An exact algorithm for the static rebalancing problem arising in bicycle sharing systems

Bicycle sharing systems can significantly reduce traffic, pollution, and the need for parking spaces in city centers. One of the keys to success for a bicycle sharing system is the efficiency of rebalancing operations, where the number of bicycles in each station has to be restored to its target value by a truck through pickup and delivery operations. The Static Bicycle Rebalancing Problem aims to determine a minimum cost sequence of stations to be visited by a single vehicle as well as the amount of bicycles to be collected or delivered at each station. Multiple visits to a station are allowed, as well as using stations as temporary storage. This paper presents an exact algorithm for the problem and results of computational tests on benchmark instances from the literature. The computational experiments show that instances with up to 60 stations can be solved to optimality within 2 hours of computing time

A dynamic approach to rebalancing bike-sharing systems

Bike-sharing services are flourishing in Smart Cities worldwide. They provide a low-cost and environment-friendly transportation alternative and help reduce traffic congestion. However, these new services are still under development, and several challenges need to be solved. A major problem is the management of rebalancing trucks in order to ensure that bikes and stalls in the docking stations are always available when needed, despite the fluctuations in the service demand. In this work, we propose a dynamic rebalancing strategy that exploits historical data to predict the network conditions and promptly act in case of necessity. We use Birth-Death Processes to model the stations' occupancy and decide when to redistribute bikes, and graph theory to select the rebalancing path and the stations involved. We validate the proposed framework on the data provided by New York City's bike-sharing system. The numerical simulations show that a dynamic strategy able to adapt to the fluctuating nature of the network outperforms rebalancing schemes based on a static schedule

