Bike sharing systems (BSSs) are an important component in today’s urban transportation system [1
]. As a more sustainable mode of transportation, bike-sharing has the potential to reduce car usage, solve the first/last mile problem, and contribute to the local retail sales [3
]. The history of bike sharing can be traced back to the 1960s when the concept was first introduced in Amsterdam, Netherlands [6
]. Over the past decades, bike sharing systems have evolved through multiple generations. Early generations involved no prior registration and failed, as many bikes were vandalized or turned into private use [6
]. Starting from 1995, prior registration has been required. A registered customer can rent and return a bicycle at a number of fixed bike stations. These systems are also known as station-based bike sharing systems (SBBSSs) [8
] and have been successfully deployed in multiple cities around the world. Leveraged by the recent advanced technologies such as smart phones, GPS, and integrated payment systems, the newest generation of bike sharing involves having no fixed bike stations. Without docking stations, the station-free bike sharing systems (SFBSSs) provide users the flexibility to use a smart phone app to locate a bike nearby and park it at any appropriate place after use. Due to the high flexibility and convenience, SFBSSs have gained considerable popularity over the past few years and have been widely adopted in many countries, including China, United Kingdom, Singapore, the United States, and the Netherlands [9
]. It was estimated that in 2018, 16 to 18 million station-free bikes were in use worldwide, compared to 3.7 million station-based bikes [10
A balanced status refers to the situation when bike supply meets bike demand. Both station-free and station-based bike sharing systems frequently suffer from the spatiotemporal fluctuations of demand, leading to the imbalance problem. Without timely rebalancing efforts, the imbalance problem may substantially degrade the system performance. For an SBBSS, the imbalance problem may lead to zero inventories at some stations and no space for parking at others. As a result, rentals and returns may be only possible at a limited number of stations, leaving many areas/demands un- or under-served [11
]. For an SFBSS, the imbalance problem is more serious. While unmet demands remain, no restriction on where a user can pick up or park a bike may lead to bikes piling up and blocking city sidewalks.
Many studies have been conducted to assess the imbalance status of an SBBSS and design the associated rebalancing strategy [12
]. While the imbalance evaluation in an SBBSS is rather straightforward [17
], due to the lack of fixed stations in an SFBSS, there is no clearly defined spatial scale or geographical areas to evaluate bike inventories, assess the imbalance status, and perform the subsequent rebalancing analysis. Existing studies have explored various analysis scales, including traffic analysis zones and regular grids of various sizes [19
]. The selection of these analysis scales has been rather arbitrary. There has been no discussion on the suitable scale needed to evaluate and address the imbalance issue in an SFBSS. On the one hand, a balanced status evaluated using large areas (e.g., 10 × 10 km grids) may contain multiple local bike shortage/surplus sites, which can significantly compromise the system performance. On the other hand, analysis conducted using small areas (e.g., 10 × 10 m grids) may greatly add to computational burden. Therefore, analysis scale, modeling/analysis, and computational requirements are related, and selection of the appropriate analysis scale is essential for the imbalance assessment of an SFBSS and the following rebalancing analysis.
2. Literature Review
Recently, a number of studies have examined bike sharing systems by focusing on two areas [23
]. The first area concerns identifying the factors affecting bike sharing demand, and these factors include socio-economic status, built environment, traffic infrastructure, air quality, and weather [27
]. The second area focuses on the imbalance issue of a bike sharing system and the associated rebalancing strategies. In this study, we are mainly interested in the latter.
