A dynamic vehicle routing problem with time-dependent travel times

In this paper we present a formulation for the dynamic vehicle routing problem with time-dependent travel times. We also present a genetic algorithm to solve the problem. The problem is a pick-up or delivery vehicle routing problem with soft time windows in which we consider multiple vehicles with different capacities, real-time service requests, and real-time variations in travel times between demand nodes.The performance of the genetic algorithm is evaluated by comparing its results with exact solutions and lower bounds for randomly generated test problems. For small size problems with up to 10 demands, the genetic algorithm provides almost the same results as the exact solutions, while its computation time is less than 10% of the time required to produce the exact solutions. For the problems with 30 demand nodes, the genetic algorithm results have less than 8% gap with lower bounds.This research also shows that as the uncertainty in the travel time information increases, a dynamic routing strategy that takes the real-time traffic information into account becomes increasingly superior to a static one. This is clear when we compare the static and dynamic routing strategies in problem scenarios that have different levels of uncertainty in travel time information. In additional tests on a simulated network, the proposed algorithm works well in dealing with situations in which accidents cause significant congestion in some part of the transportation network.     

考虑随机旅行时间与二维装载约束的越库配送车辆路径优化

面向越库配送模式下二维装载和车辆路径联合优化,考虑现实配送过程的不确定性因素,提出考虑随机旅行时间和二维装载约束的越库配送车辆路径问题.基于蒙特卡洛模拟与场景分析方法,建立以运输成本、车辆固定成本以及时间窗期望惩罚成本之和最小化为目标的带修正随机规划模型.继而根据问题特征,设计改进的自适应禁忌搜索算法和基于禁忌搜索的多重排序最佳适应装箱算法进行求解.其中,改进的自适应禁忌搜索算法在禁忌搜索算法的基础上引入自适应机制,对不同邻域算子进行动态选择,并提出基于移除-修复策略的多样性机制以增强算法的寻优能力.数值实验表明,所提出的模型与方法能够有效求解考虑随机旅行时间和二维装载约束的越库配送车辆路径问题,自适应与多样性机制能一定程度上增强算法的全局搜索能力.     

考虑时间窗与随机航行时间的船舶航线规划

良好的航线设计是船运公司降低运营成本,提高服务质量的关键。船舶运输中存在航行时间不确定,码头资源稀缺等特点,基于此将其航线问题抽象为考虑时间窗与随机旅行时间的多重流动旅行商问题。针对航行时间的随机性,设计了线性近似方法,提出了虚拟时间窗的概念,构建了初始模型与修正模型;给出了该问题的一个算例,验证了模型与算法的有效性和合理性。     

A variable neighborhood search simheuristic for the multiperiod inventory routing problem with stochastic demands

The inventory routing problem (IRP) combines inventory management and delivery route‐planning decisions. This work presents a simheuristic approach that integrates Monte Carlo simulation within a variable neighborhood search (VNS) framework to solve the multiperiod IRP with stochastic customer demands. In this realistic variant of the problem, our goal is to establish the optimal refill policies for each customer–period combination, that is, those individual refill policies that minimize the total expected cost over the periods. This cost is the aggregation of both expected inventory and routing costs. Our simheuristic algorithm allows to consider the inventory changes between periods generated by the realization of the random demands in each period, which have an impact on the quantities to be delivered in the next period and, therefore, on the associated routing plans. A range of computational experiments are carried out in order to illustrate the potential of our simulation–optimization approach.     

