Bike Sharing Rebalancing Problem Research Articles

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.

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.

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.

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.

Reducing CO2 emissions from the rebalancing operation of the bike-sharing system in Beijing

With the development of the bike-sharing system (BSS) and the introduction of green and low carbon development, the environmental impacts of BSS had received increasing attention in recent years. However, the emissions from the rebalancing of BSS, where fossil-fueled vehicles are commonly used, are usually neglected, which goes against the idea of green travel in a sharing economy. Previous studies on the bike-sharing rebalancing problem (BRP), which is considered NP-hard, have mainly focused on algorithm innovation instead of improving the solution model, thereby hindering the application of many existing models in large-scale BRP. This study then proposes a method for optimizing the CO2 emissions from BRP and takes the BSS of Beijing as a demonstration. We initially analyze the spatial and temporal characteristics of BSS, especially the flow between districts, and find that each district can be independently rebalanced. Afterward, we develop a rebalancing optimization model based on a partitioning strategy to avoid deciding the number of bikes being loaded or unloaded at each parking node. We then employ the tabu search algorithm to solve the model. Results show that (i) due to over launch and lack of planning in rebalancing, the BSS in Beijing shows great potential for optimization, such as by reducing the number of vehicle routes, CO2 emissions, and unmet demands; (ii) the CO2 emissions of BSS in Beijing can be reduced by 57.5% by forming balanced parking nodes at the end of the day and decreasing the repetition of vehicle routes and the loads of vehicles; and (iii) the launch amounts of bikes in specific districts, such as Shijingshan and Mentougou, should be increased.

The Bike-Sharing Rebalancing Problem Considering Multi-Energy Mixed Fleets and Traffic Restrictions

Nowadays, as a low-carbon and sustainable transport mode bike-sharing systems are increasingly popular all over the world, as they can reduce road congestion and decrease greenhouse gas emissions. Aiming at the problem of the mismatch of bike supply and user demand, the operators have to transfer bikes from surplus stations to deficiency stations to redistribute them among stations by vehicles. In this paper, we consider a mixed fleet of electric vehicles and internal combustion vehicles as well as the traffic restrictions to the traditional vehicles in some metropolises. The mixed integer programming model is firstly established with the objective of minimizing the total rebalancing cost of the mixed fleet. Then, a simulated annealing algorithm enhanced with variable neighborhood structures is designed and applied to a set of randomly generated test instances. The computational results and sensitivity analysis indicate that the proposed algorithm can effectively reduce the total cost of rebalancing.

The Biobjective Bike-Sharing Rebalancing Problem with Balance Intervals: A Multistart Multiobjective Particle Swarm Optimization Algorithm

The bike-sharing system (BSS), as a sustainable way to deal with the “last mile” problem of mass transit systems, is increasingly popular in recent years. Despite its success, the BSS tends to suffer from the mismatch of bike supply and user demand. BSS operators have to transfer bikes from surplus stations to deficit stations to redistribute them among stations by means of trucks. In this paper, we deal with the bike-sharing rebalancing problem with balance intervals (BRP-BIs), which is a variant of the static bike-sharing rebalancing problem. In this problem, the equilibrium of station is characterized by a balance interval instead of a balance point in the literature. We formulate the BRP-BI as a biobjective mixed-integer programming model with the aim of determining both the minimum cost route for a single capacitated vehicle and the maximum average rebalance utility, an index for the balanced degree of station. Then, a multistart multiobjective particle swarm optimization (MS-MOPSO) algorithm is proposed to solve the model such that the Pareto optimal solutions can be derived. The proposed algorithm is extended with crossover operator and variable neighbourhood search to enhance its exploratory capability. Compared with Hybrid NSGA-II and MOPSO, the computational experimental results demonstrate that our MS-MOPSO can obtain Pareto optimal solutions with higher quality.

An effective memetic algorithm for the generalized bike-sharing rebalancing problem

The generalized bike-sharing rebalancing problem (BRP) entails driving a fleet of capacitated vehicles to rebalance bicycles among bike-sharing system stations at a minimum cost. To solve this NP-hard problem, we present a highly effective memetic algorithm that combines (i) a randomized greedy construction method for initial solution generation, (ii) a route-copy-based crossover operator for solution recombination, and (iii) an effective evolutionary local search for solution improvement integrating an adaptive randomized mutation procedure. Computational experiments on real-world benchmark instances indicate a remarkable performance of the proposed approach with an improvement in the best-known results (new upper bounds) in more than 46% of the cases. In terms of the computational efficiency, the proposed algorithm shows to be nearly two to six times faster when compared to the existing state-of-the-art heuristics. In addition to the generalized BRP, the algorithm can be easily adapted to solve the one-commodity pickup-and-delivery vehicle routing problem with distance constraints, as well as the multi-commodity many-to-many vehicle routing problem with simultaneous pickup and delivery.

