Rebalancing Problem Research Articles

Battery swapping, vehicle rebalancing, and staff routing for electric scooter sharing systems

Electric scooter (e-scooter) sharing systems provide on-demand electric scooter rental services. E-scooters are equipped with swappable batteries managed by staff who visit each scooter and replace depleted batteries with charged ones. The e-scooters in this system are free-floating; they can be located anywhere without having to be returned to designated stations. Due to this characteristic of the scattered location of e-scooters, operation decisions with associated staff routing are more challenging than station-based services. Thus, it is critical to implement the efficient management of e-scooter redistribution and charging decisions with proper staff routing to successfully prepare for user demand within a limited operation time while minimizing the total operating cost. To this end, we introduce a battery swapping and vehicle rebalancing problem with staff routing for e-scooter sharing systems, formulated as a mixed integer programming (MIP) model. To derive solutions efficiently for a large-scale instance in practice, we propose a clustered iterative construction approach where the problem is decomposed into two phases. The first phase clusters regions using an approximation of intra-region and inter-region operation costs with the minimum spanning tree approach. The second phase efficiently derives multiple candidate regional sequences by our partial permutation procedure and following the sequences, iteratively solves a significantly reduced size of the problem to construct operation assignments. Our numerical experiments on the generated instances and real-world instances demonstrate that the proposed two-phase algorithm shows significantly superior performance in practically large scale instances than the benchmarks without clustering or the iterative procedures of our algorithm.

Real-time vehicle relocation and staff rebalancing problem for electric and shared vehicle systems

ABSTRACT This study addresses the challenging real-time vehicle relocation and staff rebalancing (RT-VR&SR) problem in electric carsharing services. The complexity arises from ad-hoc demand, charging requirements of electric vehicles (EVs), and staff scheduling constraints. The problem aims to maximize the profit of carsharing operators by determining strategies for vehicle relocation, vehicle charging, and staff rebalancing in real-time. It considers the uncertainty of demand and the practical nonlinear charging profile of EVs. We formulate this problem as a Markov Decision Process (MDP), and propose an efficient concurrent-scheduler-based policy. Numerical experiments are conducted to demonstrate the effectiveness of the proposed policy and methodology. The results show that the proposed policy significantly improves service level and profitability compared to a benchmark policy. It is also found that ignoring staff rebalancing in decision making can lead to overestimation of service level and profitability. In conclusion, this study presents a real-time solution for vehicle relocation and staff rebalancing in one-way electric carsharing services. The proposed policy and methodology improve performance and highlight the importance of considering staff rebalancing in decision making.

The Novel Application of Deep Reinforcement to Solve the Rebalancing Problem of Bicycle Sharing Systems with Spatiotemporal Features

Facing the Bicycle Rebalancing Problem (BRP), we established a Rebalancing Incentive System (BRIS). In BRIS, the bicycle operator proposes the method of financial compensation to encourage cylclists to detour some specific stations where the number of bikes is excessive or insufficient and access suitable sations. BRIS mainly includes two objects: the Bike Gym imitating the bicycle environment, and the Spatiotemporal Rebalancing Pricing Algorithm (STRPA) determining the amount of money which is given to the cyclist depending on time. STRPA is a deep reinforcement learning model based on the actor–critic structure, which is the core concept of this paper. In STRPA, the hierarchical principle is introduced to solve the dimensional disaster, and the graph matrix A is introduced to solve the complex node relationship. In addition, the traffic data including the bicycle have strong temporal and spatial characteristics. The gated recurrent unit (GRU), the sub-module of STRPA, can extract the temporal characteristics well, and the graph convolution network (GCN), also a sub-module of STRPA, can extract the spatial characteristic. Finally, our model is superior to the baseline model when verified on the the public bicycle data of Nanjing.

Rebalancing in bike sharing systems: Application to the Lisbon case study

This work presents a mathematical programming formulation for the static Bike Rebalancing Problem to meet the practical constraints faced by the operators of Bike Sharing Systems. Adaptating a Mixed Integer Linear Programming formulation, it now includes different types of vehicles and bicycles, the autonomy of each vehicle, the duration of its route and the stations that require inspection actions. An intermediate station is introduced to temporarily store bicycles, relaxing the restrictions imposed by the vehicles’ capacity. After incorporating different acceleration procedures, a Branch-and-Cut scheme is run for 30 min to find optimized routes for the reposition vehicle on five real instances of the Lisbon Bike Sharing System. The computed routes resulted in a 30% to 75% decrease in total length, when compared to the real routes. This decrease is mainly attributed to the integration of all the mentioned factors in one global model, encouraging its future implementation.

