“第三方代管”参与下的共享单车回收路线优化问题

以共享单车回收为背景,研究了“第三方代管”参与下的回收路线优化问题。针对代管员和调度卡车的特征,提出激励代管员将零散分布的损坏单车运送至附近的中转点,然后派遣卡车将这些集中起来的损坏单车从中转点运送至维修中心。以总成本最小为目标建立混合整数规划模型,针对问题特性设计改进遗传算法。数值实验论证了问题特性,并论证得出在所提回收策略下及时回收损坏单车,不仅可以减轻公共空间被损坏单车挤占的问题,还可以有效减少回收成本。实验结果还表明所设计算法在短时间内能获得高质量解。     

考虑多仓库的共享单车重新配置问题研究

共享单车是我国大力提倡的低碳交通出行模式,加快共享单车发展是解决最后一公里、城市拥堵和环境污染等问题的重要途径。由于人们停放共享单车的无规律性,使得共享单车系统中各车桩的单车库存量存在不平衡。如何合理的对车桩中的单车进行重新调配,来满足用户的需求,是相关企业亟待解决的问题。共享单车的调配路线优化是优化车桩库存量的重要手段之一。本文研究多仓库条件下的货车调配路线优化问题,建立了一个混合整数非线性规划模型。不同于传统的路径优化问题的研究大多是以成本或时间为目标,本文采用基于车桩库存量的非线性惩罚函数来表示用户需求,从而使得所研究的问题是一个凸函数优化问题。为了简化本文的问题,将目标函数分段线性化。基于车桩网络的特点,设计了变邻域搜索算法,以及构建初始解的贪婪算法。最后,以某共享单车公司为例,进行算例分析,来说明模型和算法的合理性和有效性。     

共享单车调度优化问题研究

针对共享单车站点经常出现的供需不平衡问题,提出人工调度策略,以提高单车利用率和用户满足率.首先将一天划分为几个用车高峰时段,根据每个站点的单车使用历史数据,计算各站点在每个时段的需求量区间;在区域内单车总投放量不变的前提下,基于每个时段初期各个站点存放的单车数量,确定单车调出站点和单车调入站点,进一步以站点之间的单车调度数量为决策变量,建立共享单车调度问题的整数规划模型,使区域内各个单车站点的供需量基本达到平衡,并且总调度成本最小.利用北京市海淀区共享单车数据进行模拟计算,对比分析了调度优化前后的共享单车利用率和用户满足率.结果显示,调度优化后,单车利用率平均提高7.78%,用户满足率平均提高13.09%;综合考虑企业调度成本和收入情况可以发现,通过调度优化,企业的平均利润增长率为7.53%.本文的研究结果可以帮助共享单车企业提升管理水平,增加利润.     

多类型公共自行车调运问题

公共自行车是我国正大力发展的低碳交通出行模式,加强公共自行车调运优化是提升自行车出行吸引力的关键要素。通过对公共自行车调运背景分析,提出了一类多类型公共自行车的调运优化问题。针对现实生活中租赁站点内公共自行车不均衡的情况,建立了以总成本最小为目标的混合整数线性规划模型,并提出一种改进的混合禁忌搜索对问题进行求解。通过数值实验分析了问题特性并验证了算法性能。实验结果表明非均衡惩罚系数决定了租赁站点各类自行车的装卸载数量,并影响了调配车辆的运行路线,是实现多类型公共自行车均衡优化的关键因素。不同类型自行车的替代策略使得调运决策更加灵活。混合禁忌搜索可以求解更大规模的问题,并能在短时间内求得较好质量的解。     

A two-phase heuristic approach to the bike repositioning problem

An approach to overcome the bike imbalance problem is to transfer excess bikes to branches with bike shortages. This study develops a constrained mathematical model to deal with a multi-vehicle bike-repositioning problem, and aims to minimize the sum of transportation and unmet demand costs over a planning horizon through bike-transfer strategies under a minimum service requirement. A two-phase heuristic based on linear programming was proposed to solve the problem and produce compromising solutions. In the first phase, the paper developed a linear programming model to quickly develop decisions related to bike inventory, unloading, and loading for all stations for each time slot. In the second phase, this paper proposed an iterative approach through two parameter sensitive mathematical models to sequentially reduce the problem scale to develop decisions related to bike transfers. Computational results show that the proposed approach is superior to a CPLEX optimizer and a hybrid heuristic based on a genetic algorithm. The proposed approach was used to analyze the bicycle system in Taiwan. The impacts of various system parameters on the system were also investigated.     

