Differential Pricing Strategies for Airport Shuttles: A Study of Shanghai Based on Customized Bus Ticketing Data

Abstract

Airport shuttle buses, as a specialized form of bus service, serve as an economical, efficient, and sustainable transportation option for air travelers. In contrast to conventional bus services, airport shuttle bus operations exhibit more pronounced market-oriented characteristics, striving to balance extensive public transport coverage with the optimization of corporate profitability. Although these services outperform regular bus transit in terms of efficiency, they incur higher operational costs. However, existing studies on enhancing profitability and optimizing resource allocation for airport shuttle buses are inadequate. This study proposes a differential pricing strategy based on historical ticketing data. Initially, we analyze the characteristics of orders, users, and reservations within the context of customized bus operations. Leveraging the differences among various groups, we employ clustering techniques to classify seat grades and segment users. Based on the clustering outcomes, we determine distinct price elasticity values for each segment. As the strategies are developed based on seat grades, booking time, and user travel patterns, the numerical experiments indicate that the proposed differentiated pricing strategy can increase the revenue of customized public transport services by at least 41%. This strategy not only enhances the efficiency of resource allocation and service accessibility but also makes the service more financially sustainable.

1. Introduction

Amidst global economic expansion, the past decade has witnessed a marked surge in air travel, with passenger volumes escalating significantly. Airport passenger traffic is expected to keep rising at a rate of 4.5% per year from 2012 to 2031. In response to the heterogeneous spatial and temporal demands of air travelers, airport shuttle bus services have emerged as a pivotal, efficient, and economical transportation alternative. These services facilitate streamlined connectivity between the airport and principal urban centers, effectively mitigating traffic congestion and diminishing parking strain. Additionally, airport shuttle buses substantially augment the quality of passenger service by enhancing accessibility for late-night and long-distance journeys, thereby offering a transportation solution that is not only expedient and economical but also minimizes urban traffic and parking challenges.

Airport shuttles buses face higher operational costs while outperforming regular bus transit services [1]. These services must therefore balance public service coverage with profitability, a challenge compounded by rising airport passenger traffic and a growing demand for customized travel options. Current research on customized bus services primarily addresses demand analysis, route optimization, and timetable optimization. However, the areas of revenue management and mining user travel behavior during operations remain less explored, representing significant gaps in enhancing the efficiency and quality of transportation services. Differential pricing, also known as price discrimination, entails the strategic setting of disparate prices for identical services within the same temporal framework, facilitated by the identification of unique service attributes and consumer heterogeneity. This approach has been rigorously analyzed and effectively implemented across multiple sectors, including aviation, railways, and e-commerce, demonstrating its versatility and effectiveness. Applying differential pricing strategies to airport shuttles by harnessing online booking data could significantly enhance operational efficiency and fiscal sustainability. Consequently, the strategic utilization of such data to develop differential pricing schemes is imperative for maintaining the viability of airport shuttle services. This method not only ensures an optimal balance between service accessibility and profitability but also catalyzes an improvement in the overall performance of customized transportation services.

To fill existing research gaps, our study examines the order characteristics and user behaviors of airport shuttle buses to develop a differential pricing strategy based on customer price elasticity. Utilizing a dataset from January 2019 to October 2020, which includes 1.5 million user order records for customized bus (CB) routes, we analyze cabin selection behaviors, booking time distributions, and travel pattern features. These insights inform tailored differential pricing strategies. We validate our approach by applying it to real-world corporate order data with fixed external parameters, comparing the generated revenue to that under the existing pricing model. This comparison assesses the impact of our strategy on overall revenue and operational efficiency.

The remainder of this paper is structured as follows: Section 2 provides an overview of the prevailing research on airport shuttles and differential pricing. Section 3 outlines the spatial and temporal dimensions of the dataset collected from an airport shuttle bus company and presents an exploratory analysis of user-order data. Building on this foundation, in Section 4, we develop a differential pricing strategy for airport shuttles, incorporating segmentation of user orders based on diverse travel characteristics. In Section 5, we assess the effectiveness of this pricing strategy by comparing its revenue outcomes with actual enterprise order revenues. We conclude the paper in Section 6, summarizing our findings and their implications.

