In recent years the total number of electric cars has grown dramatically, and this expansion has accelerated the deployment of public charging facilities. Data from public sources show that national electric car ownership surpassed 20 million at the end of 2023, while the number of public charging piles exceeded 2.7 million. However, the daily operations of these facilities reveal substantial coordination failures. Multiple charging operators independently manage their own platforms, and these platforms are seldom interconnected. From the perspective of a user, finding an available and suitable charging pile can be difficult. From the perspective of an operator, many charging stations suffer from low utilisation rates, while a small number of stations are heavily overloaded. This underutilisation and uneven demand distribution reduce revenues and lower user satisfaction. To solve these problems, charging sharing platforms have emerged as a promising solution. These platforms integrate resources from different operators and can influence user choices through dynamic pricing and recommendation mechanisms. In this study I focus on the operation strategies of such a charging sharing platform. I consider a bilevel programming framework in which the operators in the upper level set prices and service levels, while electric car users in the lower level respond according to their own preferences. I aim to maximise the total profit of the operators and to balance the utilisation rates of all charging stations simultaneously. By integrating user behaviour, optimisation theory, and real traffic data, this paper provides both theoretical and practical insights for designing efficient charging sharing services.
The motivation for this research comes from the severe mismatch between charging demand and supply in many Chinese cities. In Beijing, for example, statistics indicate that the average utilisation rate of public charging piles in the central urban area is lower than 20%, while some suburban stations experience congestion. This imbalance is related to the independent operation of different charging networks. Users cannot see real-time information from all operators unless they browse several mobile applications. Operators cannot coordinate their pricing decisions with other operators, because each station only tries to maximise its own local revenue. Charging sharing platforms attempt to bridge this gap by aggregating stations from several operators and by presenting standardised information. Nevertheless, the platform needs a careful operational strategy. Setting a uniform price for all stations is not desirable, since their service levels, distances, and congestion states differ. The platform must decide the optimal price and service level for each station after considering the likely reactions of electric car users. These reactions are heterogeneous: some users prefer cheap charging, some prefer fast charging, some dislike long detours, and some value high-quality equipment. Therefore, the platform must first understand user preferences, and then optimise its decisions with respect to these preferences. In my research I adopt discrete choice theory to quantify user preferences. Through a stated-preference survey, I estimate the sensitivity of electric car drivers to four factors: total time, travel distance, charging service level, and charging price. These estimated weights are then embedded into a lower-level choice model that simulates how each user selects a charging station. The upper-level problem is formulated as a multi-objective optimisation problem, and the solution is a set of Pareto-optimal pricing and service-level plans. To select one plan from this set, I apply the TOPSIS method with time-of-use weights. This approach allows the platform to react dynamically to electricity price changes across the day and to improve both profitability and utilisation fairness.
I. Literature Review
My review of the existing literature covers three streams of research. The first stream concentrates on charging station pricing from the perspective of charging station operators. Early studies treated charging stations as isolated entities and maximised their own profits. Static pricing models were widely proposed. Later, dynamic pricing became more common, especially for addressing grid voltage issues and reducing peak loads. However, these models often ignored the interaction among multiple operators and users. Several authors have introduced game theory, in particular Stackelberg games, to capture the sequential decision structure in which operators lead and users follow. Those models usually assume that the operator has one objective, such as profit maximisation, while user response is modelled through a simple cost-minimising utility function. These efforts have contributed to the understanding of charging pricing, but they rarely considered multiple conflicting objectives for the entire network, such as profit growth and resource balance simultaneously. Some studies have considered two types of charging stations, fast charging and slow charging, yet they did not treat the fast/slow charging ratio as a decision variable.
The second stream of research analyses charging guidance from the perspective of electric car users. Many papers model the behaviour of users explicitly through logit models or other discrete choice frameworks. The resulting user utility functions include variables such as travel time, waiting time, charging fee, and distance. A number of researchers have developed charging navigation algorithms that recommend a station to each user. The objective is generally to minimise the total time cost or to maximise user satisfaction. In these models the charging station itself is often passive: it offers a fixed price and has a fixed capacity. The operator’s profit is not the central concern. Some noteworthy contributions have incorporated multi-agent reinforcement learning or dynamic graph methods to improve user satisfaction. The limitation of this stream is that pricing and user recommendation are not jointly optimised. Operators cannot adapt their strategies to user behaviour because the user guidance module is disconnected from pricing decisions.