A multi-periodic optimization formulation for bike planning and bike utilization

The number of policy initiatives to promote the use of bike, or the combined use of bicycle and public transport for one trip, has grown considerably over the past decade as part of the search for more sustainable transport solutions. This paper presents an optimization formulation to design a bike-sharing system for travel inside small communities, or as a means to extend public transport for access and egress trips. The mathematical model attempts to optimize a bike-sharing system by determining the minimum required bike fleet size that minimizes simultaneously unmet demand, unutilized bikes, and the need to transport empty bikes between rental stations to meet demand. The proposed approach is applied to an example problem and is shown to be successful, ultimately providing a new managerial tool for planning and analyzing bike utilization more effectively.     

Multiple pickup and delivery traveling salesman problem with last-in-first-out loading and distance constraints

We extend the traveling salesman problem with pickup and delivery and LIFO loading (TSPPDL) by considering two additional factors, namely the use of multiple vehicles and a limitation on the total distance that a vehicle can travel; both of these factors occur commonly in practice. We call the resultant problem the multiple pickup and delivery traveling salesman problem with LIFO loading and distance constraints (MTSPPD-LD). This paper presents a thorough preliminary investigation of the MTSPPD-LD. We propose six new neighborhood operators for the problem that can be used in search heuristics or meta-heuristics. We also devise a two-stage approach for solving the problem, where the first stage focuses on minimizing the number of vehicles required and the second stage minimizes the total travel distance. We consider two possible approaches for the first stage (simulated annealing and ejection pool) and two for the second stage (variable neighborhood search and probabilistic tabu search). Our computational results serve as benchmarks for future researchers on the problem.     

Centralized and distributed cooperative Receding Horizon control of autonomous vehicle missions

We consider a setting where multiple vehicles form a team cooperating to visit multiple target points and collect rewards associated with them. The team objective is to maximize the total reward accumulated over a given time interval. Complicating factors include uncertainties regarding the locations of target points and the effectiveness of collecting rewards, differences among vehicle capabilities, and the fact that rewards are time-varying. We present a Receding Horizon (RH) control scheme which dynamically determines vehicle trajectories by solving a sequence of optimization problems over a planning horizon and executing them over a shorter action horizon. A key property of this scheme is that the trajectories it generates are stationary, in the sense that they ultimately guide vehicles to target points, even though the controller is not designed to perform any discrete point assignments. The proposed scheme is centralized and it induces a cooperative behavior. We subsequently develop a distributed cooperative controller which does not require a vehicle to maintain perfect information on the entire team and whose computational cost is scalable and significantly lower than the centralized case, making it attractive for applications with real-time constraints. We include simulation-based comparisons between the centralized algorithm and the distributed version, which illustrate the effectiveness of the latter.     

Effectiveness-based Voronoi partition: a new tool for solving a class of location optimization problems

In this article we provide a framework for optimal placement or deployment of facilities in a region of interest. We present a generalization of Voronoi partition, where functions modeling the effectiveness of facilities are used in the place of the usual distance measure used in the standard Voronoi partition and its variations. We illustrate the usefulness of the generalization in designing strategies for optimal deployment of multiple vehicles equipped with sensors, optimal placement of base stations in a cellular network design problem, and locational optimization of power plants.     