A multiobjective dynamic rebalancing evolutionary algorithm for free-floating bike sharing

The big challenge of free-floating bike sharing system is to rebalance the supply and demand in different places. Most studies are static rebalancing that moves bikes at night. Dynamic rebalancing considers the scheduling of transport vehicles during the day. It is more effective and difficult to solve. In this paper, a multiobjective dynamic rebalancing problem is solved. The two optimization objectives are considered: minimizing the total distance of rebalancing vehicle and minimizing the total demand unmet. A mathematic model is built to formulate the problem. A new algorithm SFMEA-AP (Sequence Flow Multiobjective Evolutionary Algorithm with Area Protected) that uses the sequence flow encoding is proposed. An novel area protected strategy that includes a non-dominated sorting with similarity comparison is proposed. It simultaneously considers the fairness and competitiveness in solution space. Six neighborhood search operators are designed. They are used as variable neighborhood search strategy. Computational experiments show that SFMEA-AP can obtain better solution quality than SFMEA-VNS, QMOEA, NSGA-II, ILS and LSMOVRPTW. The IGD values of non-dominated solutions of SFMEA-AP are better than those of SFMEA-VNS, QMOEA, NSGA-II, ILS and LSMOVRPTW. In addition, the non-dominated solution set of SFMEA-AP have good diversity.

Factors affecting the final solution of the bike-sharing rebalancing problem under heuristic algorithms

The bike-sharing rebalancing problem (BRP) belongs to a class of one-commodity pickup and delivery vehicle route problems (1-PDVRPs) which often must be solved using heuristic algorithms due to the large problem size. However, an open question is which factors affect the quality of the final solutions for the BRP with heuristic algorithms, and how they affect the solution quality. This study proposed six initial solution construction methods and two heuristic algorithms, and applied 32 instances to explore this question in greater depth. The results showed that problem size and the algorithms' searching capacity are the most important factors affecting the quality of final solutions. Furthermore, the influence of the quality and diversity of initial solutions cannot be ignored. The quality of final solutions is negatively correlated with problem size, and positively correlated with the algorithms' searching capacity, and the quality and diversity of initial solutions. The influence of the quality and diversity of initial solutions on the quality of final solutions is positively correlated with problem size. For algorithms with insufficient (powerful) searching capacity, the influence of the quality (diversity) of initial solutions is more significant than that of their diversity (quality). High-quality and rich-diversity initial solutions are very helpful for algorithms to find high-quality final solutions. In addition, the CPU time of heuristic algorithms is generally positively correlated with their searching capacity. These findings have certain universal applicability and reference value for solving the 1-PDVRPs with similar solution structures using heuristic algorithms.

Hybrid Heuristic for the Multi-Depot Static Bike Rebalancing and Collection Problem

The bike rebalancing problem is one of the major operational challenges in the urban bike-sharing system, which involves the redistribution of bikes among stations to prevent stations from being empty or overloaded. This paper investigates a new bike rebalancing problem, which considers the collection of broken bikes in the multi-depot system. The proposed problem can be classified as a two-commodity vehicle routing problem with pick-up and delivery. An integer programming model is formulated to find the optimal vehicle assignment and visiting sequences with the minimum total working time and fixed cost of vehicles. A hybrid heuristic algorithm integrating variable neighborhood search and dynamic programming is proposed to solve the problem. The computational results show that the proposed method can find 26 best solutions out of 36 instances, while the CPLEX obtains 16 best solutions. Impact of broken bikes collection and distribution of depots is examined. Comparison of different practical strategies indicates that the number of vehicles can be significantly reduced by allowing multiple visits to depots. Allowing vehicles to return to different depots can help reduce the total working time.

