# Learning from Imbalanced Datasets: The Bike-Sharing Inventory Problem Using Sparse Information +
## 2 Related Research  
### The Inventory Problem and the Rebalancing Problem  
Developing an inventory model for a traditional station-based bike-sharing service is particularly challenging as it needs to capture two features: (1) the demand for bicycles; (2) the demand for docks--i.e., finding an empty dock where the user can return the rental bicycle [11]. Therefore, to simply find the number of bicycles that serves the demand is not sufficient [7]. The uneven distribution of vehicles and docks in the system causes some stations to be empty (or entirely full), creating shortages of both bicycles and docks. To prevent this shortage, several studies introduced rebalancing techniques that aim at evenly redistribute bicycles and docks in the system [12]. Traditionally, the problem is solved using either optimization techniques [12] or ML models [8]. Optimization techniques translate the problem into a mathematical language and focus on tractability and convergence properties. The most common approach is to formulate the problem as a one-commodity pickup-and-delivery capacitated vehicle-routing problem, which is then solved using mixed-integer linear programming [12]. This approach has also been extended to other station-based shared mobility services, such as car sharing [13]. The complexity of the algorithm depends on whether the objective is to achieve a complete rebalancing (all stations are jointly optimized) or a partial one (only a subset of stations is optimized), with the former case being far more complex than the latter [14]. Traditional algorithms for solving the problem include tabu search [15] and branch-and-cut [16]. However, as exact formulations are not suited for real-life instances, heuristic models have been developed to solve the problem in practice [9; 17]. In recent years, other authors have proposed using ML instead of optimization techniques to solve the rebalancing problem. The most popular models include decision trees [8; 9], neural networks [18], deep neural networks [19; 20], and clustering techniques [2]. The main convenience of these models is that they are suited for large-scale, real-life applications and require limited assumptions of user behavior. The models discussed up to this point also present several differences in the operational approach. For instance, [15] provides a price mechanism to support rebalancing, while [9] assumes that rebalancing operations are performed by the sharing company; these approaches are translated into different parameters and objective functions. However, most repositioning studies, including those using ML, assume that the inventory level (i.e., the optimal number of docks/bicycles at any given time) is known from historical data or by using an existing demand model [7]. To date, only a few studies have focused on how to compute the optimal target levels while considering the rebalancing problem. Among the studies that have focused on the inventory levels, [21] proposed a mixed-integer program formulation to find the inventory levels that minimize the cost of rebalancing. Alternatively, [22] formulated the inventory problem as a nonstationary Markov chain model that computes the most likely optimal inventory levels during the day. Ref. [23] identifies an upper bound and a lower bound for the inventory level using historical information. A similar approach is used in [24]. Ref. [7] also identifies an upper bound and a lower bound for the inventory level using mixed-integer optimization. One of the main limits of the previous approaches, however, is that the model explicitly minimizes the journey dissatisfaction levels with respect to the user and cannot be used if the operator has different goals (such as maximizing profit). Another aspect to highlight is the role of IT technologies.