실시간 동적 계획법 및 강화학습 기반의 공공자전거 시스템의 동적 재배치 전략

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 건설환경공학부, 2020. 8. 고승영.The public bicycle sharing system is one of the modes of transportation that can help to relieve several urban problems, such as traffic congestion and air pollution. Because users can pick up and return bicycles anytime and anywhere a station is located, pickup or return failure can occur due to the spatiotemporal imbalances in demand. To prevent system failures, the operator should establish an appropriate repositioning strategy. As the operator makes a decision based on the predicted demand information, the accuracy of forecasting demand is an essential factor. Due to the stochastic nature of demand, however, the occurrence of prediction errors is inevitable. This study develops a stochastic dynamic model that minimizes unmet demand for rebalancing public bicycle sharing systems, taking into account the stochastic demand and the dynamic characteristics of the system. Since the repositioning mechanism corresponds to the sequential decision-making problem, this study applies the Markov decision process to the problem. To solve the Markov decision process, a dynamic programming method, which decomposes complex problems into simple subproblems to derive an exact solution. However, as a set of states and actions of the Markov decision process become more extensive, the computational complexity increases and it is intractable to derive solutions. An approximate dynamic programming method is introduced to derive an approximate solution. Further, a reinforcement learning model is applied to obtain a feasible solution in a large-scale public bicycle network. It is assumed that the predicted demand is derived from the random forest, which is a kind of machine learning technique, and that the observed demand occurred along the Poisson distribution whose mean is the predicted demand to simulate the uncertainty of the future demand. Total unmet demand is used as a key performance indicator in this study. In this study, a repositioning strategy that quickly responds to the prediction error, which means the difference between the observed demand and the predicted demand, is developed and the effectiveness is assessed. Strategies developed in previous studies or applied in the field are also modeled and compared with the results to verify the effectiveness of the strategy. Besides, the effects of various safety buffers and safety stock are examined and appropriate strategies are suggested for each situation. As a result of the analysis, the repositioning effect by the developed strategy was improved compared to the benchmark strategies. In particular, the effect of a strategy focusing on stations with high prediction errors is similar to the effect of a strategy considering all stations, but the computation time can be further reduced. Through this study, the utilization and reliability of the public bicycle system can be improved through the efficient operation without expanding the infrastructure.공공자전거 시스템은 교통혼잡과 대기오염 등 여러 도시문제를 완화할 수 있는 교통수단이다. 대여소가 위치한 곳이면 언제 어디서든 이용자가 자전거를 이용할 수 있는 시스템의 특성상 수요의 시공간적 불균형으로 인해 대여 실패 또는 반납 실패가 발생한다. 시스템 실패를 예방하기 위해 운영자는 적절한 재배치 전략을 수립해야 한다. 운영자는 예측 수요 정보를 전제로 의사결정을 하므로 수요예측의 정확성이 중요한 요소이나, 수요의 불확실성으로 인해 예측 오차의 발생이 불가피하다. 본 연구의 목적은 공공자전거 수요의 불확실성과 시스템의 동적 특성을 고려하여 불만족 수요를 최소화하는 재배치 모형을 개발하는 것이다. 공공자전거 재배치 메커니즘은 순차적 의사결정 문제에 해당하므로, 본 연구에서는 순차적 의사결정 문제를 모형화할 수 있는 마르코프 결정 과정을 적용한다. 마르코프 결정 과정을 풀기 위해 복잡한 문제를 간단한 부문제로 분해하여 정확해를 도출하는 동적 계획법을 이용한다. 하지만 마르코프 결정 과정의 상태 집합과 결정 집합의 크기가 커지면 계산 복잡도가 증가하므로, 동적 계획법을 이용한 정확해를 도출할 수 없다. 이를 해결하기 위해 근사적 동적 계획법을 도입하여 근사해를 도출하며, 대규모 공공자전거 네트워크에서 가능해를 얻기 위해 강화학습 모형을 적용한다. 장래 공공자전거 이용수요의 불확실성을 모사하기 위해, 기계학습 기법의 일종인 random forest로 예측 수요를 도출하고, 예측 수요를 평균으로 하는 포아송 분포를 따라 수요를 확률적으로 발생시켰다. 본 연구에서는 관측 수요와 예측 수요 간의 차이인 예측오차에 빠르게 대응하는 재배치 전략을 개발하고 효과를 평가한다. 개발된 전략의 우수성을 검증하기 위해, 기존 연구의 재배치 전략 및 현실에서 적용되는 전략을 모형화하고 결과를 비교한다. 또한, 재고량의 안전 구간 및 안전재고량에 관한 민감도 분석을 수행하여 함의점을 제시한다. 개발된 전략의 효과를 분석한 결과, 기존 연구의 전략 및 현실에서 적용되는 전략보다 개선된 성능을 보이며, 특히 예측오차가 큰 대여소를 탐색하는 전략이 전체 대여소를 탐색하는 전략과 재배치 효과가 유사하면서도 계산시간을 절감할 수 있는 것으로 나타났다. 공공자전거 인프라를 확대하지 않고도 운영의 효율화를 통해 공공자전거 시스템의 이용률 및 신뢰성을 제고할 수 있고, 공공자전거 재배치에 관한 정책적 함의점을 제시한다는 점에서 본 연구의 의의가 있다.Chapter 1. Introduction １ 1.1 Research Background and Purposes １ 1.2 Research Scope and Procedure ７ Chapter 2. Literature Review １０ 2.1 Vehicle Routing Problems １０ 2.2 Bicycle Repositioning Problem １２ 2.3 Markov Decision Processes ２３ 2.4 Implications and Contributions ２６ Chapter 3. Model Formulation ２８ 3.1 Problem Definition ２８ 3.2 Markov Decision Processes ３４ 3.3 Demand Forecasting ４０ 3.4 Key Performance Indicator (KPI) ４５ Chapter 4. Solution Algorithms ４７ 4.1 Exact Solution Algorithm ４７ 4.2 Approximate Dynamic Programming ５０ 4.3 Reinforcement Learning Method ５２ Chapter 5. Numerical Example ５５ 5.1 Data Overview ５５ 5.2 Experimental Design ６１ 5.3 Algorithm Performance ６６ 5.4 Sensitivity Analysis ７４ 5.5 Large-scale Cases ７６ Chapter 6. Conclusions ８２ 6.1 Conclusions ８２ 6.2 Future Research ８３ References ８６ 초 록 ９２Docto

