In China, based on the mobile Internet technology and global positioning system (GPS), innovative bike-sharing is different from traditional bike-sharing system with docking station, for its flexibility and convenience. However, innovative bike-sharing system faces operational challenges, especially in faulty bike-sharing recycling (FBSR) problem. In this paper, a framework is designed based on the optimization method to solve the FBSR problem so that it can minimize the total recycling costs by taking the route optimization and loading capacity ratio as constraints. The FBSR method combines the K-means method for clustering faulty bike-sharing with planning recycling route for operational decisions. Moreover, CPLEX solver is used to obtain the desired result of the FBSR model. Finally, a case study based on a certain area in Beijing, China, is used to verify the validity and applicability of the model. The results show that the value of loading capacity ratio and the number of clustering points greatly affect the results of FBSR problem. Four vehicles are designated to execute FBSR tasks required by different clustering points. This study is of considerable significance for the bike-sharing promotion in the last-mile situation to the real problems arising in the initial period.
Bike-sharing systems are becoming increasingly popular in cities around the world because they are cheap, efficient, healthy, and green. In recent years, with the development of mobile Internet and global positioning system (GPS) becoming increasingly affordable [
Spatial distribution of main dockless bike-sharing systems in China.
Compared with traditional bike-sharing [
It is worth noting that there are a large number of people cycling every day. It is unavoidable that bike-sharing may malfunction in its routine use, and accidents might take place due to its faults. According to some statistics, there are more than 10 million bicycles in bike-sharing systems, and faulty bicycles rate slightly less than 1%. If we calculate with rate of 1% faulty bicycles, there will be 100,000 faulty bicycles in China. Meanwhile, lots of bicycles will be scrapped usually in three years in China. These factors could cause the following: (a) the presence of the faulty bike-sharing severely threatens users’ safety; (b) the service quality of bike-sharing system will affect the reputation of the companies; (c) faulty bicycles in the city have a very bad effect on the city appearance. Therefore, faulty bike-sharing recycling (FBSR) is a very significant issue that should be solved. Moreover, the distribution of bicycles of innovative bike-sharing system is rather dispersed since bike-sharing can park without docking station, whereas for traditional bike-sharing system, faulty bicycles are readily discovered and easily processed at bicycle docking station. Comparatively speaking, it is more difficult for the innovative bike-sharing system to recycle faulty bicycle than traditional bike-sharing. Thus, solving the FBSR problem is the key to reduce recycling costs for the authorities and operators with the means.
Therefore, this paper presents a framework design and optimization method to solve FBSR problem. Firstly, the K-means clustering method is used to divide the faulty bike-sharing into different service points. Then, a FBSR model is established to minimize the total recycling costs with loading capacity ratio as a constraint. At last, this method is verified based on a case study in Beijing, China.
The remaining part of this paper is organized as follows. The relevant literature is reviewed in Section
Since a bike-sharing system was first introduced in the 1960s [
The existing literature on bike-sharing systems is mainly focused on the traditional bike-sharing system with docking stations including development policies and safety issues [
Recently, the new bike-sharing system without docking station has attracted attention from a few scholars. Reiss and Bogenberger [
In addition, Cervero et al. [
In this paper, three types of bicycle as faulty bicycles are defined as follows.
(i) Fault of cycling: it happens when the users unlock the bicycles and find that the bicycle cannot be used; then the users will send the information through the mobile phone app. When the bike-sharing system server receives the information of the faulty bicycle status and location, the bike-sharing company will have it repaired.
(ii) Fault of communication: it happens when bicycles are identified as faulty bike-sharing owing to GPS equipment damage, and the system server will prohibit users from using this bicycle (ignoring GPS equipment lost contact while cycling).
(iii) End of the service life: if a bicycle has reached the state’s mandatory write-off standard (generally three years in China), the bike-sharing system server will identify the bicycle as faulty bike-sharing. Then this bicycle will be forced to scrap, prohibiting users from cycling.
Multilevel faulty bike-sharing recycling network is shown in Figure
Multilevel faulty bike-sharing recycling network.
For the description, ground rules are established as follows.