An improved general variable neighborhood search for a static bike-sharing rebalancing problem considering the depot inventory

Smart shared mobility is an emerging transportation strategy that promotes sustainable and intelligent transportation. As one mode of smart shared mobility bike sharing is gaining popularity in recent years. A daily rebalancing operation is commonly carried out to keep high level service of bike-sharing systems (BSSs). The static bike-sharing rebalancing problems (SBRPs) studied in existing papers focus on determining the vehicle routes with minimal traveling cost. However, the depot inventory is rarely considered during the relocation. Thus, this paper researches the integration of the depot inventory and vehicle routing problems, with the aim of minimizing the daily operational cost including the depot inventory cost (DIC) and the traveling cost. First, two mixed integer programming (MIP) formulations are proposed to find the daily optimal decision on the vehicle routes and the numbers of bikes and vehicles employed from the depot. Based on the models, an improved general variable neighborhood search (IGVNS) algorithm is developed with a variety of neighborhood structures and a hybrid strategy. Finally, we apply a set of benchmark instances to test our proposed model and approach, and the computational results demonstrate that IGVNS can efficiently compute the SBRP and achieve lower operational cost than the existing solutions.

Tabu Search Algorithm for the Bike Sharing Rebalancing Problem

Bike sharing is a new form of transport and is becoming increasingly popular in cities around the world. In this article, we deal with the Bike Sharing Rebalancing Problem (BRP) which concerns the task of repositioning bikes among stations in self-service bike-sharing systems. We analyze its property of routes' feasible changes based insertion positions, which allow us to speed up the computation of our heuristics. Based on the speed up technique, we proposed the Capacity Range Length Heuristic (CRLH), which is a kind of classic heuristics for the BRP, and the Tabu Search Algorithm (TSA) for solving the BRP. We evaluated our algorithms on the instance sets of other literature reported. The CRLH is strongly improved the computational times on same computational environment, and the TSA also find the optimal solutions but holds lower computational times comparing to the reported results in the literature.

Inventory- Routing Mathematical Model in Transportation Fleet of a Bike Sharing Distribution Network

Todays' bike sharing system (BSS) as a non-motorised transportation system and compatible with the environment has attracted a lot of attention in the field of public transportation. One of the issues that has been considered by some researchers in recent years is bike sharing rebalancing problem that is related to the provision of the required bike for stations and their inventory management. The proposed model is an integer nonlinear programming that is able to rebalance BSS by considering the appropriate inventory policies. The purpose of this model is finding optimal routes for the fleet of vehicles (trucks) and using the suitable trucks to traverse these routes and minimising costs of rebalancing operations in multiple periods. The efficiency of the model is proved by solving two numerical examples by the GAMS software.

Distributed forecasting and ant colony optimization for the bike-sharing rebalancing problem with unserved demands.

Bike-sharing systems (BSS) have widely spread over many cities in the world as an environmentally friendly means to reduce air pollution and traffic congestion. This paper focuses on the bike-sharing rebalancing problem (BRP), which consists of two aspects: determining desired demands at each station and designing routes to redistribute bikes among stations. For the first task, we firstly apply the random forest, a very efficient machine learning algorithm, to forecast desired demands for each station, which can be easily implemented with distributed computing. For the second task, it belongs to the broad class of the vehicle routing problem with pickup and delivery (VRPPD). In most existing settings, all of the demands being strictly satisfied can lead to longer routes and add operational costs. In this paper, we propose a new model with unserved demands by relaxing demands satisfying constraints. Then, we design a distributed ant colony optimization (ACO) based algorithm with some specific modifications to increase its efficiency for the proposed model. We propose to use the percentage of average cost saving per bike as a metric to evaluate the performance of our method on cost-reducing and compare with existing methods and best-known values. Computational results on benchmarks show the advantage of our approach. Finally, we provide a real case study of BSS in Hangzhou, China, with insightful elaborations.

Rebalancing Bike Sharing Systems for Minimizing Depot Inventory and Traveling Costs

Smart shared mobility is an emerging transportation strategy that promotes sustainable and intelligent transportation. Bike sharing is one mode of smart shared mobility and is gaining popularity in recent years. To ensure a smooth operation of a bike sharing system (BSS), it is essential to redistribute the bicycles, which includes picking up returned bicycles and relocating them to best serve customers. A bike sharing rebalancing problem (BSRP) has thus emerged. This paper addresses a static BSRP which operates during the night when shared bikes are rarely utilized or when the BSS is closed. We studied a single-vehicle BSRP (sBSRP) and multi-vehicle BSRP (mBSRP) with the objective of minimizing the depot inventory cost as well as the traveling cost. For mBSRP, six formulations are presented i.e. five mixed integer programming models (mBSRP1-mBSRP5) and a mixed integer linear programming model (mBSRP6). In addition, an iterative procedure combined with the branch-and-cut algorithm in the CPLEX solver is developed to solve this problem. A real-world case study is employed to test the effectiveness of the formulations, and a set of benchmark instances are adopted to further compare the performances of mBSRP5 and mBSRP6. The experimental results show that mBSRP6 performs the best among the six models, offering the best solution quality and computational efficiency. Finally, mBSRP6 is applied to determine the depot inventory for the case study using random demand datasets.