The third stream of research explicitly considers charging platforms. These platforms connect multiple charging stations and provide information about current prices, available piles, and queue lengths. Some authors designed matching algorithms in which electric car users are assigned to stations based on cost minimisation. Others designed hierarchical game models for pricing and navigation between competing charging facilities. A common finding is that platform-based coordination can reduce average waiting times and improve convenience. However, most of this research has not incorporated a multi-dimensional user preference model estimated from real survey data. More importantly, existing papers seldom use real traffic network data to simulate user movement. Consequently, their results may be too abstract for practical deployment. Table 1 summarises how my work differs from typical existing papers with respect to key features.
| Feature | Many existing studies | This study |
|---|---|---|
| Operator interaction | rarely considered | coordinated by a shared platform |
| Decision variables | price only | price and service level |
| Utilisation equalisation | not considered | explicit objective |
| User preference estimation | simple assumptions | discrete choice model from survey data |
| Traffic environment | hypothetical networks | real road network within Beijing’s Fifth Ring Road |
| Solution algorithm | single-objective heuristics | NSGA-II plus TOPSIS |
This comparison shows that an important gap remains. The charging platform must solve a nested problem: the upper level optimises price and service levels for all participating operators; the lower level calculates how electric car users respond to these decisions. I address this gap by constructing a comprehensive bilevel model that accounts for user heterogeneity, real traffic congestion, queuing, and multi-objective optimisation. The methodology also records dynamic interactions because the time horizon is divided into hourly slots and electricity prices vary across high, flat, and low periods.
II. Bilevel Programming Framework
In this work I model the charging sharing platform as a Stackelberg leader-follower game. The platform is the leader because it publishes the charging prices and declares the service level of each station before users make any decision. Electric car users are followers because they observe those prices and service levels and then pick the station that gives them the highest utility. Since the set of users and the traffic state change from hour to hour, the game is repeated for every time slot k. The underlying structure can be expressed by the following bilevel optimisation problem.
$$ \max_{x \in X} \; F(x, y(x)) \st \min_{y} \; f(x,y), \quad g(x,y) \ge 0 $$
where \(x\) denotes the upper-level decision variables and \(y(x)\) denotes the lower-level equilibrium response. In my formulation \(x\) represents the charging price and the service level of every station. The lower-level variable \(y\) represents the charging location choice of each electric car user. The upper-level objective \(F\) contains two objectives: total profit maximisation and utilisation variance minimisation. The lower-level objective \(f\) is a user disutility function, which I convert into a choice probability.
A. Upper-level decision variables
Each station \(j\) has two decision variables in time slot \(k\): its per-kWh charging price \(p_{jk}\) and its service level \(s_{jk}\). The service level is defined by the fraction of fast charging piles in the station. Let \(u_j\) be the fast-to-slow ratio of station \(j\). After standardising all ratios across the market, I obtain
$$ s_j = \frac{u_j – U_{\min}}{U_{\max} – U_{\min}}, \qquad s_j \in [0,1], $$
where \(U_{\max}\) and \(U_{\min}\) are the maximum and minimum fast-to-slow ratios in the market. Stations with \(s_j\) close to 1 rely mainly on fast piles, while stations with \(s_j\) close to 0 rely mainly on slow piles. A higher service level reduces the average charging time, but it also increases operating cost because fast piles are more expensive to install and maintain. The operating cost of station \(j\) at time \(k\) is divided into an electricity purchase cost, a service-induced cost, and a fixed overhead:
$$ c^s_{jk} = \frac{\nu}{2} s_{jk}^2, $$
where \(\nu\) is a service cost coefficient. Including this quadratic cost in the profit expression prevents the platform from setting all stations to the highest service level.