Routing a mix of conventional,plug-in hybrid,and electric vehicles

We introduce an electric vehicle routing problem combining conventional, plug-in hybrid, and electric vehicles. Electric vehicles are constrained in their service range by their battery capacity, and may require time-consuming recharging operations at some specific locations. Plug-in hybrid vehicles have two engines, an internal combustion engine and an electric engine using a built-in rechargeable battery. These vehicles can avoid visits to recharging stations by switching to fossil fuel. However, this flexibility comes at the price of a generally higher consumption rate and utility cost.To solve this complex problem variant, we design a sophisticated metaheuristic which combines a genetic algorithm with local and large neighborhood search. All route evaluations, within the approach, are based on a layered optimization algorithm which combines labeling techniques and greedy evaluation policies to insert recharging stations visits in a fixed trip and select the fuel types. The metaheuristic is finally hybridized with an integer programming solver, over a set partitioning formulation, so as to recombine high-quality routes from the search history into better solutions. Extensive experimental analyses are conducted, highlighting the good performance of the algorithm and the contribution of each of its main components. Finally, we investigate the impact of fuel and energy cost on fleet composition decisions. Our experiments show that a careful use of a mixed fleet can significantly reduce operational costs in a large variety of price scenarios, in comparison with the use of a fleet composed of a single vehicle class.     

Charging scheduling problem of an M-to-N electric vehicle charger

This study investigates a real case of charging scheduling of an electric vehicle charger with multiple ports called M-to-N charger. The charger is designed for a multi-unit dwelling facility and can charge N electric vehicles simultaneously despite the supplied charging capacity being limited to only M electric vehicles. The electric vehicles arrive at the charger randomly and stay for their desired length of time, during which they must be charged as much as possible with minimum electric cost. The scheduling problem considers four objectives: maximizing the total charging amount, minimizing the total charging cost, minimizing the charging completion time, and maximizing the charging balance among the electric vehicles. A mixed-integer linear programming model and a relaxation-based heuristic algorithm are developed. Computational experiment results show that the proposed heuristic algorithm can generate schedules within 8 s for this case study by using an open-source linear programming solver. Compared with the mixed-integer programming algorithm, the proposed heuristic algorithm can provide solutions with less than 7% charging amount gap and 4% price gap. The proposed heuristic algorithm is successfully implemented in a real M-to-N charger.     

Locating replenishment stations for electric vehicles: application to Danish traffic data

Environment-friendly electric vehicles have gained popularity and increased attention in recent years. The deployment of a network of recharging stations is essential given their limited travel range. This paper considers the problem of locating electronic replenishment stations for electric vehicles on a traffic network with flow-based demand. The objective is to optimize the network performance, for example to maximize the flow covered by a prefixed number of stations or to minimize the number of stations needed to cover traffic flows. Two integer linear programming formulations are proposed to model the problem. These models are tested on real-life traffic data collected in Denmark.     

Dynamic repositioning strategy in a bike-sharing system; how to prioritize and how to rebalance a bike station

Bike-sharing systems are becoming increasingly popular in large cities. The natural imbalance and the stochasticity of bike’s arrivals and departures lead operators to develop redistribution strategies in order to ensure a sufficiently high quality of service for users. Using a Markov decision process approach, we develop an implementable decision-support tool which may help the operator to decide at any point of time (i) which station should be prioritized, and (ii) which number of bikes should be added or removed at each station. Our objective is to minimize the rate of arrival of unsatisfied users who find their station empty or full. The existence of an optimal inventory level at each station is proven. It may vary over time but does not depend on the capacity of the truck which operates the repositioning. Next, we compute the relative value function of the system, together with the average cost and the optimal state. These results are used to derive a policy for station’s prioritization using a one-step policy improvement method. We evaluate our policy in comparison with the optimal one and with other intuitive ones in an extended version of our model. From our numerical experiments, we show that only a little intervention of the operator can significantly enhance the quality of service, and that the rule of thumb for bike repositioning is to prioritize the closer, the more active, the closer to be full or empty, and the more imbalanced stations if no reversing in the imbalance is anticipated.     

Adapting the ng-path relaxation for bike balancing problems

This paper deals with a static bike relocation problem that deploys a fleet of vehicles to redistribute shared bicycles. To solve the problem to optimality, we present a branch-price-and-cut algorithm. In particular, a new path relaxation for the pricing problem is introduced that relaxes the constraints on the maximum number of bikes to move at each station in a similar fashion as elementary can be relaxed in vehicle routing problems. Computational results show that our algorithm outperforms the former state-of-the-art.     

