Abstract Autonomous shared electric vehicles (SAEVs) emerge as a pivotal component of future urban intelligent transportation. This study addresses the inefficiencies of traditional direct ride-hailing models by integrating ridesplitting and relay strategies. We construct a four-dimensional spatiotemporal network considering time, space, battery level, and passenger count, simplifying it to a three-dimensional model for operational optimization. A pure integer linear programming model is developed to maximize operational profit, solved via a rolling horizon approach. Case studies in Chengdu demonstrate that the proposed strategies enhance operational profit by 11.60% and 13.85% under uniform and non-uniform demand distributions, respectively, compared to the single direct ride model.
1. Introduction
The proliferation of electric vehicles (EVs) in urban mobility has driven innovations in shared transportation. SAEVs, combining autonomous driving, electrification, and sharing concepts, offer potential to optimize road utilization and reduce environmental impact . However, traditional direct ride-hailing models suffer from low vehicle utilization and limited order fulfillment rates, necessitating innovative operational strategies .
Our research focuses on integrating ridesplitting (pooling multiple passengers with similar routes) and relay (transferring passengers between vehicles at intermediate stations to address battery range constraints) to enhance SAEV system efficiency. These strategies address dual challenges: balancing battery charging needs with dynamic order fulfillment and mitigating range anxiety through collaborative vehicle operations .
Existing studies on shared EVs primarily focus on ridesplitting scenarios or static scheduling, with limited exploration of combined relay and ridesplitting strategies -. We bridge this gap by modeling SAEV operations as a spatiotemporal network, enabling dynamic decision-making for real-time demand fluctuations.
2. Problem Description
2.1 SAEV Operational Framework
The SAEV system operates within a discretized spatiotemporal domain. Let \(I = \{1, 2, \dots, m\}\) denote station zones, \(T = \{0, 1, \dots, t_{\text{max}}\}\) discrete time intervals, \(L = \{0, \Delta l, \dots, 100\%\}\) battery levels, and \(N = \{0, 1, \dots, n_{\text{max}}\}\) passenger counts. A four-dimensional node \(v = (i, t, l, n)\) represents a vehicle’s state at station i, time t, battery level l, and with n passengers, connected by arcs \(e = (i, t, l, n, j, t’, l’, n’)\) representing movements or services .
User demands \(D_{i,j,t}\) for trips from i to j at time t are single-passenger orders. The system may combine multiple orders into ridesplitting trips or use relay to transfer passengers between vehicles when battery levels are insufficient. A safety battery level \(l_s\) must be maintained post-service to ensure operational feasibility .
2.2 Relay and Ridesplitting Dynamics
Relay operations involve two vehicles: a primary vehicle transports passengers to an intermediate station k, where they transfer to a secondary vehicle with higher battery charge. For example, a trip from i to j with \(BE_{i,j} = 50\%\) battery consumption can be split into \(i \to k\) and \(k \to j\), each consuming \(30\%\), enabling two vehicles with \(40\%\) battery to collaborate .
Ridesplitting aggregates multiple single orders into one trip, reducing vehicle usage. However, it introduces detour delays, while relay may incur transfer time costs. We model these trade-offs using a spatiotemporal network to balance service efficiency and profit .
3. Optimization Modeling
3.1 Network Arc Representation
The operational network comprises diverse arcs:
- Onboarding Arc (\(\xi^{(\text{ON})}\)): Represents passenger pickup, updating state from \((i, t, l, n)\) to \((i, t+\Delta t, l-\Delta l, n+1)\) .
- Movement Arc (\(\xi^{(\text{M})}\)): Represents travel from i to j, consuming time \(TE_{i,j} = DE_{i,j}/VE\) and battery \(BE_{i,j} = TE_{i,j} \cdot CE\), where \(DE_{i,j}\) is distance, VE speed, and CE power consumption .
- Charging Arc (\(\xi^{(\text{C})}\)): Represents charging at station i, increasing battery level to \(\min(l+\Delta l, 100\%)\) .