To solve the imbalance issue in a bike-sharing system, various rebalancing strategies have been developed. Table 1
provides a summary of the recent literature on these rebalancing strategies. In particular, user-based and operator-based methods are the two major types of rebalancing strategies [8
]. In a user-based rebalancing strategy, incentives in the form of a bonus voucher or discount are often used to encourage users to move bikes from surplus areas to shortage areas. For example, in 2008, the bike sharing system Vélib’ in Paris launched a discount pricing strategy [31
] to motivate users to return bikes to uphill stations. A pricing strategy was developed by Chemla et al. [32
] to incentivize users to return bikes to the least loaded stations nearby, and a dynamic online pricing incentive strategy was proposed by Pfrommer et al. [33
] to motivate users to choose alternative locations to pick up or return bikes. However, depending on users’ participation, user-based rebalancing may not be sufficient to achieve the system level self-rebalancing [30
]. Hence, user-based rebalancing strategies are often used as a supplement to operator-based ones. These two types of strategies can be combined to help reduce rebalancing costs [33
]. Currently, most existing bike-sharing systems (e.g., Mobike and Ofo in China) employ operator-based rebalancing strategies [8
A few studies have focused on developing efficient operator-based rebalancing methods. In an operator-based rebalancing operation, a fleet of vehicles are often sent to move bikes from site to site. Among others, spatial optimization methods [42
] have been widely used to determine the number of relocation vehicles and the associated routes for performing the rebalancing operation [8
]. All the studies included in Table 1
are based on optimization methods except for Ji et al. [41
]. These problems have often been formulated using mixed integer programming (MIP) [34
]. Some of these studies integrated GIS into classic location models, including the p
-median problem and the coverage location problems, to achieve the optimal rebalancing design [8
]. A range of objectives/goals have been examined in the bike rebalancing design. These objectives include minimizing costs, varying from travel costs to the overall rebalancing costs (including travel, trucks, loading and unloading costs), and maximizing the system level balance evaluated using different metrics (e.g., minimal absolute deviation from the target number of bikes) (also see Table 1
). While some studies focused on a single objective [35
], a few studies considered multiple goals simultaneously [44
As shown in Table 1
, existing bike rebalancing models are mainly station-based and have been constructed to address the imbalance issue of an SBBSS. In an SBBSS, stations are the analysis units used to perform the imbalance evaluation and the subsequent rebalancing analysis. In an SFBSS, if we divide a region into a set of sub-areas and treat each sub-area as a “station”, we can apply a station-based rebalancing model to solve the imbalance issue in an SFBSS. In fact, traffic analysis zones [20
] and regular grids [19
] have already been used to conduct the imbalance assessment for SFBSSs. Although traffic analysis zones (TAZs) are widely used in transportation planning, they are delineated largely based on motorized traffic and are generally too coarse to capture the variation of bike supply and demand given the short distance that bike users are normally willing to walk to access bikes. As for the grid-based approaches, the selection of grid size has been either arbitrary or unspecified [19
]. To the best of our knowledge, there have been no studies exploring the impacts of analysis scale on the imbalance evaluation and the associated rebalancing design in an SFBSS. Scale can be critical in an SFBSS study: A balanced status at a large scale may contain multiple local bike shortage/surplus sites, and as a result, the rebalancing strategy designed based on a large scale might not solve the imbalance issue completely. In contrast, analysis conducted using fine scales may encounter computational challenges, and a scale that is too fine (such as 1 m) might not be necessary or even meaningful.
also summarizes the number of analysis units (i.e., sub-areas/grids in an SFBSS or stations in an SBBSS) used in current bike rebalancing studies, ranging from 28 to 1185. Since a rebalancing problem can be computationally intractable when a large number of analysis units are involved, many studies focused on small cities/areas or used a coarse scale [19
]. For example, the model proposed by Chemla et al. [32
] was unable to simulate the user-based rebalancing process for more than 250 stations because of the large problem size. Focusing on small areas or using coarse scale analysis units may provide limited insights into effective rebalancing strategies for a large urban area.
Therefore, identifying the appropriate analysis scale and designing efficient and effective bike rebalancing strategies are needed for SFBSSs in large cities. In this study, we aim to fill in the research gaps by focusing on two important questions: (1) how scale impacts the imbalance evaluation of an SFBSS and the associated rebalancing design, and (2) how to deal with computational challenges for large sized rebalancing problems. We develop a spatial optimization model to strategically optimize bike rebalancing efforts. We also propose a region decomposition method to solve large-sized problems that are constructed based on fine analysis scales. We apply the approach to study the SFBSS in downtown Beijing. Based on the empirical study, we discuss the strengths and weaknesses associated with alternative analysis scales and make recommendations on scale choice for different rebalancing strategies.