An arc cover–path-cover formulation and strategic analysis of alternative-fuel station locations

In this study, we present a new formulation of the generalized flow-refueling location model that takes vehicle range and trips between origin–destination pairs into account. The new formulation, based on covering the arcs that comprise each path, is more computationally efficient than previous formulations or heuristics. Next, we use the new formulation to provide managerial insights for some key concerns of the industry, such as: whether infrastructure deployment should focus on locating clusters of facilities serving independent regions or connecting these regions by network of facilities; what is the impact of uncertainty in the origin–destination demand forecast; whether station locations will remain optimal as higher-range vehicles are introduced; and whether infrastructure developers should be willing to pay more for stations at higher-cost intersections. Experiments with real and random data sets are encouraging for the industry, as optimal locations tend to be robust under various conditions.     

Minimizing the number of workers in a paced mixed-model assembly line

We study a problem of minimizing the maximum number of identical workers over all cycles of a paced assembly line comprised of m stations and executing n parts of k types. There are lower and upper bounds on the workforce requirements and the cycle time constraints. We show that this problem is equivalent to the same problem without the cycle time constraints and with fixed workforce requirements. We prove that the problem is NP-hard in the strong sense if $m=4$ and the workforce requirements are station independent, and present an Integer Linear Programming model, an enumeration algorithm and a dynamic programming algorithm. Polynomial in k and polynomial in n algorithms for special cases with two part types or two stations are also given. Relations to the Bottleneck Traveling Salesman Problem and its generalizations are discussed.     

Dynamic control of a flexible server in an assembly-type queue with setup costs

We consider a queueing system with multiple stations attended by a single flexible server. An order arriving at this system needs to go through each station only once but there is no particular precedence relationship among these stations. One can also think of this system as an assembly system where each station processes a different component of an order and once all the components associated with an order are processed they are assembled instantaneously. A holding cost is charged for keeping the orders in the system and there is a penalty associated with the switches of the server between stations. Our objective is to minimize the long-run average costs by dynamically assigning the server to stations based on the system state. Using sample-path arguments, we provide partial characterizations of the optimal policy and provide sufficient conditions under which a simple state-independent policy that works on one order at a time is optimal. We also propose three simple threshold policies and present a numerical study that provides supporting evidence for the superior performance of our double-threshold heuristic.     

Exact algorithms for the vehicle routing problem,based on spanning tree and shortest path relaxations

We consider the problem of routing vehicles stationed at a central facility (depot) to supply customers with known demands, in such a way as to minimize the total distance travelled. The problem is referred to as the vehicle routing problem (VRP) and is a generalization of the multiple travelling salesman problem that has many practical applications. We present tree search algorithms for the exact solution of the VRP incorporating lower bounds computed from (i) shortest spanningk-degree centre tree (k-DCT), and (ii)q-routes. The final algorithms also include problem reduction and dominance tests. Computational results are presented for a number of problems derived from the literature. The results show that the bounds derived from theq-routes are superior to those fromk-DCT and that VRPs of up to about 25 customers can be solved exactly.     

A robust counterpart approach to the bi-objective emergency medical service design problem

The paper presents a bi-objective robust program to design a cost-responsiveness efficient emergency medical services (EMS) system under uncertainty. The proposed model simultaneously determines the location of EMS stations, the assignment of demand areas to EMS stations, and the number of EMS vehicles at each station to balance cost and responsiveness. We develop a robust counterpart approach to cope with the uncertain parameters in the EMS system. Extensive numerical studies are performed to demonstrate the benefits of our robust optimization approach.     

The Geometry of Railway Geometric Overthrow Revisited Using Computer Algebra Methods

There are size standards for railway coaches and freight wagons in order to allow trains to pass from one railway line or even network to another. The maximum size and shape of the rolling stock is denoted gauge. On curves, vehicles sweep a larger path than on straight track. We shall focus on the geometric overthrow of the different kind of rolling stock (the geometric overthrow is that part of the vehicle element offset which is due to the track curve). We shall detail the influence of the kind of vehicle (two axles, classic bogies, shared bogies or Talgo vehicles) in the geometric overthrow. The computations can be easily carried out with a computer algebra system such as Maple and some curious results are obtained (for instance, a negative value (!) is obtained for Talgo coaches).