2. Literature Review

2.1. Airport Shuttle Services Based on Customized Buses

Airport shuttle services provide passengers with convenient, rapid, and comfortable transit that is specifically designed to cater to similar spatial and temporal travel requirements [2]. As a specialized segment of CB services, they offer efficient transportation solutions for medium and long distances, characterized by stations located primarily at the start and endpoints, with minimal intermediate stops [3,4]. Their tailored routing and scheduling grant them a significant competitive advantage over traditional fixed-route buses [5].

Research on CBs mainly focuses on demand analysis, route optimization, and timetable optimization, aiming to enhance the efficiency and responsiveness of these services. From the demand analysis perspective, Ref. [6] emphasizes that understanding the evolution of demand is essential for the strategic design and operational sustainability of CBs. This has led to a series of studies exploring the factors that influence passengers’ service choices, primarily using travel surveys. Ref. [7] employs mixed logit models and tree-based models, augmented with explainable machine learning techniques, to investigate the determinants of passenger decision-making. Additionally, Ref. [8] finds that higher fares and longer travel times reduce the attractiveness of CBs, whereas middle-class commuters tend to prefer these services, indicating that socio-economic factors play a critical role in transportation preferences.

From the service design perspective, optimization techniques are crucial at various operational levels. CB operators strategically optimize routes and stop locations to minimize travel time and maximize passenger convenience [9], with time window constraints playing a vital role in the effective routing of CBs [10]. Furthermore, Ref. [11] introduces a two-period Hotelling game model to enhance CB operation strategies by considering passengers’ choice behaviors and service levels, thereby enabling more dynamic and informed service adjustments.

Typically, timetable optimization is integrated with route design, and the challenge of CB routing and scheduling is conceptualized as a pickup and delivery model that incorporates time windows [12]. At present, most domestic CB companies rely on heuristic methods to develop their timetables [13]. These methods entail gathering data about users’ origins, destinations, and preferred departure/arrival times via online questionnaires. Subsequently, timetables are manually crafted, taking into consideration user demand and vehicle capacity constraints [14].

Currently, research on customized bus (CB) services predominantly focuses on pre-operational elements, including demand analysis, route optimization, and timetable optimization. However, areas such as revenue management, particularly those based on user travel behavior during operations, remain under-explored. These components are critical for enhancing the economic viability and responsiveness of CB services to passenger needs.

2.2. Differentiated Pricing

Differential pricing, also known as price discrimination, involves suppliers setting varying prices for the same product within the same time period [15]. This pricing strategy can target different consumer groups or apply different prices during varying times, such as peak versus off-peak hours. Beneficial for operators seeking to maximize revenue, differential pricing has been extensively implemented and studied across multiple sectors, including aviation [16], railways [17], and e-commerce [18]. This approach not only enhances profitability but also optimizes resource allocation and service accessibility.

Differential pricing is extensively employed in the aviation industry, where it forms a cornerstone of airline revenue management. This approach focuses primarily on two key aspects: seat inventory control and pricing strategies. Seat inventory control involves tactical adjustments to the pricing, availability, and booking limitations of various seat classes to maximize ticket revenue. This is achieved through the implementation of both discrete and continuous inventory control strategies [19,20]. Pricing strategies, on the other hand, utilize time-variant pricing that aligns with the demand functions of air passengers. Airlines deploy optimization models [21], dynamic programming [22], and reinforcement learning [23], among other techniques, to devise effective pricing strategies. These methods ensure that pricing dynamically adapts to changing market conditions and passenger behavior, thereby optimizing revenue. Inspired by the aviation industry, the adoption of differential pricing in the railway sector is less advanced but focuses on passenger segmentation to tailor pricing strategies [24]. This approach benefits from segment-specific pricing policies that cater to different passenger needs and value perceptions.