Let \(\delta_{ijk}\) be a binary variable equal to one when electric car user \(i\) chooses station \(j\) in slot \(k\), and zero otherwise. Let \(q^*_{ik}\) be the optimal charging quantity of that user, which is derived in the lower-level charging model. The marginal cost of purchasing electricity is \(mc^c_{jk}\). Additional fixed costs are denoted \(C^o_{jk}\). The hourly profit of station \(j\) is written as
$$ r_{jk} = \sum_{i} \delta_{ijk} \left( p_{jk} – mc^c_{jk} \right) q^*_{ik} – \frac{\nu}{2} s_{jk}^2 – C^o_{jk}. $$
Different charging stations belong to different operators, but in this paper I view them as members of a single platform alliance. The platform maximises their total profit:
$$ \max_{p_{jk}, s_{jk}} \; R_k = \sum_{j=1}^{J} r_{jk}. $$
At the same time the platform tries to equalise utilisation among stations. I measure utilisation as the total energy delivered by station \(j\) over its capacity \(Q_j\):
$$ ur_{jk} = \frac{ \sum_{i} pr(J = j, i, k) \, q^*_{ik} }{ Q_j }, $$
where \(pr(J = j, i, k)\) is the probability that user \(i\) selects station \(j\). The upper-level second objective is to minimise the variance of these utilisation rates:
$$ \min_{p_{jk}, s_{jk}} \; V_k = \frac{1}{J} \sum_{j=1}^{J} \left( ur_{jk} – \overline{ur}_k \right)^2, $$
where \(\overline{ur}_k\) is the average utilisation of all stations in slot \(k\). Since profit and utilisation variance are generally conflicting objectives, I treat them as a multi-objective problem rather than assigning fixed weights. Therefore the upper-level problem is
$$ \max_{p_{jk}, s_{jk}} \left( R_k(p_{jk},s_{jk}), \; – V_k(p_{jk}, s_{jk}) \right) $$
subject to the bounds:
$$ p_{\min} \le p_{jk} \le p_{\max}, $$
$$ s_{j,\min} \le s_{jk} \le s_{j,\max}. $$
Station 1 is given a lower service-level cap so that it mainly uses slow piles. Station 2 is allowed a medium range, and station 3 is allowed a high fast-charging ratio.
B. Lower-level user choice model
The platform’s decisions influence user choices through the utility function. I use a random utility framework. The systematic part of the utility that electric car user \(i\) obtains from station \(j\) in slot \(k\) is written as
$$ U_{ijk} = \theta_1 t_{ijk} + \theta_2 d_{ij} + \theta_3 s_{jk} + \theta_4 p_{jk}, $$
where \(t_{ijk}\) is the total time spent (driving, queuing and charging), \(d_{ij}\) is the shortest road distance from user \(i\) to station \(j\), \(s_{jk}\) is the station’s service level, and \(p_{jk}\) is the charging price. The coefficients \(\theta_1, \dots, \theta_4\) represent sensitivities to each factor. They are estimated from questionnaire data using a mixed logit model. More specifically, I designed a stated-choice survey with nine hypothetical choice sets. Through 526 valid responses, I obtained the mean preference weights shown in Table 2.
| Attribute | Notation | Estimated mean weight | Interpretation |
|---|---|---|---|
| Total time | \(\theta_1\) | -0.21 | Users dislike longer time |
| Travel distance | \(\theta_2\) | -0.40 | Users dislike farther stations |
| Service level | \(\theta_3\) | +0.43 | Higher service attracts users |
| Price | \(\theta_4\) | -0.62 | Users dislike higher prices |
The negative price coefficient is larger in magnitude than the other coefficients, suggesting that price is the most influential factor for the average electric car user. However, the mixed logit standard deviations are significantly different from zero. This result indicates considerable heterogeneity in preferences, which is consistent with the existence of price-sensitive and service-sensitive user groups.
The probability that user \(i\) chooses station \(j\) is given by the following logistic expression derived from the random utility model:
$$ pr(J = j, i, k) = \frac{ \exp\left( U_{ijk} \right) }{ \sum_{j’=1}^{J} \exp\left( U_{ij’k} \right) }, \quad \forall j,i,k. $$
The total time \(t_{ijk}\) includes three components:
$$ t_{ijk} = t^{tra}_{ijk} + t^{que}_{ijk} + t^{cha}_{ijk}, $$
where \(t^{tra}_{ijk}\) is the travel time from the current position of user \(i\) to station \(j\). I calculate this travel time using the real road network and the average traffic speed during slot \(k\):
$$ t^{tra}_{ijk} = \frac{d_{ij}}{v_{ik}}, $$
with \(v_{ik}\) obtained from hourly traffic-speed data. I find the shortest road path by applying the Floyd-Warshall algorithm to the network model. The travel distance \(d_{ij}\) is thus the network shortest-path length.