Rebalancing and Charging Scheduling With Price Incentives for Car Sharing Systems

This paper studies the joint problem of optimal pricing, charging scheduling and rebalancing for one-way car sharing systems. Firstly, a price driven customers travel mechanism is given which represents the customers ride demand as a linear function of the ride price. Then, a joint framework ensuring load balance and profit maximization of the system is introduced, in which the migration of vehicles and customers in the system is captured by fluid models, while the charging procedure of electric vehicles in the charging stations is described by multi-server queues. The well-posedness and equilibrium of the fluid model are analyzed, which yields the minimum fleet size needed. Next, a rebalancing method is derived to maximize the operating income while the stations operate at an equilibrium state, i.e., vehicles available and no waiting customers. To make the system better adapt to the changing customers demand in highly dynamic environments, a real-time rebalancing policy is developed by introducing a customer arrival predicting scheme based on exponential smoothing. Numerical experiments and case studies in Chengdu show that the proposed method can significantly improve the quality of service and rebalancing performance.

Network Rebalance and Operational Efficiency of Sharing Transportation System: Multi-Objective Optimization and Model Predictive Control Approaches

Sharing transportation systems can significantly promote travelers convenience and efficiency. As a vital part, bike-sharing system (BSS) has effectively solved “the-last-mile” problem during transportation interchange, but bike imbalance between docks severely deteriorates operational efficiency of BSS. In this paper, we present multi-objective optimization and predictive control approaches to tackle the bike rebalancing problem, where optimal redistributing strategies can maximize the operational efficiency of BSS with respects to equilibrium state and redistribution cost. A dock-based BSS dynamic network is modeled based on a proximity graph, in which connection relation, bike usage, and redistribution flow are formulated. To measure the operational efficiency, a performance metric is presented to consider both benefits of user and operator. To satisfy bike renting, returning, and redistributing requirements, model predictive control (MPC) is then employed to compute feasible and optimal redistribution strategies based on the network model. The effectiveness of multi-objective optimization and MPC is verified on different topologies of BSS. Experimental results show that when the BSS reaches the equilibrium state, the operational efficiency will be maximized in the proposed approaches.

A holistic approach for modeling and predicting bike demand

Bike-sharing systems have enjoyed tremendous success in many major cities around the world today as a new means of urban public transportation offering a green and facile solution for daily commuters and tourists. One common problem featured in these systems is that the distribution of bikes among stations can be quite uneven, due to various factors including topography, location of dockings, hours of service, safety and security, weather, rush hours or even during the occurrence of major events around the city. Such imbalances often result in shortage of bikes or bike parking racks. An unbalanced bike system indicates an unreliable form of transportation and disappointed users. Current studies in the literature are limited as they are not designed to handle fluctuating, high or unpredictable demand during large city events that typically affect multiple stations and require real-time rebalancing, during the event, to ensure seamless operation. In this work we solve the bike rebalancing problem while considering fluctuating demand that leads to an imbalance between supply and demand. We present “SmartBIKER”, a holistic and cost-effective framework for bike sharing systems addressing both normal operation and operation during major city events. SmartBIKER models bike demand during both normal operation and major events, identifies bike stations with low or high demand using two different forecasting models and determines a relocation strategy that maximizes the utility of the stations while minimizing the relocation cost. Our experimental evaluation shows that our approach is practical, efficient and outperforms state-of-the-art relocation and prediction schemes.

Branch-and-Price-and-Cut for the Heterogeneous Fleet and Multi-Depot Static Bike Rebalancing Problem with Split Load

Heterogeneous Fleet and Multi-Depot Static Bike Rebalancing Problem with Split Load (HFMDSBRP-SD) is an extension of the Static Bike Rebalancing Problem, considering heterogeneous fleet multiple depots, allowing split load. It consists of finding a set of least-cost repositioning vehicle routes and determining each station’s pickup or delivery quantity to satisfy the demand of each station. We develop a branch-and-price-and-cut (BPC) where a tabu search column generator and a heuristic label-setting algorithm are introduced to accelerate the column generation procedure, the subset-row (SR) inequalities, the strong minimum number of vehicles (SMV) inequalities, and the enhanced elementary inequalities are extended fitting this problem and applied to speed up the global convergence rate. Computational results demonstrate the effectiveness of the BPC algorithm. Among 360 instances with a maximum size of 30, there are 298 instances capable of achieving optimality within two hour time limitation.