In parallel, the e-commerce industry has experienced rapid growth facilitated by the widespread adoption of smart devices and the maturation of mobile internet technologies [25]. Leveraging extensive user information and consumption data, e-commerce platforms have extensively implemented differential pricing strategies [26]. The process of establishing price discrimination in e-commerce involves three critical steps: constructing detailed user profiles [27], identifying target populations [28], and formulating nuanced pricing strategies [29]. These strategies are often underpinned by sophisticated optimization models or machine learning algorithms, enabling what is known as “personalized pricing”. Such strategies are designed to maximize platform revenue by dynamically adjusting prices based on real-time user behavior and preferences [30]. This method not only optimizes economic returns but also enhances user engagement by offering prices that reflect individual purchasing power and inclination.

Differential pricing, a strategy rigorously investigated and successfully implemented across various sectors, fundamentally depends on identifying product attributes and user diversity. To mitigate the challenges of inadequate revenue management in airport shuttle services, analyzing user-order patterns from observational data is essential. This analysis underpins the development of tailored pricing strategies that effectively address different user segments. By adopting such customized pricing models, the service can adapt to the varied preferences and behaviors of passengers, thereby improving customer satisfaction and potentially boosting profitability.

3. Materials

3.1. Data Scope

This research utilized operational data from E-Drive Bus, one of Shanghai’s largest customized bus (CB) service providers, specializing in the battery-electric vehicles (BEVs) primarily serving the Shanghai Hongqiao International Airport. This study’s datasets comprised CB routes and ticketing information spanning from January 2019 to October 2020, which included a comprehensive collection of approximately 1.5 million user order records.

Figure 1 presents a box plot illustrating passenger flow vs. run changes per month for the customized bus company. Before the COVID-19 outbreak in 2019, E-Drive Bus expanded its services by introducing additional bus routes, resulting in an overall upward trend in user orders. However, fluctuations occurred during seasonal holidays such as the Spring Festival and National Day. Peak ridership during this period reached 103,071 passengers per day. The COVID-19 pandemic significantly impacted user engagement, with February 2020 marking a sharp decline to just 5724 orders. Following the outbreak, order volumes gradually recovered, peaking at 72,452, which represented approximately 70% of the pre-pandemic levels.

The CB company’s extensive service network is illustrated in Figure 2, showcasing coverage across most districts in Shanghai. A notable feature of the network is the prevalence of longer routes that connect suburban areas with the city center. For example, the Auto City (Anting)–Hongqiao Express Line connects the Anting Auto City in Jiading District to the Hongqiao Business District. This route serves as a critical shuttle link to the Hongqiao Airport and plays a key role in facilitating the dispersal of passengers from peripheral areas into the central business hub.

Table 1. Statistics across alternative travel modes.

Attributes of Travel Alternatives	Mean	Std
Customized bus
Travel distance (in km)	17.74	23.29
Travel time (in min)	23.91	28.73
CB fares (in CNY)	8.44	16.43
Public transit
Travel distance (in km)	20.29	23.85
Travel time (in min)	61.38	44.93
Transit fares (in CNY)	3.81	3.45
Number of transfers	4.31	1.86
Ride-hailing
Travel distance (in km)	16.62	20.38
Travel time (in min)	20.28	18.65
Ride-hailing fares (in CNY)	40.47	49.85
Cycling
Travel distance (in km)	15.50	19.49
Travel time (in min)	86.72	108.71

Std: standard deviation.

presents statistical comparisons across alternative travel modes, revealing that CB travel time is significantly shorter than public transit but marginally longer than ride-hailing services. Despite CB fares being higher than public transit, they amount to only one-third of ride-hailing costs. These findings underscore CB’s competitive advantage in providing a balanced alternative, optimizing both travel time and cost relative to public transit and ride-hailing services. However, fluctuations in CB pricing could potentially compromise its competitive position against public transit or ride-hailing. Thus, meticulous pricing strategies are critical to ensuring internal profitability and maintaining competitiveness in the market.

3.2. Order Characteristics

The historical order data analyzed in this study include detailed records of passengers’ actual boarding and alighting stations, booking times, riding prices, and seating choices. This research specifically focuses on the differentiated customization of services; therefore, basic pricing factors such as distance and time are intentionally excluded from the scope of the analysis. This approach allows for a concentrated examination of the factors that influence tailored pricing and service strategies.

