A robust optimization approach for the capacitated vehicle routing problem with demand uncertainty

In this paper we introduce a robust optimization approach to solve the Vehicle Routing Problem (VRP) with demand uncertainty. This approach yields routes that minimize transportation costs while satisfying all demands in a given bounded uncertainty set. We show that for the Miller-Tucker-Zemlin formulation of the VRP and specific uncertainty sets, solving for the robust solution is no more difficult than solving a single deterministic VRP. Our computational results on benchmark instances and on families of clustered instances show that the robust solution can protect from unmet demand while incurring a small additional cost over deterministic optimal routes. This is most pronounced for clustered instances under moderate uncertainty, where remaining vehicle capacity is used to protect against variations within each cluster at a small additional cost. We compare the robust optimization model with classic stochastic VRP models for this problem to illustrate the differences and similarities between them. We also observe that the robust solution amounts to a clever management of the remaining vehicle capacity compared to uniformly and non-uniformly distributing this slack over the vehicles.     

A hybrid genetic algorithm for the multi-depot open vehicle routing problem

This paper studies the multi-depot open vehicle routing problem (MDOVRP), a variant of the vehicle routing problem (VRP), in which vehicles start from several depots and are not required to return to the depot. Despite the vast amount of literature about VRPs, the MDOVRP has received very little attention from researchers. In this paper, a new hybrid genetic algorithm is presented for finding the routes that minimize the traveling cost of the vehicles. Computational results on a number of test instances indicate the proposed algorithm dominates the CPLEX solver and the existing approach in the literature. Meanwhile, experiments are conducted on multi-depot VRP benchmarks, and the results are compared with a sophisticated tabu search approach and an exact method.     

求解VRP问题的混沌模拟退火萤火虫算法

目的使萤火虫优化算法(GSO)能够适用于车辆路径问题(VRP)的求解,同时提高该算法的求解性能。方法通过对GSO算法的改进,提出求解VRP问题的混沌模拟退火萤火虫优化算法(CSAGSO)。首先,设计改进的GSO算法(IGSO)使IGSO算法能够适应VRP问题的求解;其次,在IGSO算法中引入模拟退火机制,提出模拟退火萤火虫优化算法(SAGSO),使IGSO算法可有效避免陷入局部极小并最终趋于全局最优。然后,在SAGSO算法中引入混沌机制,提出CSAGSO算法,对SAGSO算法的荧光素浓度值进行混沌初始化和混沌扰动;最后,对标准算例集进行仿真测试。结果与遗传算法、蚁群算法和粒子群算法相比,CSAGSO算法的全局寻优能力、收敛速度及稳定性均改善了50%以上。结论对GSO算法的改进是合理的,且CSAGSO算法的全局优化能力、收敛速度和稳定性均优于遗传算法、蚁群算法和粒子群算法。     

面向快递同城运输的车辆路径问题研究

为降低运输成本,研究了快递同城运输中的车辆路径问题。建立多车型,含时间窗约束、容量约束、车辆限行约束,并考虑错峰交货的,以最小化运输成本为目标的混合整数规划模型。提出以点到点集的距离之和作为邻域搜索优先指标的构造性启发式算法,设计了基于“路径−车型对”的列生成算法,初始列由启发式算法求得。实验结果显示,对于120个点的大规模问题,列生成算法只需175秒就能得到近似最优解,验证了该算法的有效性及对一定规模内快递同城运输问题的适用性。     

Ant colony optimisation algorithm for distribution-allocation problem in a two-stage supply chain with a fixed transportation charge

In a fixed charge transportation problem, each route is associated with a fixed charge (or a fixed cost) and a transportation cost per unit transported. The presence of the fixed cost makes the problem difficult to solve, thereby requiring the use of heuristic methods. In this paper, an algorithm based on ant colony optimisation is proposed to solve the distribution-allocation problem in a two-stage supply chain with a fixed transportation cost for a route. A numerical study on benchmark problem instances has been carried out. The results obtained for the proposed algorithm have been compared with that for the genetic algorithm-based heuristic currently available in the literature. It is statistically confirmed that the proposed algorithm provides significantly better solutions.     