The queuing time \(t^{que}_{ijk}\) is computed from an \(M/M/c\) queueing model. User arrivals to station \(j\) follow a Poisson process at rate \(\lambda_{jk}\), and each charger has an exponential service time with rate \(\mu_{jk}\). The number of chargers in the station is \(c\). The service rate is linked to the upper-level service-level variable through the expression
$$ \mu_{jk} = \frac{1}{s_{jk} T_f + (1 – s_{jk}) T_s}, $$
where \(T_f\) and \(T_s\) are the average charging time for fast and slow piles, respectively. Let \(\rho_{jk} = \lambda_{jk}/(c \mu_{jk})\) be the traffic intensity. If the queue is stable, the average queue length is
$$ L^{que}_{jk} = P_0 \frac{(c \rho_{jk})^c \rho_{jk}}{c! (1- \rho_{jk})^2}, $$
where \(P_0\) is the probability that the system is empty. The average waiting time in the queue is obtained with Little’s law:
$$ t^{que}_{ijk} = \frac{L^{que}_{jk}}{\lambda_{jk}}. $$
Finally, the charging time is
$$ t^{cha}_{ijk} = \frac{q^*_{ik}}{CP_j}, $$
where \(CP_j\) denotes the average charging power of all piles at station \(j\). To determine \(q^*_{ik}\), I use a concave utility function for the charging quantity. User \(i\) balances the benefit of obtaining electricity against the charging cost. The marginal valuation function is linear:
$$ \pi(q_{ik}) = a \, q_{ik} – \frac{b}{2} q_{ik}^2 – p_k q_{ik}, $$
where \(p_k\) is the average electricity price level in slot \(k\). The user maximises \(\pi(q_{ik})\) subject to bound constraints:
$$ q^{\min}_{ik} \le q_{ik} \le q^{\max}_{ik}. $$
Solving the first-order condition gives
$$ q^*_{ik} = \frac{a – p_k}{b}. $$
If this value falls outside the bounds, the optimal solution becomes the closest feasible bound. In line with observed charging behaviour, I sample the initial battery state of charge from a normal distribution with a standard deviation of 10%, and the minimum remaining battery level is chosen so that users do not deplete the battery.
III. Solution Method
The bilevel model described above is nonlinear, nested, and includes two conflicting objectives in the upper level. Conventional exact algorithms require the lower-level optimality conditions to be converted into constraints. Such a conversion is difficult when user choices involve discrete choice probabilities and queueing delays. Therefore I designed an iterative nested algorithm. In each iteration I fix the upper-level prices and service levels, evaluate the lower-level user responses, compute the resulting charging probabilities and station utilisations, feed these quantities to the upper level, and then update the upper-level decisions with a multi-objective evolutionary algorithm. Because the platform and users play a Stackelberg game, I solve the upper-level problem with NSGA-II and let the lower-level choice model act as the response function. The algorithm is summarised in Table 3.
| Step | Description |
|---|---|
| 1 | Initialise a population of price and service-level vectors |
| 2 | For each vector, solve the lower-level user choice problem |
| 3 | Compute total profit and utilisation variance |
| 4 | Apply non-dominated sorting and crowding distance assignment |
| 5 | Generate offspring by crossover and mutation |
| 6 | Combine parent and offspring populations, repeat steps 2–5 |
| 7 | Stop when the maximum generation is reached and output Pareto front |
NSGA-II is particularly suitable for this problem because it maintains a diverse set of Pareto-optimal solutions. In my simulation I set the population size to 200 and the maximum number of generations to 100. The crossover probability is 0.7 and the mutation probability is 0.5. The Pareto front provides many possible trade-offs between profit and utilisation variance. To choose one operational strategy for each hour, I use the TOPSIS method. TOPSIS ranks alternatives by their distance from an ideal solution. In my implementation I define the ideal solution as the one with maximum total profit and minimum utilisation variance. The weights reflect the operating mode of the day: during peak price periods, I put more weight on utilisation fairness to prevent overload; during off-peak periods, I put more weight on total profit to take advantage of lower electricity costs. The weights are listed in Table 4.
| Time-of-use period | Profit weight | Variance weight |
|---|---|---|
| Peak hours | 0.4 | 0.6 |
| Moderate hours | 0.5 | 0.5 |
| Off-peak hours | 0.6 | 0.4 |
By changing the weights according to the electricity tariff, the platform automatically adapts its recommendation to grid conditions and profit opportunities.
