A Decision Model for Bike Sharing Based on Big Data Analysis

Currently, bike sharing companies are striving to establish a decision support system for their services based on big data technology. However, the application of big data analysis is bottlenecked by the inaccurate prediction of relevant data, such as the number of bikes to be rented and returned at a bike station in the next half an hour. The inaccuracy stems from the overlook of business evolution and external impacts in previous prediction methods [1-4], all of which solely depend on statistical analysis of historical data samples.

Many scholars have attempted to optimize the scheduling of bike sharing. For example, Khatri et al. [5] designed a suitable scheduling plan for bike sharing through GPS data analysis. Sun et al. [6] analyzed the use mode of bike sharing through spatiotemporal clustering, a nonlinear autoregressive neural network method, and then studied the scheduling of bike sharing. With the aid of backpropagation neural network (BPNN), Gao et al. [7] forecasted the initial scheduling of bike sharing, constructed a scheduling model to minimize the scheduling times, and obtained the optimal scheduling times by solving the model on simulation software. Kacem et al. [8] improved the single-station scheduling model for the static scheduling of bike sharing, and designed two algorithms to separately solve the scheduling model, namely, the hybrid variable neighborhood algorithm and the large neighborhood search algorithm. Li et al. [9] examined the time-varying features of scheduling benchmark threshold, bike turnover rate, and rental volume difference at bike stations, and developed a method for obtaining the dynamic scheduling time domain of bike sharing system based on self-flow model.

To effectively schedule the bike sharing system, this paper designs a decision model for bike sharing based on linear regression and the BPNN. Firstly, the bike sharing demands in different regions were predicted based on the BPNN. Next, several assumptions and constraints were proposed on the optimization of bike sharing scheduling.  On this basis, an area scheduling model for rush hours was constructed with a fixed time window, aiming to minimize the scheduling cost. Then, the genetic algorithm (GA) was improved to solve the model. The effectiveness of our model and the improved GA were verified through a case analysis.

This research makes the following contributions: the proposed model helps to minimize the supply-demand gap of bikes in rush hours in different areas of the target city; the effective prediction of bike sharing demand makes it possible to analyze and forecast the rent/return behavior of each user, and to build an automatic bike supply and monitoring system; the results of spatiotemporal analysis can be fed back to bike sharing companies, providing decision support to the scheduling of bike sharing system; the research provides a reference for optimizing the operation and management of bike sharing, and promotes the public transport in large cities.

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Next, each day in the week was evenly split into 24 periods. The number of rented bikes was calculated for each period on each day in the week to reveal the variation of bike sharing with hours.

As shown in Figure 2, the hourly distribution of bike sharing had three peaks from Monday to Friday, including 7:00-8:00 in the morning, 11:00-12:00 at noon, and 17:00-18:00 in the evening. The morning and evening peaks were much higher than the noon peak and the other segments of the hourly distribution curves. This is because commuters are the leading bike sharers on workdays. The number of rented bikes is maximized in the morning and evening rush hours. During the lunch hours, some commuters rent bikes to visit restaurants or canteens, resulting in a rise of short-distance ridings. 

By contrast, the hourly distribution of bike sharing on weekends was relatively balanced, without any obvious peaks in the morning, at noon, or in the evening.

3.4 Typical day analysis

Through the above analysis, it is learned that lots of bikes were rented on May 17. Hence, the geographical coordinates of the start locations in the morning peak and those of the end locations in the evening peak were analyzed based on the data on May 17.

The analysis shows that, in the early peak, most rented bikes ended at rail transit stations; in the evening peak, most rented bikes left from rail transit stations. Overall, the density of rented bikes peaked around rail transit stations, and gradually decreased with the distance away from these stations. This confirms that most bikes are rented by commuters in the morning and evening rush hours on workdays.

Over the time, the rented bikes are rode to different areas. The number of bikes entering or leaving an area varies from place to place. This leads to the imbalance of bike supply and demand in many areas. The supply-demand gap must be bridged through proper scheduling of the bike sharing system.

According to the above analysis, in terms of time, the bike sharing demand concentrated in morning and evening rush hours on workdays; in terms of space, the rented bikes clustered in hotspots, i.e. rail transit stations, during the morning and evening rush hours. Therefore, the scheduling of bike sharing in an area should focus on the rush hours in the hotspots, when there is a large demand for bike sharing.

5.1 Area scheduling model

The scheduling of bike sharing is a complex, systematic problem, involving multiple variables and constraints [18]. To ensure the feasibility and explanatory power of our model, the following assumptions were made prior to modelling:

(1) There is only one station in the area, which sends/collects bikes to/from multiple hot spots. The station has enough bikes to meet the needs of all hotspots.

(2) The geographical coordinates of the station and each hotspot are known, so is the distance between the station and each hotspot. The effects of external factors like weather and traffic conditions on the scheduling process are not considered.

(3) The scheduling demand of each hotspot in the current cycle is known and stable.

(4) The bikes to be sent/collected to/from a hotspot are transported by a vehicle at only one time.

(5) The vehicle only passes through the target hotspot once.

(6) The damage and maintenance of the vehicle are not considered.

(7) The bike supply and demand are balanced in all hotspots at the start of the scheduling cycle.