Conceptualizing tools for autonomous vehicle storage and retrieval systems

Autonomous vehicle storage and retrieval systems utilize rail-guided vehicles moving in rectilinear paths within and between the aisles of unit load storage racks. Vertical vehicle movement is provided by lifts installed at fixed locations along the rack periphery. As an alternative to traditional automated storage and retrieval systems, autonomous vehicle systems enable users to match vehicle fleet size and the number of lifts to the level of transactions demand in a storage system. Analytical conceptualizing tools based on the features of autonomous vehicle systems are proposed for modelling expected performance as a function of key system attributes including storage capacity, rack configuration and fleet size. The models are demonstrated for a sample problem and compared with analytical conceptualizing tools used for automated storage and retrieval systems.     

Transportation Routing Problem—A Survey

In the Transportation Routing Problem, a manager or analyst must schedule an existing fleet of vehicles, each with a capacity constraint, to visit a set of stops or destinations and deliver or pick up goods or services at each stop such that one and only one vehicle visits each stop. The problem is to assign these vehicles to the stops so as to minimize total cost which is assumed to be directly proportional to the total distance traveled. Much work has been done on this problem and heuristic as well as optimal seeking methods have been developed. This paper examines the problem, develops a standard formulation, reviews the literature on the problem, and mentions some new approaches.     

Optimisation of the multi-depots pick-up and delivery problems with time windows and multi-vehicles using PSO algorithm

Many sectors in the transport industry are concerned about the vehicle routing problem (VRP), hence the growing interest of researchers for this type of problem and its variants. This is due essentially to its many real applications in logistics for the transport of goods. The originality and contribution of our work is that we have dealt a problem that combines several variants: multiple vehicles (m), multiple depots (MD), pickup and delivery problem (PDP) with time windows (TW). Hence the notation of our problem: m-MDPDPTW. In this paper, we present the m-MDPDPTW, which is an optimisation problem belonging to the category of NP Hard problems. This problem must meet requests for transport between customers and suppliers satisfying precedence, capacity and time constraints. The goal is to find the best solution, which is the best route minimising the total travelled distance. To solve and optimise our m-MDPDPTW, we have developed a new algorithm based on the particle swarm optimisation (PSO) method. The performance of this new approach is tested on data set instances of Li and Lim's benchmark problems in which we have added multiple depot locations. Comparing with prior works, our proposed approach gave better results by decreasing the distance for several studied instances.     

分割配送的生鲜产品库存-路径优化研究

目的 基于供应商管理库存策略,优化协调第三方物流（3rd Party Logistics,3PL）参与的二级供应链系统中库存补充与补货配送的关系,在满足配送需求的同时降低系统的库存和运输成本。方法 综合考虑3PL物流模式下的库存-路径系统中生鲜产品的运输距离、质量时间窗以及需求分割配送策略在时间上的调整等因素,以异质车队车辆行驶燃油成本、车辆调用固定成本、配送超时腐坏成本以及各零售商的库存成本为目标函数,建立多品种生鲜产品库存-路径优化模型。结果 通过改进的遗传算法计算并进行配送量调整优化,得到最终的生鲜配送方案,其系统总成本比配送量调整前减少了9.98%。结论 通过在时间上对配送量进行拆分调整可以有效地节约供应链系统总成本。     

Supply chain optimisation with both production and transportation integration: multiple vehicles for a single perishable product

This paper deals with an extension of the integrated production and transportation scheduling problem (PTSP) by considering multiple vehicles (PTSPm) for optimisation of supply chains. The problem reflects a real concern for industry since production and transportation subproblems are commonly addressed independently or sequentially, which leads to sub-optimal solutions. The problem includes specific capacity constraints, the short lifespan of products and the special case of the single vehicle that has already been studied in the literature. A greedy randomised adaptive search procedure (GRASP) with an evolutionary local search (ELS) is proposed to solve the instances with a single vehicle as a special case. The method has been proven to be more effective than those published and provides shorter computational times with new best solutions for the single vehicle case. A new set of instances with multiple vehicles is introduced to favour equitable future research. Our study extends previous research using an indirect resolution approach and provides an algorithm to solve a wide range of one-machine scheduling problems with the proper coordination of single or multiple vehicles.     