Scale is critical in the imbalance evaluation and rebalancing design of an SFBSS. Analysis conducted based on large scales (e.g., 1 km or coarser) provides a regional picture of the imbalance status and is computational efficient. From the operator-based rebalancing point of view, a large-scale analysis helps a strategic rebalancing planning. A rebalancing strategy based on a large-scale analysis usually involves repositioning fewer bikes and a consequent smaller fleet size and less costs associated with bike loading and unloading. However, given that large-scale analysis may miss many local imbalance sites, the effectiveness of a rebalancing operation based on a large-scale analysis may be compromised. In addition, a large-scale analysis might be less helpful for designing a user-based rebalancing approach, because users are unlikely to walk long distances to participate in the rebalancing process.
Analysis using small scales (e.g., 100, 200 m) identifies a large amount of bikes that need to be repositioned. For an operator-based rebalancing approach, repositioning a large amount of bikes would require high costs for bike loading and unloading. However, given that imbalance sites can be more accurately identified when fine analysis scales are used, an operator-based rebalancing strategy designed based on fine scales will be more effective than that using a coarse scale. Small scale analysis also provides valuable insights into the design of effective user-based rebalancing strategies. Our empirical results suggest that many local bike surplus and shortage can be addressed by moving bikes between neighboring areas. For example, at the 200 m scale the majority of rebalancing trips would involve a bike repositioning of less than 300 m. In this case, incentives might be effective for users to help rebalance the system.
Based on the empirical study, we would recommend 800 m as the suitable scale for designing operator-based rebalancing strategies. At the 800 m scale, the percentage of imbalanced bikes reaches the maximum. It suggests that at this scale many local imbalance sites are identified without introducing too many non-relevant areas. In addition, at the scale of 800 m, the rebalancing problem size is reasonable and solving the rebalancing problem is efficient, making it possible to design real-time dynamic rebalancing strategies. Furthermore, even if local shortage/surplus sites exist within an 800 m grid, considering that 800 m is the median distance of walking trips [47
], it is acceptable for many users to walk from a local shortage site to a local surplus site to pick up a bike.
As for user-based rebalancing strategies, we would recommend fine scales, such as 100 and 200 m, as the analysis unit. At the 100 m scale, the empirical study suggests that a lot of rebalancing could be achieved within a very short repositioning distance (100 m on average). In this case, consumers do not need to walk far and will be highly motivated to participate in the rebalancing process. Our study also shows that on average only a few bikes need to be redistributed between an OD pair, so in most cases, a small number of users are needed to help move bikes between two specific sites. At the fine scale, many sites could serve as the transfer “stations”, which allows users the flexibility to participate in one or multiple segments of rebalancing trips.
In general, large-sized rebalancing problems present problem–solution challenges. In this study, we introduce the region decomposition heuristic to solve large-sized problem instances. The empirical study shows that the heuristic can be used to solve problems that cannot be handled by existing commercial optimization software. We note that the heuristic solution quality highly relies upon the delineation of “self-contained” sub-regions. In the empirical study, we use a random approach to delineate these sub-regions, and solutions generated by the heuristic are slightly worse than the optimal solution. Future study can focus on developing strategies to identify effective self-contained sub-regions and the associated scale to improve solution quality.
It should be acknowledged that this study has some limitations. First, similar to many existing methods, in an SFBSS, we partition a region into a number of sub-areas and treat each sub-area as a “station” with all bikes inside the same sub-area aggregated at the center of the sub-area. Such an approach might be problematic when the analysis units/sub-areas are large, as bikes inside a sub-area are more likely to be far from the center of a sub-area. Second, in the rebalancing model, we allow an SFBSS to deviate slightly from the complete balance status by introducing a rebalancing upper bound and lower bound. In the empirical study, we examine a lower bound of 0.9 and an upper bound of 1.1. Future work should examine whether and how varying upper/lower bounds affect the appropriate scale selection in the SFBSS rebalancing analysis.