전기 마이크로 모빌리티 공유 시스템에서의 배터리 교체와 재배치 작업 최적화

학위논문 (석사) -- 서울대학교 대학원 : 공과대학 산업공학과, 2021. 2. 박건수.In this thesis, we consider a battery swapping and mobility inventory rebalancing problem arising in electric micro-mobility sharing systems. Vehicles are equipped with swappable batteries and they are managed by staffs' visiting each vehicle and changing depleted batteries. With the free-floating property of the system, vehicles can locate anywhere in a service area without designated stations, which increases the difficulty to visit and collect every single vehicle. In order to successfully meet user demand during the daytime, operators have to redistribute the vehicles with the right number in the right place and swap batteries with insufficient levels into fully charged ones overnight. Therefore, it is essential that operators take battery charging(swapping), staff routing, rebalancing problem all together into consideration. We aim to satisfy demand as much as possible and at the same time minimize routing and swapping costs. We formulate this problem in a mixed integer linear programming. Target inventory level for rebalancing, an important parameter used in the system, is suggested by analyzing a stochastic process that incorporates demand changes. Being a special case of vehicle routing problem with pickup and delivery, it shares the difficulty and complexity of VRP in practically large size. So as to give efficient solutions in large size problems, we develop a Cluster-first Route-second heuristic where a set partitioning problem considers inventory imbalances and approximates routing distances. We benchmark our heuristic approach on a pure MLIP formulation. The experimental result confirms that the heuristic is good at decomposing a large problem and gives efficient solutions even in practically large instances.본 연구는 교체형 배터리를 이용하는 전기 마이크로 모빌리티 공유 시스템에서의 배터리 교체 및 차량 재배치를 효율적으로 수행하는 방법을 제시하고자 한다. 수요를 성공적으로 충족시키기 위해선 모빌리티의 공급과 이용자의 수요를 맞춰주기 위한 차량 재고 차원에서의 재배치 작업과 배터리 수준을 유지시켜주는 배터리 관리 차원에서의 교체 작업이 필수적이다. 또한 충전소로 차량을 옮길 필요 없이 바로 교체할 수 있으므로 담당 직원이 산발적으로 위치한 각 모빌리티들을 순회하며 위 작업들을 진행해야 한다. 이동하며 작업하는 비용과 시간이 대부분이기 때문에 이동 순서를 함께 최적화하는 것이 비용 개선에 필수적이다. 따라서 작업 결정과 경로 결정을 동시에 고려하는 충전 및 재배치 모형을 제시한다. 이때 free-floating 모빌리티 공유시스템의 이용 수요를 효과적으로 반영하고자 수요를 stochastic process로 모델링하고 이를 이용하여 재배치 목표 수량을 구한다. 문제의 크기가 큰 경우 효율적으로 본 충전 및 재배치 모형의 좋은 해를 얻기 위한 방법으로, 해당 서비스지역의 각 구역들을 클러스터링하고 그 뒤에 스태프들의 경로와 작업을 결정하는 휴리스틱을 제안한다. 여러 스태프를 순회시키는 복잡한 형태를 클러스터링으로써 작은 크기의 문제들로 분해하여 빠르게 문제를 풀고자 한다. 이를 위해 각 클러스터에는 한 명의 스태프가 배정되고, 한 클러스터 내에서 소속된 구역들이 필요로 하는 작업들을 한 명의 스태프가 모두 진행하도록 구성한다. 최소걸침나무 근사법을 적용한 set partitioning 문제를 풀어 클러스터링을 진행한다. 계산실험 결과, 고안된 휴리스틱은 차량의 수가 많아 크기가 큰 상황에서도 빠른 시간내에 더 좋은 해를 냈다.Chapter 1. Introduction 1 1.1 Background 1 1.2 Related literature 6 1.2.1 Rebalancing in bike sharing systems 6 1.2.2 Charging and rebalancing in free-floating electric vehicle(FFEV) sharing 9 1.2.3 Charging of electric micro-mobility with swappable batteries 10 1.3 Motivation and contributions 12 1.4 Organization of the thesis 14 Chapter 2. Mathematical formulations 15 2.1 Basic assumptions and problem description 15 2.2 Demand Modeling and Target Inventory 18 2.3 Mixed integer linear programming formulation 23 Chapter 3. Heuristic approach 30 3.1 Cluster-first route-second approach 31 3.2 Clustering problem with routing cost approximation 33 3.2.1 Minimum spanning tree approximation 33 3.2.2 Clustering problem 35 3.2.3 Cluster-first Route-second heuristic 41 Chapter 4. Computational experiments 42 4.1 Design of experiment 42 4.2 Comparative Analysis 47 Chapter 5. Conclusion 52Maste