Harmony search optimization algorithm for a novel transportation problem in a consolidation network

This article presents a new harmony search optimization algorithm to solve a novel integer programming model developed for a consolidation network. In this network, a set of vehicles is used to transport goods from suppliers to their corresponding customers via two transportation systems: direct shipment and milk run logistics. The objective of this problem is to minimize the total shipping cost in the network, so it tries to reduce the number of required vehicles using an efficient vehicle routing strategy in the solution approach. Solving several numerical examples confirms that the proposed solution approach based on the harmony search algorithm performs much better than CPLEX in reducing both the shipping cost in the network and computational time requirement, especially for realistic size problem instances.     

Study on the vehicle routing problem considering congestion and emission factors

To meet the requirement of greening transportation in poor traffic condition, vehicle routing problem (VRP) with consideration of fuel consumption and congestion is studied. We formulated a time-dependent green vehicle routing problem (TD-GVRP) model with minimised total cost as the objective function which includes fuel consumption cost, and the measurement of fuel consumption is based on the Comprehensive Modal Emissions Model (CMEM). In the model, the situation of waiting at customer nodes to avoid bad traffic is defined. To solve this model, a Response Surface Method (RSM)-based hybrid algorithm (HA) that combines genetic algorithm (GA) and particle swarm optimisation (PSO) is constructed. Finally, using instances from PRPLIB database, the following experiments are carried out and the corresponding conclusions are drawn. (i) Comparison of the proposed objective and traditional VRP objectives shows that fuel consumption can be greatly reduced by introducing fuel consumption factor into the objective function. (ii) Sensitivity analysis of congestion duration provides the influence of congestion duration on fuel consumption and travel time. (iii) Experiments based on different waiting time reveal that the optimisation of departure time can reduce fuel consumption and total cost to some extent.     

Cooperation schemes for heterogeneous material-handling vehicle fleets

This study deals with an organization which utilizes wire-guided vehicles as its material-handling system and undergoes an expansion, as a result additional material-handling devices are required. In the event, choosing similar vehicles to those currently operating in the manufacturing facility is not a viable alternative, the organization can still decide to maintain a homogeneous vehicle fleet by replacing all vehicles with advanced more expensive free-ranging vehicles. On the other hand, the organization can decide to reuse the old wire-guided vehicles while purchasing only a few new free-ranging vehicles, creating a heterogeneous vehicle fleet. This study presents two different cooperation schemes to control a heterogeneous vehicle fleet, which achieve similar operational performances as a homogeneous fleet of free-ranging vehicles. The study uses simulation to develop control strategies and to determine the system's parameters. Three different scenarios are used to test these control strategies. Finally, an operational and economical comparison analysis between the different cooperation schemes is performed.     

An optimization algorithm for a capacitated vehicle routing problem with time windows

In this paper, vehicle routing problem (VRP) with time windows and real world constraints are considered as a real-world application on google maps. Also, tabu search is used and Hopfield neural networks is utilized. Basic constraints consist of customer demands, time windows, vehicle speed, vehicle capacity and working hours. Recently, cost and on-time delivery are the most important factors in logistics. Thus, the logistic applications attract attention of companies. In logistic management, determining the locations of delivery points and deciding the path are the vital components that should be considered. Deciding the paths of vehicles provides companies to use their vehicles efficiently. And with utilizing optimized paths, big amounts of cost and time savings will be gained. The main aim of the work is providing the best path according to the needs of the customers, minimizing the costs with utilizing the VRP and presenting an application for companies that need logistic management. To compare the results, simulated annealing is used on special scenarios. And t-test is performed in the study for the visited path in km with p-value of 0.05.     