Currently, ticket pricing for customized buses is uniform across seats, with variations only based on route and boarding/alighting locations. In contrast, air and rail transportation sectors have adopted a more granular pricing approach by offering different prices for different seat classes, taking into account individual passenger needs. This approach enhances operational efficiency. Within a single bus, factors such as seat comfort, convenience of boarding and alighting, views during the ride, and social distancing can significantly affect passenger experience. Recognizing these differences can enable operators to categorize seats, thereby laying the groundwork for implementing personalized pricing strategies that better meet diverse passenger preferences.

To accurately assess user preferences and mitigate potential data distortion from extraneous factors, this study focuses on the seat selection choices of the first four users from each bus shift. Figure 3 illustrates the limited seating capacity in each vehicle and underscores the importance of maintaining adequate social distancing among passengers. The left side depicts actual bus seats, while the right side shows corresponding data labels, with the last column marked according to numbering rules.

Monthly data from the top four users per shift were normalized to analyze seat selection frequencies, as depicted in Figure 4 and Figure 5 spanning from February 2019 to May 2020. The analysis revealed a notable preference for front seats, likely due to perceived enhanced comfort. Seat selection trends also demonstrate seasonal variations. In summer, the first three rows, especially the first row for its superior view, are more popular. Additionally, seats (B, 5) and (B, 8), positioned near the door, are favored for their convenience in boarding and alighting, proximity to the aisle, and increased personal space. Conversely, during winter, there is a noticeable shift in user preferences towards health-conscious seat choices. Users increasingly opt for more dispersed seating arrangements to uphold social distancing, thereby reducing the risk of disease transmission. This seasonal variability in seat preferences underscores the potential for implementing dynamic, seasonally adjusted pricing strategies in customized bus services.

3.3. Booking Characteristics

Customized bus services, which leverage an internet-based reservation system, illustrate that earlier bookings can enhance service delivery. Moreover, the lead time of reservations reflects the urgency of passengers’ travel needs. In the aviation sector, differential pricing strategies based on reservation timing are frequently employed to optimize airline profitability. Therefore, it is advisable for customized bus services to adopt a similar approach. By analyzing variations in reservation timing, targeted interventions can be devised to improve the operational efficacy of these services. This method allows for strategic adjustments in pricing and service deployment, aligning more closely with passenger demands and enhancing operational efficiency.

The data depicted in Figure 6a illustrate significant variations in the distribution of booking times within the dataset, including multiple peak periods. However, it is evident that the current pricing shown in Figure 6b for orders does not substantially increase in correlation with the advanced booking times. This observation suggests a potential misalignment between pricing strategies and booking behavior, indicating an opportunity to refine pricing models to better capitalize on booking time variations.

3.4. User Characteristics

Travel pattern characteristics significantly influence user price elasticity; for example, users who travel during peak periods are more likely to accept higher fares. The initial step involves analyzing the distribution of users’ travel distances and frequencies, followed by calculating the number of high-frequency origin–destination (OD) pairs. Furthermore, to delve deeper into user travel behaviors, analyses of hourly order frequency and monthly usage days are undertaken. To facilitate a general understanding, heatmaps are generated to visualize the distribution of travel times within a week, elucidating user travel patterns comprehensively. This analysis also includes the identification of high-frequency travel intervals and differentiates between weekday and weekend travel behaviors. Such detailed examination enhances the understanding of user travel patterns, enabling the development of more precisely targeted pricing strategies that reflect the dynamic nature of travel demand. This facilitates understanding of user behaviors and the development of tailored pricing strategies that reflect the temporal dynamics of travel demand.

Figure 7 illustrates significant variability in travel distances, ranging from under 1 km to a maximum of 95 km. The distribution displays a multi-modal pattern with prominent peaks at 6 and 25 km, which corresponds to the service’s focus on long-distance commuters. Particularly, the peak at 25 km, indicative of residential-to-work commutes, underscores the perceived advantages of customized buses in comfort and punctuality compared to traditional bus services within this distance range. The corresponding order data, including distance and passenger frequency, highlight the preference for customized buses. We utilized the Gaode Map Driving Navigation API to accurately capture the distances based on the boarding and alighting location coordinates for each order.

