplitting and relay services, SAEV systems can better balance charging demands and service requests, leveraging the connectivity of autonomous technologies. This article presents a comprehensive model and solution approach for dynamic SAEV operations, validated through a case study in Chengdu, China.
The SAEV system operates within a network of stations derived from historical demand data, partitioned into Voronoi cells. Each station serves as a hub for vehicle charging and passenger pickup/drop-off. The operational timeline is discretized into intervals, and vehicle states—including location, time, battery level, and passenger count—are tracked. Key strategies include ridesplitting, where multiple passengers share a single electric vehicle, and relay services, where two vehicles collaborate to complete a long-distance trip via an intermediate station. These approaches mitigate range anxiety and charging congestion, common challenges in electric vehicle operations.
To model the system, I construct a four-dimensional spatiotemporal network incorporating time, space, battery level, and passenger count. This network is simplified into a three-dimensional structure by merging arcs representing sequential actions like pickup, movement, and drop-off. The objective is to maximize operational profit, formulated as a pure integer linear programming model. The profit function accounts for revenues from direct rides, ridesplitting (with discounts), relay services, and charging costs. Constraints include fleet size limits, station parking capacity, flow conservation, and demand fulfillment.
The optimization problem is solved using a rolling horizon framework, which divides the operational period into overlapping time windows. This approach handles dynamic demand by periodically updating vehicle states and order information. Heterogeneous services—such as direct rides, ridesplitting, and relay—are assigned different forward-looking time windows to ensure computational feasibility. The GUROBI solver is employed to solve subproblems within each window, achieving real-time decision-making capabilities.
In the case study, I analyze the Chengdu road network with 30 stations over a 5-hour period (16:00–21:00). The fleet consists of 600 electric vehicles with an average speed of 30 km/h and a battery capacity of 50 kWh. Charging stations have a power output of 20 kW, and vehicles maintain a safety battery level of 20%. Demand scenarios vary in spatial distribution: Scenario 1 features tidal patterns with high demand at hubs, while Scenario 2 has more uniform demand. Results demonstrate that integrating ridesplitting and relay strategies increases operational profit by 11.60% in Scenario 1 and 13.85% in Scenario 2 compared to direct ride-hailing alone.
The mathematical model is defined as follows. Let the set of stations be $I = \{1, 2, \dots, 30\}$, time intervals $T = \{0, 1, \dots, 60\}$ (with $\Delta t = 5$ minutes), battery levels $L = \{0\%, 3.3\%, \dots, 100\%\}$, and passenger counts $N = \{0, 1, 2, 3\}$. The decision variables are flows on arcs in the simplified network. The objective function is:
$$ \text{Maximize} \sum_{n \in N} \left( \sum_{s \in \zeta^{(Z)}} n P_n P_z f_s + \sum_{w \in \zeta^{(W)}} n P_n P_w f_w \right) – \sum_{e \in \zeta^{(C)}} P_c f_e $$
where $P_n$ is the discount factor for ridesplitting with $n$ passengers, $P_z$ and $P_w$ are profits per minute for direct and relay services, and $P_c$ is the charging cost. Constraints include:
- Fleet size: $\sum_{s \in \zeta^{(SC)}} f_s \leq FS$
- Station capacity: $\sum_{s \in \zeta^{(SC)} \cup \zeta^{(C)}} f_s \leq PA_{i,t}$ for all $i \in I, t \in T$
- Flow conservation: $\sum_{s \in \zeta^{-}(o)} f_s = \sum_{s \in \zeta^{+}(o)} f_s$ for all nodes $o$
- Demand fulfillment: $\sum_{s \in \zeta^{(Z)}} n f_s + \sum_{w \in \zeta^{(W)}} n f_w \leq D_{i,j,t}$ for all $i,j \in I, t \in T$
The rolling horizon algorithm uses control window $T_c = 5$ minutes, direct service allocation window $T_z = 45$ minutes, relay allocation window $T_w = 5$ minutes, and planning window $T_t = 90$ minutes. This configuration ensures solutions are obtained within 300 seconds, meeting real-time requirements.
Experimental results highlight the impact of demand distribution and ridesplitting limits. Under moderate demand (pressure coefficient RN=0.8), allowing up to 3 passengers per electric vehicle increases profit by 13.85% in uniform distributions and 11.60% in tidal distributions. The table below summarizes profit comparisons for different scenarios:
| Demand Scenario | Service Type | Profit (USD) | Profit Increase | Order Fulfillment Rate | Relay Rate | Ridesplitting Rate |
|---|---|---|---|---|---|---|
| Scenario 1 (Tidal) | Direct Only | 33,011.20 | — | 58.47% | 0.00% | 0.00% |
| Scenario 1 (Tidal) | Ridesplitting + Relay | 36,840.87 | 11.60% | 66.35% | 11.87% | 18.52% |
| Scenario 2 (Uniform) | Direct Only | 33,504.70 | — | 59.86% | 0.00% | 0.00% |
| Scenario 2 (Uniform) | Ridesplitting + Relay | 38,147.60 | 13.85% | 68.44% | 11.23% | 17.21% |
Additionally, the effect of passenger capacity on profit is analyzed for different demand pressures:
| Passenger Capacity | Demand Pressure (RN) | Profit (USD) | Relay Rate | Ridesplitting Rate | Order Fulfillment Rate |
|---|---|---|---|---|---|
| 1 | 0.6 | 28,685.87 | 10.35% | 0.00% | 65.94% |
| 2 | 0.6 | 27,855.12 | 10.13% | 13.46% | 66.48% |
| 3 | 0.6 | 29,502.62 | 9.95% | 9.85% | 70.00% |
| 1 | 0.8 | 36,009.14 | 11.46% | 0.00% | 61.73% |
| 2 | 0.8 | 36,840.87 | 11.87% | 18.53% | 66.35% |
| 3 | 0.8 | 37,615.78 | 10.98% | 14.52% | 67.67% |
| 1 | 1.0 | 39,363.82 | 13.24% | 0.00% | 54.23% |
| 2 | 1.0 | 40,328.53 | 12.96% | 24.26% | 59.30% |
| 3 | 1.0 | 41,488.04 | 11.86% | 16.99% | 61.11% |
The integration of relay and ridesplitting significantly improves the utilization of electric vehicles in China EV applications. For instance, relay services enable low-battery vehicles to participate in long trips by transferring passengers at intermediate stations, while ridesplitting consolidates multiple orders into one vehicle journey. The model’s efficiency is evident in the high solving speed of subproblems, which aligns with the dynamic nature of urban mobility. Future work could extend to multi-passenger orders and real-time pricing strategies, further enhancing the adaptability of SAEV systems in evolving electric vehicle landscapes.
In conclusion, the proposed framework demonstrates substantial benefits for shared autonomous electric vehicle operations, emphasizing the synergy between relay and ridesplitting in maximizing profit and service quality. As the China EV market continues to expand, such innovations will play a crucial role in shaping sustainable and intelligent transportation networks.