A Modular and Transferable Reinforcement Learning Framework for the Fleet Rebalancing Problem

Mobility on demand (MoD) systems show great promise in realizing flexible and efficient urban transportation. However, significant technical challenges arise from operational decision making associated with MoD vehicle dispatch and fleet rebalancing. For this reason, operators tend to employ simplified algorithms that have been demonstrated to work well in a particular setting. To help bridge the gap between novel and existing methods, we propose a modular framework for fleet rebalancing based on model-free reinforcement learning (RL) that can leverage an existing dispatch method to minimize system cost. In particular, by treating dispatch as part of the environment dynamics, a centralized agent can learn to intermittently direct the dispatcher to reposition free vehicles and mitigate against fleet imbalance. We formulate RL state and action spaces as distributions over a grid partitioning of the operating area, making the framework scalable and avoiding the complexities associated with multiagent RL. Numerical experiments, using real-world trip and network data, demonstrate that this approach has several distinct advantages over baseline methods including: improved system cost; high degree of adaptability to the selected dispatch method; and the ability to perform scale-invariant transfer learning between problem instances with similar vehicle and request distributions.

Bike-sharing rebalancing problem by considering availability and accessibility

This paper presents an extended study of the bike-sharing rebalancing problem by considering the impact of availability (the likelihood of successfully finding a bike) and accessibility (the walking distance required to reach a bike) on user demand. The problem is formulated into a Mixed Integer Linear Program (MILP) model with the objective of maximising the net profit for the time horizon. Numerical studies were conducted to demonstrate the impact of availability and accessibility on the net profit of the bike-sharing company and the carbon dioxide emissions of the transit vehicles and buses. The results show that by considering the effects of availability and accessibility, the operator can both make more net profit and reduce potential carbon dioxide emissions. Besides, the potential demand coverage also increases. Furthermore, the results show that increasing vehicle capacity can increase net profit and reduce total potential carbon dioxide emissions to a certain extent.

Practical method to improve usage efficiency of bike‐sharing systems

Bicycle- or bike-sharing systems (BSSs) have received increasing attention as a secondary transportation mode due to their advantages, for example, accessibility, prevention of air pollution, and health promotion. However, in BSSs, due to bias in bike demands, the bike rebalancing problem should be solved. Various methods have been proposed to solve this problem; however, it is difficult to apply such methods to small cities because bike demand is sparse, and there are many practical issues to solve. Thus, we propose a demand prediction model using multiple classifiers, time grouping, categorization, weather analysis, and station correlation information. In addition, we analyze real-world relocation data by relocation managers and propose a relocation algorithm based on the analytical results to solve the bike rebalancing problem. The proposed system is compared experimentally with the results obtained by the real relocation managers.

Mean–Variance Portfolio Efficiency under Leverage Aversion and Trading Impact

This paper addresses the optimal rebalancing problem of a long–short portfolio with high net asset value under trading impact losses. The fund manager may employ leveraging as a tool to increase portfolio returns. However, to mitigate potential leverage risks, frequent rebalancing may become necessary, which leads to significant slippage losses that dampen portfolio performance ex post. We consider the problem in an integrated framework by incorporating trading impact and leverage restrictions ex ante within a mean–variance framework, where leverage control is imposed using a chance constraint. The resulting mean–variance–leverage optimization model (MVL) is non-convex, and we develop an efficient scheme to obtain the optimal portfolio. We investigate how portfolio leverage modifies the MV efficient frontier in the presence of trading impact, and highlight the significant outperformance of the proposed model relative to the standard mean–variance model. Increased target means require less restrictions on leverage, which result in higher rates of slippage losses. Our analysis supports the notion that leverage restrictions contribute to choosing high beta assets, even in the presence of trading impact.

A New Intelligent Rebalancing Management Method for Multiperiod and Multiobjective Bike-Sharing System Based on Machine Learning-Enabled Signal Processing Techniques