- Relay Arc (\(\xi^{(\text{R})}\)): Comprises two sequential arcs \((e_1, e_2)\), where \(e_1\) transfers passengers to a relay station, and \(e_2\) continues to the destination .
3.2 Network Reconstruction
The four-dimensional network’s complexity is reduced by merging arcs to form a three-dimensional (time-space-battery) network. For a n-passenger direct ride from i to j, the merged arc is:\(s^{(z)} = (i, t, l, j, t + 2n\Delta t + TE_{i,j}, l – 2n\Delta l – BE_{i,j})\) For a relay trip, the merged arc is:\(w = \left( \begin{array}{l} (i, t, l, k, t + n\Delta t + TE_{i,k}, l – n\Delta l – BE_{i,k}), \\ (k, t + n\Delta t + TE_{i,k}, q, j, t + 2n\Delta t + TE_{i,k} + TE_{k,j}, q – n\Delta l – BE_{k,j}) \end{array} \right)\) where k is the relay station -.
3.3 Mathematical Model
The objective function maximizes operational profit:\(\max P = \sum_{n \in N} nP_nP_z\sum_{s \in \varsigma_n(Z)} f_s + \sum_{n \in N} nP_nP_w\sum_{w \in \varsigma_n(W)} f_w – \sum_{e \in \varsigma^{(C)}} P_c f_e\) Subject to:
- Fleet size constraint:\(\sum_{s \in \varsigma^{(\text{SC})}} f_s \leq FS\)
- Parking capacity constraint:\(\sum_{s \in S_{i,t}^{(\text{S})} \cup S_{i,t}^{(\text{C})}} f_s \leq PA_{i,t} \quad \forall i \in I, t \in T\)
- Flow balance:\(\sum_{s \in \varsigma_o^{(-)}} f_s = \sum_{s \in \varsigma_o^{(+)}} f_s \quad \forall o \in O\)
- Demand satisfaction:\(\sum_{s \in \varsigma_{n,i,j,l}^{(Z)}} nf_s + \sum_{w \in \varsigma_{n,i,j,l}^{(W)}} nf_w \leq D_{i,j,t} \quad \forall i,j \in I, t \in T\) where \(P_z\), \(P_w\), \(P_c\) are profits per minute for direct rides, relay rides, and charging costs; \(f_s\), \(f_w\) are arc flows; and FS is the fleet size -.
4. Solution Algorithm: Rolling Horizon Optimization
4.1 Multi-horizon Framework
To handle dynamic demand, we use a rolling horizon approach, dividing the operational period into subwindows. Let \(T_c\) be the control period, \(T_z\) the direct ride allocation window, and \(T_w\) the relay allocation window (\(T_w < T_z\)) to prioritize high-profit direct rides -.
The framework updates demand predictions and vehicle states at each \(T_c\), solving subproblems for the next \(T_t = T_z + T_1\) period, where \(T_1\) ensures feasibility for ongoing services. This balances real-time responsiveness with long-term optimization -.
4.2 Time Window Calibration
Testing different window lengths reveals:
- Longer \(T_z\) increases profit but raises computation time (Table 1).
- Shorter \(T_w\) for relay avoids depleting fleet resources for subsequent windows (Table 2).
Table 1: Effect of Direct Allocation Window Length on Profit and Solving Time
| Direct Window (\(T_z\), min) | Planning Window (\(T_t\), min) | Profit (USD) | Max Solving Time (s) | Order Fulfillment Rate (%) |
|---|---|---|---|---|
| 30 | 60 | 33,678.20 | 10.3 | 60.00 |
| 30 | 75 | 33,798.68 | 10.99 | 60.50 |
| 30 | 90 | 34,067.34 | 14.59 | 60.59 |
| 45 | 60 | 36,934.73 | 151.06 | 66.47 |
| 45 | 75 | 37,497.03 | 223.64 | 67.46 |
| 45 | 90 | 37,242.28 | 456.81 | 67.04 |
| 60 | 75 | >300 s | – | – |
Table 2: Relay Allocation Window Calibration
| Planning Window (\(T_t\), min) | Relay Window (\(T_w\), min) | Direct Window (\(T_z\), min) | Profit (USD) | Order Fulfillment (%) | Relay Rate (%) | Solving Time (s) |
|---|---|---|---|---|---|---|
| 75 | 5 | 45 | 36,763.07 | 66.07 | 11.21 | 15.48 |
| 75 | 10 | 45 | 36,813.52 | 66.28 | 10.82 | 18.67 |
| 75 | 15 | 45 | 36,968.50 | 66.43 | 10.87 | 41.10 |
| 90 | 5 | 45 | 36,840.87 | 66.35 | 11.87 | 21.20 |
5. Case Study: Chengdu Urban Network
5.1 Experimental Setup
We model Chengdu’s urban area with 30 zones, operating from 16:00–21:00. Key parameters:
- Fleet size \(FS = 600\), initial battery \(l_{\text{ini}} = 70\%\) .