The daily travel patterns shown in Figure 8a demonstrate pronounced peak demands during the morning and evening rush hours, predominantly involving short, low-cost journeys. Clustering based on usage days and frequency allows for the identification of high-frequency and low-frequency travelers, enabling tailored service adaptations to effectively meet the diverse needs of these distinct user segments in Figure 8b.

Figure 9 illustrates the proportion of travel frequencies across different time periods, showing higher demand during morning peaks compared to evenings. This highlights the need for adjusting service frequencies during peak hours to maintain timeliness and reliability. Moreover, notable differences between weekday and weekend travel behaviors indicate varying levels of dependence on the service. These insights are pivotal for developing differential pricing strategies that accommodate diverse demand patterns, thereby improving service efficiency and enhancing customer satisfaction.

In summary, customized bus users exhibit distinct variations in terms of time, space, and frequency of travel. Different travel characteristics influence the sensitivity to service quality and pricing. Therefore, to enhance the operational services and the benefits of customized bus companies, it is essential to segment users based on their historical travel characteristics. By adopting differentiated operational strategies for various user types, companies can achieve a balance between service quality and price management, optimizing both customer satisfaction and operational efficiency.

4. Differentiated Pricing Model Based on User Order Characteristics

4.1. Differential Pricing Method Based on Order Characteristics

K-means in Algorithm 1 is a prevalent clustering algorithm that segregates a dataset into K discrete, non-overlapping subsets using various distance metrics to assess similarity. The primary objective of this algorithm is to minimize intra-cluster variance, thereby optimizing homogeneity within each cluster. This is accomplished by assigning each datum to the closest cluster center, commonly referred to as the centroid. The standard metric for measuring distance in K-Means is the Euclidean distance; however, the choice of the distance metric can be tailored to accommodate the specific attributes of the dataset or the particular needs of the application domain. This adaptability allows K-means to be effectively applied across a diverse range of disciplines and use cases.

$$d(x_i,x_j)=\sqrt{{\mathrm{\Sigma }}_{k=1}^K{(x_{ik}-x_{jk})}^2}$$

(1)

Here, $d(x_i,x_j)$ represents the distance between two personal $x_i$ and $x_j$ in K-dimensional space, where K represents the number of order characteristic features.

Algorithm 1: K-means clustering.

1: Input: Data points $X=\{x_1,x_2,\cdots ,x_n\}$, Number of clusters K 2: Output: Cluster assignments for each data point 3: procedureKMeans($X,K$) 4:     Randomly initialize centroids $C=\{c_1,c_2,\cdots ,c_K\}$ 5:     repeat 6:         for each $x_i\in X$ do 7:            Assign $x_i$ to the closest centroid $c_k$ $$k=arg\underset{k}{min}d(x_i,c_k)$$ 8:         end for 9:         for each $c_k\in C$ do 10:            Update $c_k$ to be the mean of all points assigned to cluster k $$c_k={\displaystyle \frac{1}{|S_k|}}\sum _{x_i\in S_k}{x}_i$$ 11:            where $S_k$ is the set of points assigned to k 12:         end for 13:     until centroids C do not change 14: end procedure

According to user preferences, customized bus seats can be divided into two levels: first-class and second-class seats. The clustering results are shown in Figure 10. Before the epidemic, there were 16 first-class seats, including the first three rows of seats and the front and back of the rear door. After the epidemic, due to the consideration of user spacing, the inner window position is no longer popular because it is too close to other users, so it is excluded from the first-class seat option. In addition, (D, 6) seats are divided into first-class seats, because they are close to the aisle and close to the door.

4.2. User Features

Customized bus users display varying sensitivities to service quality and pricing, influenced by distinct travel behaviors. Building on previous analyses, travel mode characteristics are extracted, and clustering methods are used to categorize these modes. Firstly, we classify travel times into four categories based on the regularity of high-frequency travel periods. Secondly, the ratio of trips made on working days to total trips highlights differences in user needs and types, providing insight into users’ temporal travel patterns. Thirdly, we analyze the frequency of different origin–destination (OD) pairs, identifying the number of popular OD combinations frequented by users. Fourthly, the average travel distance is calculated to discern the spatial extent of users’ travel related to their life and work zones. Lastly, distinguishing between high-frequency and low-frequency users offers a perspective on travel frequency, enabling targeted strategies to meet diverse user preferences and requirements effectively.