Therefore, there are two key issues to deal with to complete one FBSR in an area:
(i) How to determine the number and the location of bike-sharing service points that are available for recycling vehicles.
(ii) How to determine routes for recycling vehicles to traverse all service points from maintenance station.
Based on the analysis of faulty bike-sharing definition, classification, and recycling rules, the flowchart of faulty bike-sharing recycling is shown in Figure
Flowchart of faulty bike-sharing recycling.
There are three types of faulty bike-sharing in the section above. For type 1, the system server will directly set it as faulty bike-sharing to be processed. For type 2, when the location information of bike-sharing is lost, the system needs to record the last received location information. Type 1 and type 2 bicycles will be stored in the faulty bike-sharing database. For type 3, when a bike-sharing company launches bicycles in the city every time, the system server will set the time of the bicycles’ service life, after which the time of service life of these bicycles will be stored in the faulty bike-sharing database by system server. By confirmation and processing of three types above, the bike-sharing company will have these faulty bikes fixed.
Faulty bike-sharing clustering is represented by lower network as shown in Figure
Planning recycling route is represented by the upper network as shown in Figure
According to the result of Step
It is worth noting that Step
Based on framework design of faulty bike-sharing recycling, the FBSR model in this paper mainly consists of two parts: faulty bike-sharing clustering and recycling route modeling.
K-means algorithm [
We develop a recycling route model, where the decision-maker (the transit authority or operator) wishes to determine recycling route while minimizing total recycling costs. It is assumed that the result of faulty bike-sharing clustering remains unchanged throughout that period. Consider a network rooted at depot (the maintenance station) named All route cycles are repeated with identical characteristics. The round-trip distance between the two service points is the same. The location of the faulty bicycle without positioning is accurate.
Thus, the optimization problem is
The objective function minimizes the total recycling costs. It is multiplied by
The objective includes two components. The first refers to the objective function (
Let us define
where
In order to improve the utilization rate of recycling vehicles, we propose a constraint to restrict load capacity as follows:
where
Besides, in order to avoid the loop in the route, it is sufficient that problem includes the following bonding constraint:
where
In the process of problem solving, the recycling route model belongs to 0-1 integer programming model. Considering the scale of the problem, it can be solved by CPLEX solver with branch and bound approach for its advantages of the direct and concise input and strong computation ability.
In this section, a real-world bike-sharing from an area of Beijing, China, was selected as a case study. The test area is a square area that has a side length of 2.6 km and Haidian Huang Zhuang subway station is selected as areal maintenance station. We set the number of recycling vehicles in a maintenance station as 4, and the capacity of each vehicle is 30 bicycles. There are 1900 bicycles (Figure
Heat map of bike-sharing.
We set up 1 to 14 groups clustering experiment. The times of iterations of each clustering algorithm are not more than 20, which proves that the computation is highly efficient. The
The SSE graph of K-means.
Latitude and longitude coordinates of the clustering centers are obtained by the K-means algorithm and their locations on a map are shown in Figure
The graph of clustering centers by K-means.
Considering the result of faulty bike-sharing clustering by K-means algorithm of 12 service points,
The optimal result of FBSP model.
Vehicle | Capacity ratio | Route | Travel time/min | Carrying time/min | Total time/min | Total costs/RMB |
---|---|---|---|---|---|---|
1 | 80% | | 17 | 95 | 112 | 141 |
2 | 76.7% | | 17 | 176 | 193 | 181.5 |
3 | 83 | | 24 | 182 | 206 | 223 |
4 | 76.7% | | 12 | 131 | 143 | 131.5 |
Total | 70 | 584 | 654 | 677 |
In this example, we can see that the total costs are 677 RMB from the FBSR model. In Table
The comparison experiment for the coefficient of load capacity ratio was conducted. Figure
The optimal result of FBSP model for the different capacity ratio.
| Vehicle | route | Travel time/min | Carrying time/min | Total costs/RMB |
---|---|---|---|---|---|
0.4 | 1 | | 67 | 584 | 660.5 |
2 | | ||||
3 | | ||||
4 | | ||||
0.5 | 1 | | 68 | 584 | 666 |
2 | | ||||
3 | | ||||
4 | | ||||
0.6 | 1 | | 69 | 584 | 671.5 |
2 | | ||||
3 | | ||||
4 | | ||||
0.7 | 1 | | 70 | 584 | 677 |
2 | | ||||
3 | | ||||
4 | |
The number of bicycles loaded for the coefficient of load capacity ratio.