基于遗传算法的共享助力车调度问题研究

为了减少调度运营成本,减少调度时间,研究共享助力车的调度问题。将助力车调度和电池配送统一进行,考虑载重对燃油调度车的油耗影响,以燃油调度车固定使用成本和耗油成本最小为目标函数,构建助力车重分配的调度模型。通过AP算法对大范围内的电子围栏进行区域划分,确定助力车的服务范围和调度中心选址的基础上,用遗传算法对各个区域分别求解最小成本的路径规划方案。用算例验证了本模型与算法的有效性和可行性。     

供应链中随机需求车辆选径问题的研究

结合供应链的需要给出了允许两次服务失败的数学模型,提出了一种混沌神经网络求解算法,对该问题进行了求解,并与SA算法进行了比较.结果表明该算法具有很强的避免陷入局部极小点的能力,较大地提高了优化的性能和搜索效率,适用于求解车辆选径问题.     

用节约法解决带有时间窗的满载车辆调度问题

建立了具有时间约束的满载VSP问题的线性规划模型,给出了一种基于节约值比较的旨在最小化成本的启发式算法.该算法将满载车辆路线分为三种基本结构,即两点往返、多点连续实载、多点间隔实载,将车辆固定成本和变动成本同时加入到节约值计算中,根据路线结构计算更新节约值,在考虑时间约束的基础上参考节约值最大或机会节约值最大两种策略选择任务连接,得出车辆调度路线.经算例证明,该算法求得优化的调度路线.     

带时间窗的时变多目标危险化学品道路运输路径优化

研究了危险化学品道路运输路径优化（VRP）问题,考虑了该问题的3个方面：1）路径选择涉及运输时间与运输风险两个目标;2）运输时间与风险具有时变特性;3）道路节点的服务时间窗限制。本文以运输时间和风险为多目标,综合考虑以上约束,建立了该问题的数学模型并设计了蚁群算法进行求解。求解结果表明该算法可以有效计算帕累托最优路径,决策者可结合实际问题和决策偏好作出最合适的决策,同时运输企业可依据不同时刻的运输结果制定车辆的出发时刻表,监管部门可通过合理规划各路径的服务时间窗及允许停留等待的节点来调节各路径运输时间及风险。     

改进分散搜索算法求解包装废弃物回收路径规划问题

目的 将包装废弃物回收路径规划归纳为一个带回路和时间窗的逆向物流车辆路径问题(RL-VRPBTW),以最小化回收成本、发车成本和时间窗惩罚为联合优化目标进行建模。方法 引入“车辆剩余空间回收能力”因素,改进经典节约里程算法,求得较好的初始解;基于分散搜索框架,设计基于初始解改进的分散搜索算法(ISISS),根据问题模型,采用含0的编码方式,通过多样性产生、参考集更新、子集产生、子集合并、解改进等5个步骤实现算法功能。结果 在“部分回收点分布较密集”的城市型地理场景下,针对快消企业的低值固废包装,生成回收点数量分别为50、100、200的3种规模算例,并考虑大小两种车型进行仿真实验。将ISISS算法与改进节约里程、遗传和分散搜索3种算法比较后可知,ISISS算法在大规模包装废弃物回收车辆路径问题上具有更优的求解性能。结论 仿真实验结果表明,ISISS是一种求解多目标大规模包装废弃物回收路径规划问题的较优算法。     

应用蜜蜂繁殖进化型粒子群算法求解车辆路径问题

为了提高粒子群算法求解车辆路径问题时收敛速度和全局搜索能力,将蜜蜂繁殖进化机制与粒子群算法相结合,应用到CVRP问题的求解。该算法中,最优的个体作为蜂王与通过选择机制选择的雄蜂以随机概率进行交叉,增强了最优个体信息的应用能力;同时,随机产生一部分雄蜂种群,并将其与蜂王交叉增加了算法的多样性。实例分析表明该算法具有较好的全局搜索能力,验证了该算法的可行性。