The characteristics of user groups include both categorical and continuous variables, which necessitates a specialized approach for effective segmentation. Traditional clustering methods like k-means, which are tailored for continuous variables only, fall short when applied to mixed data types. To address this, we utilize the K-prototypes clustering algorithm, which combines the Minkowski distance for continuous variables and the Hamming distance for categorical variables. This method effectively handles mixed data types, allowing for accurate and efficient user segmentation. This integrated distance calculation approach enables nuanced analyses, ensuring that the clustering reflects the comprehensive characteristics of the user base.

$$d(x_i,x_j)={\mathrm{\Sigma }}_{l=1}^{n_c}{(x_{il}^c-x_{jl}^c)}^2+\gamma {\mathrm{\Sigma }}_{l=1}^{n_d}\sigma (x_{il}^d,x_{jl}^d)$$

(2)

Here, $X_i$ is the i-th order characteristics vector, $X_{il}^c$ denotes the l-th continuous feature, $n_c$ represents the total number of continuous variable features, $X_{il}^d$ denotes the l-th discrete feature, $n_d$ represents the number of discrete variable features, $\sigma$ is the function for computing the distance between discrete features, and $\gamma$ represents the coefficient used in calculating the distance between discrete variable features.

In Figure 11, the clustering metrics reveal a significant transition among four user clusters. Based on this observation, the users were categorized into four distinct groups. The hourly order frequency distribution and the relationship between frequency and days are depicted in Figure 12. These findings can be interpreted as follows:

• Group 1: Loyal users. This group consists of frequent travelers who primarily use customized bus services on weekdays for commuting. They have a high number of travel days, with an average travel distance of approximately 20 km. Their travel times and origin–destination (OD) pairs vary widely, reflecting their diverse commuting needs and high dependence on this service. These users are crucial for the focused attention of customized bus companies due to their consistent usage.
• Group 2: Long-distance users. Users in this category travel less frequently but primarily on weekdays, with occasional trips on non-working days. They engage in long-distance travel, averaging about 65 km per trip, and they typically have a single travel OD during a given time period. This user group is drawn to customized buses for their cost-efficiency and timely service over long distances.
• Group 3: Occasional users. Representing the largest proportion of the groups, these users infrequently use customized bus services. Their travel is mainly restricted to working days, with very limited travel frequency and days, and they tend to have a single travel time and OD pair. This indicates that while they rely on customized buses for specific needs, they have access to alternative transport modes, leading to their sporadic use of this service.
• Group 4: Non-weekday users. This group primarily uses customized bus services on non-working days. They have a low frequency of use and limited days of travel, with consistent travel periods and OD pairs. These users may rely on customized buses due to the absence of company shuttle services on non-working days or for other needs such as shopping or leisure activities during weekends.

4.3. Differential Strategies

Passenger travel demand is influenced by price elasticity, which typically reflects the variation in demand relative to changes in price. Generally, higher prices lead to lower demand for the product. According to Ref. [31], which provides an in-depth discussion of pricing strategies and the role of elasticity in determining optimal prices, this article assumes that the demand function adheres to this pattern:

$$Q=K{P}^{-\alpha }$$

(3)

where Q represents the quantity demanded, P denotes the price of the product, K is a constant, and $\alpha$ is the price elasticity coefficient.

Figure 11. Clustering results based on user characteristics.

Figure 11. Clustering results based on user characteristics.

Figure 12. Analysis of CB user frequency and active days. (a) Hourly order frequency. (b) Relationship between frequency and days.

Figure 12. Analysis of CB user frequency and active days. (a) Hourly order frequency. (b) Relationship between frequency and days.

Smaller $\alpha$ values indicate that users are less sensitive to changes in price, while larger values suggest greater sensitivities. Typically, products that are necessities or those on which users highly depend tend to have a lower price elasticity, meaning their demand is less affected by price changes. Conversely, luxury items and products with strong substitutes exhibit higher price elasticity.

$$Revenue=QP=K{P}^{1-\alpha }$$

(4)

The formula reveals that when the price elasticity coefficient a is between 0 and 1, an increase in price leads to higher revenue. Conversely, when a is greater than 1, lowering prices is beneficial for increasing revenue. When a equals 1, the revenue remains constant, regardless of price changes. Implementing differentiated pricing strategies tailored to the specific price elasticity of different user groups can effectively increase revenue. This approach allows companies to optimize their pricing based on how sensitive their customers are to price changes, thereby maximizing financial outcomes.