Table
The effects of the number of clustering points.
Network | | Travel time | Carrying time | Total time | Total costs |
---|---|---|---|---|---|
10-node | 0.4 | 65 | 710 | 775 | 712.5 |
0.5 | 65 | 710 | 775 | 712.5 | |
0.6 | 65 | 710 | 775 | 712.5 | |
0.7 | 65 | 710 | 775 | 712.5 | |
12-node | 0.4 | 67 | 584 | 651 | 660.5 |
0.5 | 68 | 584 | 652 | 666 | |
0.6 | 69 | 584 | 653 | 671.5 | |
0.7 | 70 | 584 | 654 | 677 | |
14-node | 0.4 | 69 | 546 | 615 | 652.5 |
0.5 | 71 | 546 | 617 | 663.5 | |
0.6 | 72 | 546 | 618 | 669 | |
0.7 | 74 | 546 | 620 | 680 |
10-node travel time matrix for each point (unit: min).
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|---|
0 | 0 | 2 | 6 | 9 | 12 | 4 | 7 | 4 | 7 | 3 | 4 |
1 | 2 | 0 | 4 | 14 | 2 | 6 | 6 | 5 | 12 | 6 | 7 |
2 | 6 | 4 | 0 | 17 | 1 | 12 | 8 | 9 | 16 | 13 | 8 |
3 | 9 | 14 | 17 | 0 | 13 | 7 | 8 | 10 | 7 | 4 | 12 |
4 | 12 | 2 | 1 | 13 | 0 | 12 | 9 | 11 | 13 | 11 | 7 |
5 | 4 | 6 | 12 | 7 | 12 | 0 | 8 | 6 | 8 | 4 | 7 |
6 | 7 | 6 | 8 | 8 | 9 | 8 | 0 | 5 | 4 | 7 | 6 |
7 | 4 | 5 | 9 | 10 | 11 | 6 | 5 | 0 | 7 | 6 | 5 |
8 | 7 | 12 | 16 | 7 | 13 | 8 | 4 | 7 | 0 | 9 | 11 |
9 | 3 | 6 | 13 | 4 | 11 | 4 | 7 | 6 | 9 | 0 | 6 |
10 | 4 | 7 | 8 | 12 | 7 | 7 | 6 | 5 | 11 | 6 | 0 |
12-node travel time matrix for each point (unit: min).
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 0 | 2 | 6 | 7 | 12 | 4 | 4 | 3 | 5 | 5 | 4 | 5 | 11 |
1 | 2 | 0 | 4 | 13 | 2 | 6 | 5 | 4 | 6 | 12 | 7 | 6 | 16 |
2 | 6 | 4 | 0 | 15 | 1 | 12 | 6 | 13 | 13 | 14 | 8 | 6 | 19 |
3 | 7 | 13 | 15 | 0 | 17 | 11 | 5 | 9 | 4 | 7 | 14 | 3 | 5 |
4 | 12 | 2 | 1 | 17 | 0 | 12 | 12 | 11 | 12 | 12 | 7 | 10 | 16 |
5 | 4 | 6 | 12 | 11 | 12 | 0 | 6 | 6 | 5 | 4 | 7 | 9 | 5 |
6 | 4 | 5 | 6 | 5 | 12 | 6 | 0 | 3 | 3 | 9 | 8 | 6 | 8 |
7 | 3 | 4 | 13 | 9 | 11 | 6 | 3 | 0 | 5 | 6 | 5 | 6 | 12 |
8 | 5 | 6 | 13 | 4 | 12 | 5 | 3 | 5 | 0 | 8 | 7 | 7 | 9 |
9 | 5 | 12 | 14 | 7 | 12 | 4 | 9 | 6 | 8 | 0 | 7 | 8 | 12 |
10 | 4 | 7 | 8 | 14 | 7 | 7 | 8 | 5 | 7 | 7 | 0 | 7 | 11 |
11 | 5 | 6 | 6 | 3 | 10 | 9 | 6 | 6 | 7 | 8 | 7 | 0 | 10 |
12 | 11 | 16 | 19 | 5 | 16 | 5 | 8 | 12 | 9 | 12 | 11 | 10 | 0 |
14-node travel time matrix for each point (unit: min).