IV. Simulation Scenario
I evaluate the proposed model through a simulation based on real road network data from the city of Beijing. The study area is restricted to a quadrilateral inside the Fifth Ring Road, approximately covering 8–10 square kilometres of the Haidian District. The road network contains 51,434 nodes and 68,206 edges. I extracted the hourly average travel speed from traffic conditions for one typical working day in 2023. Using ArcGIS, I superimposed the network onto an OpenStreetMap base layer. Figure 1 already illustrated the rapid growth of electric cars in China, and this growth determines the charging demand in the study area.
Within the road network, I place three charging stations at fixed locations. The locations are chosen so that each station has a different surrounding traffic density and a different distance to the most populated area of the subnetwork. In all simulations, the charging stations are numbered from station 1 to station 3. Station 1 is constrained to have a low service level, meaning a fast-charging pile ratio below 0.3. Station 3 has a high service-level range from 0.6 to 1.0, and station 2 lies in a middle range. The price boundaries are identical for all stations, ranging from 0 to 3 RMB per kWh. However, in the optimal solution each station selects a different portion of this range owing to its service-level constraints and user demand. Table 5 summarises the principal parameter settings.
| Parameter | Value | Source/Note |
|---|---|---|
| Fixed operating cost per charger | 10 RMB/h | Charging alliance report |
| Service cost coefficient \(\nu\) | 50 | Charging station planning literature |
| Charging price limits | [0, 3] RMB/kWh | Market service fee report |
| Station capacities | 500 kWh | Technical standard for scattered EV charging |
| Electricity tariffs | 0.3766 / 0.6770 / 0.9864 RMB/kWh | Beijing time-of-use pricing |
| Average charging power | 10 kW | National charging alliance data |
| User preference coefficients | \(-0.21,-0.40,0.43,-0.62\) | Mixed logit estimation |
| Number of simulated electric cars | 50 (base case) | local road network scale |
| Speed range | 10–70 km/h | Beijing traffic safety rules |
For the lower-level queueing model, I set the fast-charging average duration to 45 minutes and the slow-charging average duration to 4 hours. The number of charging points per station is set to 10. User arrivals are generated from a Poisson process whose rate depends on the number of electric cars in the area and on the average charging demand in each hour. I run the simulation for 24 consecutive hours. Each hour is optimised separately, and the optimal decisions from one hour do not modify the stock of vehicles in the next hour except through the initial state of charge distribution, which I resample independently. Although this means that I do not track individual vehicle trajectories across the entire day, the approach is sufficient for analysing hourly pricing and guidance policies in a stationary environment.
V. Results and Discussion
A. Pareto front and operator strategies
After running NSGA-II for 100 generations, I obtain a Pareto front in each hour. One representative front is displayed in Figure 2; it shows the trade-off between total profit and utilisation variance. Because higher profits often coincide with more uneven utilisation when some station is especially attractive, the front has a descending shape. The Pareto front allows the platform manager to choose a strategy according to the external situation. For example, during peak electricity periods, TOPSIS selects a solution with lower utilisation variance and slightly lower profit. During off-peak periods, it selects a solution with larger profit and somewhat higher variance.
A key result of the simulation is that the three charging stations adopt distinct equilibrium strategies. Station 1 usually charges a low price and offers a low service level. Its price lies roughly between 1.0 and 1.5 RMB/kWh, while its service level remains between 0.08 and 0.27. Station 2 charges a middle price around 1.5–2.0 RMB/kWh and has a service level in the range 0.38–0.62. Station 3 charges the highest price, more than 2.0 RMB/kWh and sometimes up to 3.0 RMB/kWh, while also offering the highest service level, usually above 0.6. This differentiation is not imposed by the algorithm as a label; instead, it emerges from the upper-level objective that rewards both profit margin and utilisation balance. The low-price station attracts price-sensitive users, the high-price station attracts users who value time and convenience, and the middle station serves the remaining market. This result mirrors the typical three-tier service design found in many public charging markets.
B. Optimisation versus uncoordinated pricing
To verify the effectiveness of the proposed optimisation, I compare it with a benchmark scenario that mimics the uncoordinated pricing behaviour of independent operators. In the benchmark, all stations have the same price and service bounds as in the optimised model, but no platform-level objective is used. Instead, each station greedily chooses a price from its own price interval and a service level from its service interval. The intervals partly overlap: station 1 price range is [1,2], station 2 is [1.5,2.5], and station 3 is [2,3]. Users still use the identical choices model. I record the total profit and utilisation variance for both strategies over 100 independent simulation runs.