In the airline and hotel industries, extensive research reveals that the price elasticity of demand varies significantly depending on the proximity to the departure or booking date. Early booking periods typically exhibit a higher price elasticity, indicating more price sensitivity among consumers, whereas closer to the departure or booking date, elasticity tends to decrease as options become limited and dependence on the service increases, as depicted in Figure 13. This study applies a similar principle to customized bus services, where the price elasticity coefficient $\beta$ is analyzed relative to predetermined shift times. Using the mean predetermined time as a reference point, if the scheduled time exceeds this average, $\beta$ remains constant, with a damping coefficient of 1. Conversely, for times below the average, $\beta$ shows a linear relationship with the predetermined time, with the minimum value (corresponding to a scheduled time of 0) defining the baseline elasticity.

Citing findings from Ref. [32], which explores public transport fare elasticities derived from smartcard data, the elasticities across different zone groups range from 0.51 to 1.81. Therefore, this study adopts a range of 0.5 to 1.5 for the price elasticity coefficient, aligning with established trends in transport economics.

5. Results

Based on the analysis of differences in user order seat classifications, booking time variations, and travel pattern characteristics, establishing different prices for different categories of users can facilitate the implementation of a final differential pricing strategy.

Implementing a differential pricing strategy for various types of transit users can optimize revenue generation. For users who are highly dependent on customized bus services and lack viable transportation alternatives, increasing prices can enhance overall profits. Conversely, for users with a lower dependence on customized buses, where alternative transportation options are readily available, reducing prices may encourage more frequent use of the service. Based on initial user segmentation, Group 1 (loyal users) and Group 2 (long-distance users) are considered to have a high dependence, and their price elasticity coefficient ${\alpha }_1$ is smaller than 1, indicating that lowering prices may not significantly increase their usage frequency, but modest price increases are unlikely to drastically reduce their demand. Group 3 (occasional users) and Group 4 (non-weekday users) have alternative travel modes, and their dependence on customized buses is small, so their price elasticity coefficient ${\alpha }_2$ is large, which should be above 1.

Figure 14 indicates that due to the finite capacity of the vehicle, overall revenue initially rises but eventually levels off. Additionally, employing a price reduction strategy for users with a higher price elasticity ${\alpha }_2$ leads to an increase in demand, potentially displacing users with a lower price elasticity ${\alpha }_1$. Notably, the optimal revenue is realized when ${\alpha }_1=0.5$ and ${\alpha }_2=1.5$. This scenario underscores that the greater the differences in user price sensitivity, the more significant the benefits derived from a differential pricing strategy. This finding highlights the effectiveness of tailoring prices to diverse user groups, particularly in contexts where capacity constraints and varying price elasticity interact.

To assess the impact of tiered seating pricing on revenue, it is essential first to consider the variations in price sensitivity among different passengers. If the price for first-class seats increases by gamma $\gamma$, the corresponding selection probability will adjust to $1+\gamma$, representing the likelihood that a user chooses a first-class seat. Given the limited number of first-class seats, it is necessary to employ a random sampling method to determine the allocation of these seats.

Figure 15 indicates that as the price of first-class seats rises, ticket revenue also increases. However, the growth trend gradually diminishes, because excessively high prices lead some passengers to forego choosing first-class seats. Notably, higher revenues are achieved when the price elasticity is set at $alpha=0.5$ and $alpha=1.5$. This outcome suggests that passengers with a price elasticity of $\alpha =0.5$, who are more sensitive to price changes, are more likely to opt for first-class seats, thereby enhancing overall revenue. This analysis underscores the importance of strategically managing seat pricing to optimize revenue while considering passenger price sensitivities and the finite availability of premium seating options.