With the rapid development of information technology, the sharing economy has developed rapidly all over the world as a new mode of distributing business profit, among which the bike-sharing system (BSS) has become popular in many cities because of its low cost, convenience, and environmental protection. The application of the 5th generation mobile communication technology (5G) in BSS makes users to search the bikes more accurately and quickly and enables operators to spot noncompliant bike sharing as soon as possible, significantly improving the efficiency of bike-sharing management. However, one of the thorny issues for operators is the bike-sharing rebalancing problem (BRP). It is the key to improve the efficiency of rebalancing, reduce the rebalancing cost, and realize the sustainable development of BSS on how to excavate the huge amount of customer cycling data, respond quickly to customer demand, and use intelligence optimization algorithm to rebalance bikes among stations. However, most of the previous studies dealt with only one period BRP and rarely considered multiperiod issues. At the same time, most researches have focused on minimizing the total cost or time of rebalancing or customer dissatisfaction, but few have aimed at minimizing the rebalancing amount. In addition, the demand gap can reflect the real rental and returning requirements of customers over a certain period of time, which is rarely considered in solving BRP. First of all, this paper presents a multiperiod and multiobjective bike-sharing rebalancing problem (MMBRP). Secondly, a mathematical model is formulated with the objective of minimizing both the total rebalancing cost and amount. In order to solve MMBRP, an improved multiobjective backtracking search genetic algorithm (IMBSGA) is designed. Finally, the effectiveness and competitiveness of IMBSGA in solving MMBRP are verified by numerous experiments comparing with state-of-the-art algorithms.

Bike-Sharing Fleet Allocation Optimization Based on Demand Gap and Cycle Rebalancing Strategies

In Bike-Sharing System (BSS), the initial number of bikes at station will affect the time interval and the amount of rebalancing, which is usually empirically determined and does not reflect the characteristics of consumer demand in finer time granularity, thus possibly leading to biased conclusions. In this paper, a fleet allocation method considering demand gap is first proposed to calculate the initial number of bikes at each station. Then, taking the number of demand gap periods as the decision variable, an optimization model is built to minimize the total rebalancing amount. Furthermore, the research periods are divided into multiple subcycles, the single-cycle and multicycle rebalancing strategies are presented, and the additional subcycle rebalancing method is introduced to amend the number of bikes between subcycles to decrease the rebalancing amount of the next subcycle. Finally, our methods are verified in effectively decreasing the rebalancing amount in a long-term rebalancing problem.

Real-Time Vehicle Relocation and Staff Rebalancing Problem for Electric and Shared Vehicle Systems

Real-Time Vehicle Relocation and Staff Rebalancing Problem for Electric and Shared Vehicle Systems

Static bike repositioning problem with heterogeneous distribution characteristics in bike sharing systems

Bike sharing is one of the recent trends in urban areas as a solution for the mobility problem, where it is seen as a significant component of local transportation due to the need to ensure last-mile transportation. Bike sharing systems enable bicycles to be rented at a station for a ride and be dropped off at another station which provides flexibility to users. However, incorporating a bike sharing system into the transportation network of a city involves its own challenges including balancing the supply and demand within stations, and scheduling bikes’ repositioning.The bike repositioning scheduling problem arises due to the variable demand for various types of bicycles that can be rented from and left to any station. In order to ensure sustainability in bike sharing operations, bikes should be redistributed to the stations considering the demand, during for example a day or night. In this context, with the ultimate motivation of proposing a bike sharing system to meet within-day demand dynamics in a metropolitan city, we address the Static Bike sharing Rebalancing Problem (SBRP) with multiple capacitated vehicles for redistribution of bicycles. On purpose, we formulate a mixed-integer linear program in which the objective is minimizing the total cost subject to a set of constraints including truck capacity, demand satisfaction, inventory balance, and flow preservation. We have obtained the results from solutions to the SBRP through a real case study discussing the tendency on bike sharing systems before and during Covid-19 pandemic, in which total distance traveled according to the repositioning schemes for different months in a year, repositioning, and the truck type requirements for different days in a week, and the unsatisfied demand concerning the actual demands are analyzed. Computational experiments have shown that the distance traveled by trucks varies for the days of the week in different months of the year depending on the change in demand.

Bike sharing rebalancing problem with variable demand

This paper investigates an extended bike-sharing rebalancing problem called the bike-sharing rebalancing problem with variable demand (BRPVD), which considers the influence of the number of bikes distributed by the operator on users’ demand. The solutions to the BRPVD aim at maximizing the profit of bike-sharing operators by making routing plans of transport vehicles and determining the target number of bikes at each station after redistribution operation. The problem is modeled as a mixed-integer non-linear programming model and is linearized into a mixed-inter linear programming model. The model is tested in cases adopting real Beijing Mobike data, revealing that the rebalancing behavior significantly impacts users’ demand, hence guiding the operator.