Under the above assumptions and with a fixed time window, the area scheduling model for rush hours was constructed to minimize the scheduling cost:

$\begin{aligned} \min F=C_{1} \times N_{c} &+C_{0} \sum_{i=1}^{M} \sum_{j=1}^{M} \sum_{c=1}^{C} x_{i j c} \times d_{i j} \\ &+C_{2} \\ & \times \sum_{c=1}^{C} \max \left\{\sum_{i=1}^{M} \sum_{i=1}^{M} x_{i j c}\right.\\ &\left.\times\left(t_{i j c}+s_{i c}+s_{i c}\right)-1 | 0\right\} \end{aligned}$   (2)

where, N_c is the number of vehicles required for scheduling; C₀ is the travel cost per unit distance; C₁ is the fixed cost; C₂ is the penalty cost; x_ijc is a binary variable (if vehicle c completes the task from hotspot i to hotspot j, x_ijc=1; otherwise, x_ijc=0); t_ijc is the travel time of vehicle c from hotspot i to hotspot j; s_ic and s_jc are the service times of vehicle c in hotspot i to hotspot j, respectively.

The objective function aims to minimize the total scheduling cost, which covers the fixed cost, the travel cost, and the penalty cost of each vehicle. Specifically, the fixed cost refers to the fixed scheduling cost of each vehicle; the total fixed cost is proportional to the number of vehicles. The travel cost refers to the cost incurred by all vehicles in the area, which is proportional to the total travel distance. The penalty cost refers to the penalty imposed on a vehicle that fails to complete the task in the time window (1h). No penalty cost will be incurred if the task is completed within 1h. The above model faces the following constraints:

$0 \leq R_{i c} \leq P$  (3)

$\sum_{c=1}^{C} \gamma_{i c}=1$ (4)

$\sum_{i=1}^{M} \sum_{j=1}^{M} x_{i j c} \times d_{i j} \leq D_{c}$ (5)

$x_{i j c}, \gamma_{i c} \in\{0,1\}$   (6)

5.2 Model solving

Considering the conditions of area scheduling of bike sharing, the traditional GA was improved to solve the above model. The solving process can be broken down into six steps:

Step 1. Coding

The station in the area was given the number of 0, and the n hotspots to be served by the vehicles were numbered in turn as 1, 2, …, n. Then, the path of each vehicle could be expressed based on these serial numbers. If a vehicle leaves from the station, serves hotspots 2, 4 and 5 in turn, and then returns to the station, then the path of the vehicle can be encoded as 0, 2, 4, 5, 0.

Step 2. Population initialization

The population was initialized by random. The population size, i.e., the number of individuals in the population, was designed empirically. Then, the population size was modified repeatedly through model simulation. The size (200) that led to the best simulation effect was taken as the optimal population size. 

Step 3. Fitness calculation

The fitness of each individual was calculated by:

$f i t\left(x_{i}\right)=1 /\left(f\left(x_{i}\right)+f(x)_{\min }+1\right)$   (7)

where, f(x_i) is the objective function value of an individual; f(x)_min is the global minimum of f(x_i) in the population.

Step 4. Selection

The individuals were chosen by roulette selection, that is, an individual with a high fitness is more likely to be selected. Let N be the number of individuals in the population. Then, the selection probability of individual i  can be derived from the fitness function:

$P_{i}=f i t\left(x_{i}\right) / \sum_{i=1}^{N} f i t\left(x_{i}\right)$   (8)

Step 5. Crossover

The individuals were subjected to sequential crossover at the probability of 0.8. The genes at a few randomly selected positions of parent chromosome A were copied to the same positions of child chromosome A. Then, the genes at the other positions of parent chromosome B were copied to the other positions of child chromosome A. The child chromosome B was obtained in a similar manner.

Step 6. Mutation

Mutation aims to maintain the diversity of the population, and ensure the local search ability of the algorithm. Here, the individuals are subjected to reverse mutation at the probability of 0.1.

5.3 Experimental analysis

To verify their effectiveness, the decision model and the improved GA were applied to schedule the bike sharing system in a city in China. The MATLAB was adopted as the simulation platform.

The original data were collected on May 17 in that city. The samples in the morning peak (7:00-8:00) were selected for modelling, and the entire city was divided into 22 areas. Then, the BPNN model was employed to predict the bike sharing demand of each area the scheduling cycle. The results are listed in Table 2 below.

Table 2. The predicted bike sharing demand of each area

To solve the decision model, a station was set up at the center of each area. Each vehicle must leave from the station half-loaded with bikes, visit each hotspot to be served, and then return to the station. On the return journey, the vehicle should not be overloaded.

According to field survey and relevant research [19, 20], the parameters of the decision model were empirically configured as shown in Table 3.

The proposed decision model was solved separately by the traditional GA and the improved GA. During solving process of the traditional GA, the optimization objective stabilized after 1,300 iterations; During the solving process of the improved GA, the optimization objective stabilized after 750 iterations, that is, the optimization speed increased by almost 40%. In addition, the improved GA reduced the scheduling cost by 9.2% from the level of the traditional GA. Overall, the improved GA outperformed the traditional GA in optimization ability and efficiency. Therefore, our decision model, coupled with the improved GA, can effectively optimize the scheduling of bike sharing system.

Table 3. Parameter values