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 0 | 2 | 6 | 8 | 12 | 4 | 4 | 2 | 4 | 5 | 4 | 6 | 6 | 8 | 7 |
1 | 2 | 0 | 4 | 13 | 2 | 6 | 11 | 10 | 12 | 12 | 7 | 11 | 15 | 17 | 16 |
2 | 6 | 4 | 0 | 14 | 1 | 12 | 8 | 8 | 13 | 12 | 8 | 8 | 16 | 18 | 17 |
3 | 8 | 13 | 14 | 0 | 17 | 11 | 6 | 9 | 6 | 7 | 14 | 5 | 9 | 5 | 4 |
4 | 12 | 2 | 1 | 17 | 0 | 12 | 9 | 8 | 13 | 11 | 5 | 9 | 15 | 17 | 16 |
5 | 4 | 6 | 12 | 11 | 12 | 0 | 5 | 6 | 5 | 4 | 7 | 8 | 4 | 5 | 4 |
6 | 4 | 11 | 8 | 6 | 9 | 5 | 0 | 3 | 3 | 8 | 8 | 5 | 7 | 10 | 7 |
7 | 2 | 10 | 8 | 9 | 8 | 6 | 3 | 0 | 4 | 8 | 4 | 5 | 8 | 10 | 9 |
8 | 4 | 12 | 13 | 6 | 13 | 5 | 3 | 4 | 0 | 8 | 7 | 7 | 8 | 8 | 7 |
9 | 5 | 12 | 12 | 7 | 11 | 4 | 8 | 8 | 8 | 0 | 6 | 8 | 3 | 6 | 6 |
10 | 4 | 7 | 8 | 14 | 5 | 7 | 8 | 4 | 7 | 6 | 0 | 6 | 9 | 10 | 10 |
11 | 6 | 11 | 8 | 5 | 9 | 8 | 5 | 5 | 7 | 8 | 6 | 0 | 10 | 9 | 8 |
12 | 6 | 15 | 16 | 9 | 15 | 4 | 7 | 8 | 8 | 3 | 9 | 10 | 0 | 3 | 2 |
13 | 8 | 17 | 18 | 5 | 17 | 5 | 10 | 10 | 8 | 6 | 10 | 9 | 3 | 0 | 2 |
14 | 7 | 16 | 17 | 4 | 16 | 4 | 7 | 9 | 7 | 6 | 10 | 8 | 2 | 2 | 0 |
This paper introduces the framework design and optimization method to solve FBSR problem. In China, the number of bike-sharing systems grows rapidly due to its flexibility and convenience for the users. However, they face operational challenges such as FBSR problem. For this reason, we presented a framework design of FBSR to solve the problem of recycling faulty bike-sharing. Then, we propose FBSR optimization model that is able to minimize the total recycling costs through the K-means clustering method that is used to divide the faulty bike-sharing into different service points. It can provide bike-sharing company’s managers with good insight into the design of a FBSR problem. The comparison among different service points can help decision-makers to choose the best solution. In addition, the vehicle capacity restriction should be included in a FBSR optimization model to improve the number of bicycles loaded for each vehicle.
A typical example solved by CPLEX solver was created to illustrate the proposed model. The results of a case study show that the model works well. It is indicated that the best route recycles the faulty bicycles according to the clustering points. Compared with the values of capacity ratio models in the FBRS model, we can find that travel time and capacity ratio have positive correlation. And the comparison experiment has shown that the number of clustering points has a significant impact on total recycling costs, which needs to be considered carefully in the FBSR model.
In the future, with bike-sharing systems growing in China, we will present a solution model for dealing with dynamic faulty bike-sharing recycling. In addition, random searching for faulty bicycle without GPS should also be considered by the researchers.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
This research is supported by the National Natural Science Foundation of China (no. U1434207 and no. U1734204).