| Indicator (24-h average) | Optimised pricing | Uncoordinated pricing | Relative improvement |
|---|---|---|---|
| Total operator profit (RMB) | 6032.71 | 3791.24 | +59.1% |
| Average utilisation variance | 0.017 | 0.0436 | -61.0% |
| Peak hourly utilisation max | 0.50 | 0.90 | — |
| Negative-profit hours in stations | almost none | several | — |
The optimised strategy clearly outperforms the uncoordinated one. Total profit is about 59% higher, and utilisation variance is about 61% lower. In the box plots, the median total profit of the optimised approach is 243.75 RMB per hour, while the benchmark yields 131.47 RMB per hour. This gain is driven by two channels: first, the platform shifts demand away from congested high-price stations to moderately priced stations; second, it prevents excessive price wars by aligning service levels with the supporting operating costs. The benchmark stations often alternate between extremely high utilisation and near-idle states. Station 3 in the benchmark can lose money during some hourly intervals because its high service cost is not compensated by enough users, while during other hours it earns a windfall profit. This variability is undesirable for long-term investment decisions.
Figure 5 shows the hourly utilisation trajectories under both strategies. In the optimised solution, station 1 utilisation varies between 0.20 and 0.50, station 2 between 0.16 and 0.51, and station 3 between 0.08 and 0.33. In the uncoordinated case, station 1 may reach 0.9 utilisation, while station 3 may be below 0.05. The equalised pattern not only improves fairness among operators but also reduces the probability of long queues at popular stations.
C. Price and utilisation dynamics
The upper-level optimisation reacts systematically to time-of-use electricity prices. Figure 6 shows the 24-hour price evolution. Prices are higher from 10:00 to 14:00 and from 18:00 to 21:00, which coincides with the time windows having an electricity cost of 0.9864 RMB/kWh. In the early morning, from 23:00 to 5:00, the prices are lowest. The average prices of station 1, station 2, and station 3 are 1.28, 1.76, and 2.46 RMB/kWh, respectively. These values reflect both the cost of electricity and the service-level difference. The standard deviations of hourly prices are 0.09, 0.23, and 0.21, suggesting moderate fluctuations around the daily average.
Total charging demand per hour is relatively stable under the optimised strategy, with a maximum of 546.01 kWh and a minimum of 291.52 kWh. In the uncoordinated benchmark the maximum reaches 578.62 kWh and the minimum falls to 288.68 kWh. The hourly demand standard deviation is 72.64 kWh in the optimised case and 74.40 kWh in the benchmark. An additional benefit is that the optimised price pattern encourages users to move some charging demand away from the high-demand evening hours to the lower-demand afternoon period. This shift leads to better utilisation of existing infrastructure without requiring new construction.
VI. Sensitivity Analysis
A. Cost electricity price
Electricity purchase cost is an external factor that strongly shapes profitability. Renewable energy integration is likely to reduce spot electricity prices in the future. I consider three scenarios: base tariffs, a 15% decrease in all tariffs, and a 30% decrease. The total profit of all three stations over 24 hours increases from 6032.71 RMB in the base scenario to 6484.93 RMB when tariffs fall by 15%, and to 6973.73 RMB when tariffs fall by 30%. Thus a 30% reduction in the electricity price increases profit by approximately 15.6%. The sources of this growth are twofold. First, the price-cost margin increases directly. Second, the model lowers the retail price slightly, which stimulates demand and increases total charging amount. Table 6 shows the average blended price margin and total daily energy for the three scenarios.
| Scenario | Average price margin (RMB/kWh) | Total daily charging energy (kWh) | Total profit (RMB) |
|---|---|---|---|
| Base tariffs | 1.1507 | 394.72 (hourly avg.) | 6032.71 |
| 15% lower tariffs | 1.4229 | 410.21 (hourly avg.) | 6484.93 |
| 30% lower tariffs | 1.7494 | 428.66 (hourly avg.) | 6973.73 |
The result implies that charging sharing platforms should actively track wholesale and retail electricity markets and pass part of the cost saving to electric car users through lower prices. Because the price sensitivity of users is substantial, such a strategy yields higher demand and even higher profit than keeping prices unchanged.