- Speed \(VE = 30 \, \text{km/h}\), charging power \(C_c = 20 \, \text{kW}\), safety battery \(l_s = 20\%\) .
- Profits: \(P_z = 0.3 \, \$/{\text{min}}\), \(P_w = 0.27 \, \$/{\text{min}}\), 2-passenger discount \(P_2 = 0.6\) .
Two demand scenarios:
- Tidal demand (Scenario 1): High demand at transport hubs and industrial zones.
- Uniform demand (Scenario 2): Balanced demand across zones .
5.2 Results and Analysis
Table 3: Operational Performance Under Different Demand Distributions
| Demand Scenario | Order Type | Total Profit (USD) | Profit Improvement | Order Fulfillment (%) | Relay Rate (%) | Ridesplitting Rate (%) |
|---|---|---|---|---|---|---|
| Scenario 1 | Direct ride | 33,011.20 | – | 58.47 | 0.00 | 0.00 |
| Ridesplitting+relay | 36,840.87 | 11.60% | 66.35 | 11.87 | 18.52 | |
| Scenario 2 | Direct ride | 33,504.70 | – | 59.86 | 0.00 | 0.00 |
| Ridesplitting+relay | 38,147.60 | 13.85% | 68.44 | 11.23 | 17.21 |
In both scenarios, combining ridesplitting and relay strategies significantly boosts profit. Scenario 2 shows higher profit improvement due to better fleet-demand matching -.
Table 4: Impact of Ridesplitting Passenger Limit
| Passenger Limit (\(n_{\text{max}}\)) | Demand Pressure (RN) | Profit (USD) | Relay Rate (%) | Ridesplitting Rate (%) | Order Fulfillment (%) |
|---|---|---|---|---|---|
| 1 | 0.6 | 28,685.87 | 10.35 | 0.00 | 65.94 |
| 1 | 0.8 | 36,009.14 | 11.46 | 0.00 | 61.73 |
| 1 | 1.0 | 39,363.82 | 13.24 | 0.00 | 54.23 |
| 2 | 0.6 | 27,855.12 | 10.13 | 13.46 | 66.48 |
| 2 | 0.8 | 36,840.87 | 11.87 | 18.53 | 66.35 |
| 2 | 1.0 | 40,328.53 | 12.96 | 24.26 | 59.30 |
| 3 | 0.6 | 29,502.62 | 9.95 | 9.85 | 70.00 |
| 3 | 0.8 | 37,615.78 | 10.98 | 14.52 | 67.67 |
| 3 | 1.0 | 41,488.04 | 11.86 | 16.99 | 61.11 |
Higher \(n_{\text{max}}\) enhances order fulfillment under high demand but may reduce profit under low demand due to discounting -.
6. Conclusion
This study presents a novel framework for dynamic SAEV operations integrating ridesplitting and relay strategies. Key findings include:
- The four-dimensional spatiotemporal network simplifies to a three-dimensional model, enabling efficient profit maximization modeling .
- Rolling horizon optimization with differentiated time windows balances real-time demand and computational feasibility .
- Case studies confirm 11.60–13.85% profit improvements versus traditional direct rides, validating strategy effectiveness .
Future work will explore multi-passenger order integration and stochastic demand modeling to further enhance SAEV operational resilience.