The Static Bike Sharing Rebalancing Problem with Forbidden Temporary Operations

This paper introduces and solves the static bike rebalancing problem with forbidden temporary operations. In this problem, one aims at finding a minimum cost route in which a vehicle performs a series of pickup and delivery operations while satisfying demand and capacity constraints. In addition, a vehicle can visit stations multiple times but cannot use them to temporarily store or provide bikes. Apart from bike rebalancing, the problem also models courier service transportation and repositioning of inventory between retail stores, where temporary operations are frequently disliked because they require additional manual work and service time. We present some theoretical results concerning problem complexity and worst-case analysis, and then propose three exact algorithms based on different mathematical formulations. Extensive computational results on instances involving up to 80 stations show that an exact algorithm based on a minimal extended network produces the best average results. The online appendix is available at https://doi.org/10.1287/trsc.2018.0859 .

The Bike sharing Rebalancing Problem with Stochastic Demands

In this paper we deal with the stochastic version of a problem arising in the context of self-service bike sharing systems, which aims at determining minimum cost routes for a fleet of homogeneous vehicles in order to redistribute bikes among stations. The Bike sharing Rebalancing Problem with Stochastic Demands is a variant of the one-commodity many-to-many pickup and delivery vehicle routing problem where demands at each station are represented by random variables, with associated probability distributions, that depend on stochastic scenarios. We develop stochastic programming models that are solved using different approaches, in particular, the L-Shaped and branch-and-cut. Moreover, we also propose heuristic algorithms based on an innovative use of positive and negative correlations among stations’ stochastic demands, as well as an efficient strategy for checking feasibility. The proposed solution approaches are evaluated and compared by means of extensive computational experiments on newly realistic benchmark instances.

Developing a multi-commodity multi-period mathematical model based on the travelling salesman problem for solving bike sharing rebalancing problem

Developing a multi-commodity multi-period mathematical model based on the travelling salesman problem for solving bike sharing rebalancing problem

Developing a multi-commodity multi-period mathematical model based on the travelling salesman problem for solving bike sharing rebalancing problem

The rebalance problem in the bike sharing system includes operational decisions to respond to demand fluctuations in the kidneys Bicycle stations, so that by redistributing bikes among the stations...

A heuristic algorithm for a single vehicle static bike sharing rebalancing problem

The static bike rebalancing problem (SBRP) concerns the task of repositioning bikes among stations in self-service bike-sharing systems. This problem can be seen as a variant of the one-commodity pickup and delivery vehicle routing problem, where multiple visits are allowed to be performed at each station, i.e., the demand of a station is allowed to be split. Moreover, a vehicle may temporarily drop its load at a station, leaving it in excess or, alternatively, collect more bikes from a station (even all of them), thus leaving it in default. Both cases require further visits in order to meet the actual demands of such station. This paper deals with a particular case of the SBRP, in which only a single vehicle is available and the objective is to find a least-cost route that meets the demand of all stations and does not violate the minimum (zero) and maximum (vehicle capacity) load limits along the tour. Therefore, the number of bikes to be collected or delivered at each station must be appropriately determined in order to respect such constraints. We propose an iterated local search (ILS) based heuristic to solve the problem. The ILS algorithm was tested on 980 benchmark instances from the literature and the results obtained are competitive when compared to other existing methods. Moreover, our heuristic was capable of finding most of the known optimal solutions and also of improving the results on a number of open instances.

Models and algorithms for the optimization of real-world routing and logistics problems

Logistics involves planning, managing, and organizing the flows of goods from the point of origin to the point of destination in order to meet some requirements. Logistics and transportation aspects are very important and represent a relevant costs for producing and shipping companies, but also for public administration and private citizens. The optimization of resources and the improvement in the organization of operations is crucial for all branches of logistics, from the operation management to the transportation. As we will have the chance to see in this work, optimization techniques, models, and algorithms represent important methods to solve the always new and more complex problems arising in different segments of logistics. Many operation management and transportation problems are related to the optimization class of problems called Vehicle Routing Problems (VRPs). In this work, we consider several real-world deterministic and stochastic problems that are included in the wide class of the VRPs, and we solve them by means of exact and heuristic methods. We treat three classes of real-world routing and logistics problems. We deal with one of the most important tactical problems that arises in the managing of the bike sharing systems, that is the Bike sharing Rebalancing Problem (BRP). We propose models and algorithms for real-world earthwork optimization problems. We describe the 3DP process and we highlight several optimization issues in 3DP. Among those, we define the problem related to the tool path definition in the 3DP process, the 3D Routing Problem (3DRP), which is a generalization of the arc routing problem. We present an ILP model and several heuristic algorithms to solve the 3DRP.