As the departure time for the customized bus approaches, user dependency on the service increases, leading to a decrease in their price elasticity, which is their sensitivity to price changes. Consequently, operators have an opportunity to raise ticket prices to enhance revenue. All the departures scheduled before the average time for all the services are adjusted to the basic discount rate, C, taking into account the time-dependent decay of the price elasticity coefficient, denoted by $\beta$.

According to Figure 16, it is observed that a larger $\beta$ value indicates that as the departure time approaches, users become increasingly dependent on the customized bus service and less sensitive to price changes. Therefore, even after ticket prices are increased, a considerable number of users continue to choose the customized bus, leading to higher overall ticket revenue.

Integrating the strategies based on user group segmentation, seat classification, and booking time, we analyze ticket revenue using various parameters. Figure 17, Figure 18 and Figure 19 depict settings with different user price elasticity coefficients, ${\alpha }_1$ and ${\alpha }_2$. In each figure, the rows maintain a constant decay coefficient, $\beta$, and the columns keep the same ratio for the increase in the prices of advanced booking orders C. Within each subplot, the increased ratio for first-class seats, $\gamma$, varies. These figures also illustrate the overall revenue following adjustments in base prices, showing how these strategies influence financial outcomes under different pricing dynamics and user sensitivities.

When ${\alpha }_1=0.9$ and ${\alpha }_2=1.1$, examining different rows reveals that a lower attenuation coefficient, $\beta$, of the price elasticity coefficient results in diminished price sensitivity as the departure time approaches, thereby justifying a price increase to enhance revenue. Within the same row, the analyses show that a higher price increase ratio for orders under the predetermined time threshold, $C=0.5$, leads to increased ticketing income. Specifically, at $\beta =0.5$ and $C=50\%$, a price adjustment ratio of 40% across different user groups yields the maximum comprehensive income, surpassing the operational costs of customized public transportation. However, when $\beta$ is set at 0.7 or 0.9, revenue initially increases but subsequently declines with larger price changes. This trend is attributed to the excessive demand generated by substantial price reductions for users whose price elasticity exceeds 1, which displaces highly dependent users and reduces overall income. This illustrates that simply raising ticket prices does not universally increase total revenue.

Comparative analyses across subgraphs demonstrate that greater differences between user groups significantly enhance the effectiveness of differentiated pricing strategies, thereby increasing revenue. This study assesses income based on nine different parameter sets, depicted in nine subgraphs. As shown in Figure 17, under various parameter configurations, the optimal differentiated pricing strategy can increase the overall income of customized public transportation by at least 41%, confirming its efficacy.

6. Conclusions

This paper proposes targeted differentiated pricing strategies and analyzes their benefits under different scenarios to provide decision-making insights for improving customized bus operations. This study initially conducts an exploratory analysis of order, booking, and user features using customized bus ticketing data, examining temporal, spatial, and frequency differences. Subsequently, clustering methods are applied to uncover travel characteristics and classify seat classes into first and second class, categorizing passengers into distinct groups. The results demonstrate that integrating differentiated pricing strategies based on seat classification, booking timing, and user travel characteristics can significantly enhance customized public transportation income by at least 41%.

While the effectiveness of these strategies is evident, future research and practical implementation must address several considerations. Firstly, integrating competition from traditional buses, private cars, and taxis into pricing strategy analyses is crucial to optimize strategies and maximize benefits by understanding their influence on passenger decisions. Secondly, while this paper evaluates how differentiated pricing strategies impact revenue for customized public transportation, further discussion on potential limitations and result variability would provide a more comprehensive perspective. Thirdly, ensuring study credibility requires verifying the validity and adaptability of parameter settings to real-world scenarios, as well as validating the experimental results to confirm the anticipated practical outcomes.

In conclusion, this study illustrates the potential of differentiated pricing strategies to substantially increase income in customized public transportation. Future research should concentrate on developing optimization models with precise algorithms to dynamically adjust pricing, adapting to market changes and enhancing revenue management. Furthermore, these strategies extend beyond financial gains, influencing industry norms and customer expectations within the broader transport sector. Addressing these areas in future research will contribute to a more comprehensive understanding and application of strategic pricing in competitive transport markets, fostering sustainable development in public transportation.