B. Number of electric cars
The number of electric cars in the service area directly influences the arrival rate at charging stations. I simulate four vehicle fleet sizes: 25, 50, 75, and 100 electric cars. The results at 9:00 a.m. indicate that median hourly total profit increases from 341.13 RMB with 25 cars to 1347.40 RMB with 100 cars. However, the marginal profit increase is not constant. From 25 to 50 cars, profit grows by about 43%; from 50 to 75 cars, by 99.6%; and from 75 to 100 cars, by 38.2%. The slower growth near 100 cars implies that stations approach their capacity limit. In contrast, utilisation variance shows an inverted-U relationship: it increases when the fleet grows from 25 to 50 cars, then declines as the fleet reaches 75 and 100 cars because all stations become busier and demand is more uniformly distributed. This observation suggests that station capacity and location planning should be re-evaluated once vehicle density exceeds a critical threshold.
C. User preference heterogeneity
I further split the survey respondents by income and estimate two separate discrete choice models. The low-income group is strongly price-sensitive; its price coefficient is \(-1.10\), while the service coefficient is only \(0.54\). The high-income group is more service-sensitive; its price coefficient is \(-0.57\), while its service coefficient reaches \(1.31\). These two parameter vectors are then used to simulate two possible market scenarios. When all users behave like the price-sensitive group, the average equilibrium price falls by about 18%, and station 1, the low-price station, receives 52.3% of all demand. Total profit decreases by 19.1% relative to the baseline, and utilisation variance increases by 78%. This finding indicates that extreme price competition cannot sustain high profits for operators. When users behave like the service-sensitive group, the average service level rises by 30%, station 3 receives a greater share of demand, total profit grows by 8.5%, and utilisation variance shrinks by 21.3%. Thus the platform should implement different marketing strategies according to the socio-economic characteristics of its users. It could also design price-service bundles that appeal to both segments simultaneously.
VII. User Guidance Optimisation
In the previous sections I assumed that the platform sends each user a recommendation based on the full utility function. I now compare this comprehensive recommendation strategy with a conventional recommendation method that only considers total time. Both methods are evaluated with 50 electric cars over 24 hours. The comprehensive strategy chooses the station that maximises full user utility, including distance, price, and service level. The time-only method chooses the station that minimises total time regardless of other dimensions. Table 7 reports the daily aggregate results.
| Indicator | Time-only recommendation | Comprehensive recommendation | Difference |
|---|---|---|---|
| Total time (min) | 1171.49 | 1421.75 | +21.4% |
| Total travel distance (km) | 167.32 | 147.92 | -11.6% |
| Total charging price (RMB) | 1419.20 | 1218.40 | -14.1% |
| Total service level (scaled) | 173.80 | 164.10 | -5.6% |
| Average user utility (scaled) | -1118.11 | -1042.58 | +6.8% |
The comprehensive recommendation increases total time because it deliberately sends some users to farther but cheaper or less congested stations. Yet it significantly reduces the travel distance and the total money spent by users. The average user utility, which is the weighted sum of time, distance, service, and price, improves by about 6.8%. This improvement confirms that the time-only recommendation, though appealing at first glance, ignores the fact that many electric car users are willing to drive a little longer to obtain lower prices or faster charging equipment. The comprehensive recommendation strategy is therefore more suitable for a charging sharing platform that seeks to balance user satisfaction and station resource utilisation.
VIII. Conclusion
In this paper I have studied the operation of charging sharing platforms for electric cars via a bilevel programming model. The upper-level objective maximises the total profit of all participating operators and minimises the variance of charging station utilisation. The lower-level model captures the choices of electric car users, who react to price, service level, time, and distance according to preferences estimated from a stated-choice survey. I solved the model using NSGA-II and TOPSIS in an iterative nested framework. A simulation based on real road network data from Beijing’s Fifth Ring Road area validated the proposed approach. The findings demonstrate that a platform-coordinated strategy significantly outperforms independent operator pricing. Total profit increases by about 59%, while utilisation variance decreases by about 61%. The optimal pricing pattern follows the time-of-use electricity tariff, and the stations naturally differentiate into high-price high-service, medium-price medium-service, and low-price low-service types. Compared with a time-only recommendation, the proposed comprehensive user guidance strategy improves mean user utility by about 7%. Sensitivity analysis reveals that a 30% reduction in electricity purchase cost increases total profit by nearly 16%, and that the charging infrastructure can be better utilised when the number of electric cars in the area is neither too low nor too high. These conclusions provide actionable insights for the charging sharing platform industry and for urban transport policy, particularly in cities where public charging station utilisation remains low. I hope that this framework can serve as a foundation for future studies that incorporate wider spatial scales, more detailed battery degradation models, and real-time learning of user preferences.