The Effects of Urban Density on the Efficiency of Dockless Bike Sharing System - A Case Study of Beijing, China

abstract: Bicycle sharing systems (BSS) operate on five continents, and they change quickly with technological innovations. The newest “dockless” systems eliminate both docks and stations, and have become popular in China since their launch in 2016. The rapid increase in dockless system use has exposed its drawbacks. Without the order imposed by docks and stations, bike parking has become problematic. In the areas of densest use, the central business districts of large cities, dockless systems have resulted in chaotic piling of bikes and need for frequent rebalancing of bikes to other locations. In low-density zones, on the other hand, it may be difficult for customers to find a bike, and bikes may go unused for long periods. Using big data from the Mobike BSS in Beijing, I analyzed the relationship between building density and the efficiency of dockless BSS. Density is negatively correlated with bicycle idle time, and positively correlated with rebalancing. Understanding the effects of density on BSS efficiency can help BSS operators and municipalities improve the operating efficiency of BSS, increase regional cycling volume, and solve the bicycle rebalancing problem in dockless systems. It can also be useful to cities considering what kind of BSS to adopt.Dissertation/ThesisMasters Thesis Urban and Environmental Planning 201

A Data-Driven Based Dynamic Rebalancing Methodology for Bike Sharing Systems

Mobility in cities is a fundamental asset and opens several problems in decision making and the creation of new services for citizens. In the last years, transportation sharing systems have been continuously growing. Among these, bike sharing systems became commonly adopted. There exist two different categories of bike sharing systems: station-based systems and free-floating services. In this paper, we concentrate our analyses on station-based systems. Such systems require periodic rebalancing operations to guarantee good quality of service and system usability by moving bicycles from full stations to empty stations. In particular, in this paper, we propose a dynamic bicycle rebalancing methodology based on frequent pattern mining and its implementation. The extracted patterns represent frequent unbalanced situations among nearby stations. They are used to predict upcoming critical statuses and plan the most effective rebalancing operations using an entirely data-driven approach. Experiments performed on real data of the Barcelona bike sharing system show the effectiveness of the proposed approach

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

A multiple type bike repositioning problem

This paper investigates a new static bicycle repositioning problem in which multiple types of bikes are considered. Some types of bikes that are in short supply at a station can be substituted by other types, whereas some types of bikes can occupy the spaces of other types in the vehicle during repositioning. These activities provide two new strategies, substitution and occupancy, which are examined in this paper. The problem is formulated as a mixed-integer linear programming problem to minimize the total cost, which consists of the route travel cost, penalties due to unmet demand, and penalties associated with the substitution and occupancy strategies. A combined hybrid genetic algorithm is proposed to solve this problem. This solution algorithm consists of (i) a modified version of a hybrid genetic search with adaptive diversity control to determine routing decisions and (ii) a proposed greedy heuristic to determine the loading and unloading instructions at each visited station and the substitution and occupancy strategies. The results show that the proposed method can provide high-quality solutions with short computing times. Using small examples, this paper also reveals problem properties and repositioning strategies in bike sharing systems with multiple types of bikes.published_or_final_versio

Toward Sustainability: Bike-Sharing Systems Design, Simulation and Management

The goal of this Special Issue is to discuss new challenges in the simulation and management problems of both traditional and innovative bike-sharing systems, to ultimately encourage the competitiveness and attractiveness of BSSs, and contribute to the further promotion of sustainable mobility. We have selected thirteen papers for publication in this Special Issue

Surrogate-based optimization of a periodic rescheduling algorithm

Periodic rescheduling is an iterative method for real-time decision-making on industrial process operations. The design of such methods involves high-level when-to-schedule and how-to-schedule decisions, the optimal choices of which depend on the operating environment. The evaluation of the choices typically requires computationally costly simulation of the process, which-if not sufficiently efficient-may result in a failure to deploy the system in practice. We propose the continuous control parameter choices, such as the re-optimization frequency and horizon length, to be determined using surrogate-based optimization. We demonstrate the method on real-time rebalancing of a bike sharing system. Our results on three test cases indicate that the method is useful in reducing the computational cost of optimizing an online algorithm in comparison to the full factorial sampling.Peer reviewe