行驶时间随机的分批配送车辆路径问题模型与算法

为研究分批配送和等待时间对行驶时间随机的车辆路径问题（VRP）的影响,针对行驶时间随机的分批配送车辆路径问题,在软时间窗下考虑等待时间,建立带修正的随机规划模型;同时设计改进的粒子群优化（PSO）算法进行求解：使用需求点可多次出现的整数编码,设计改进的相对位置索引算法进行解码以解决粒子中出现分批需求点问题;将自适应选择用于速度更新以解决各向量长度不同的问题;将路径重连算法用于位置更新过程以解决粒子在离散空间和连续空间转换时信息丢失的问题,适应允许分批配送的特点。通过对调整的Solomon算例测试,考虑等待时间将造成总费用平均增加约3%,且更倾向于分批配送。分批配送能有效降低总费用（2%）和减少使用的车辆数（0.6）;在部分算例,特别是R2类算例中,分批配送能有效降低等待时间,平均降低0.78%。     

A heuristic for the vehicle routing problem with due times

This paper studies the vehicle routing problem with due times. The vehicles are supposed to visit customers within the due times, and a penalty cost is imposed in case the vehicle arrives past the due times. The objective is to minimize the weighted sum of the traveling time of vehicles and the tardiness of the service customers receive. A mixed integer programming formulation and a heuristic based on the tabu search for a practical use are suggested. Route-perturb and route-improvement method for the neighborhood generation is proposed. Performances are compared with other heuristics appeared in the literature using the bench-mark data set modified to be fit to the model. It is shown that the suggested heuristic gives a good solution in a short computation time.     

分支定价方法求解带二维装箱约束的车辆路径问题EI北大核心CSCD

面向家具、电器等货物的物流配送场景,研究带二维装箱约束的车辆路径问题(2L–CVRP),构建了2L–CVRP的混合整数线性规划模型.为求解大规模2L–CVRP,构建了该问题集合划分模型,提出基于分支定价的方法.针对分支节点的松弛模型,基于列生成策略将其分解为线性规划主问题、带资源和二维装箱约束的最短路径子问题,并提出基于ng-route松弛策略的标签算法和基于禁忌搜索的装箱算法有效求解复杂子问题.仿真结果表明,提出的方法可高效求解大规模2L–CVRP,其中ng-route松弛策略能有效提升算法求解效率,研究成果为装箱约束下大规模车辆路径问题的高效求解提供了有效途径.     

Online vehicle routing and scheduling with dynamic travel times

The developments in mobile communication technologies are a strong motivation for the study of dynamic vehicle routing and scheduling problems. In particular, the planned routes can be quickly modified to account for the occurrence of new customer requests, which might imply diverting a vehicle away from its current destination. In this paper, a previously developed problem-solving approach for a vehicle routing problem with dynamic requests and dynamic travel times is extended to account for more sophisticated communication means between the drivers and the central dispatch office. Computational results are reported to empirically demonstrate the benefits of this extension.     

Vehicle routing problem with stochastic travel times including soft time windows and service costs

This paper studies a vehicle routing problem with soft time windows and stochastic travel times. A model is developed that considers both transportation costs (total distance traveled, number of vehicles used and drivers' total expected overtime) and service costs (early and late arrivals). We propose a Tabu Search method to solve this model. An initialization algorithm is developed to construct feasible routes by taking into account the travel time stochasticity. Solutions provided by the Tabu Search algorithm are further improved by a post-optimization method. We conduct our computational experiments for well-known problem instances. Results show that our Tabu Search method performs well by obtaining very good final solutions in a reasonable amount of time.     

A simheuristic algorithm to set up starting times in the stochastic parallel flowshop problem

This paper addresses the parallel flowshop scheduling problem with stochastic processing times, where a product composed of several components has to be finished at a particular moment. These components are processed in independent parallel factories, and each factory can be modeled as a permutation flowshop. The processing time of each operation at each factory is a random variable following a given probability distribution. The aim is to find the robust starting time of the operations at each factory in a way that all the components of the product are completed on a given deadline with a user-defined probability. A simheuristic algorithm is proposed in order to minimize each of the following key performance indicators: (i) the makespan in the deterministic version; and (ii) the expected makespan or a makespan percentile in the stochastic version. A set of computational experiments are carried out to illustrate the performance of the proposed methodology by comparing the outputs under different levels of stochasticity.     

A memetic algorithm for the multi-compartment vehicle routing problem with stochastic demands

The multi-compartment vehicle routing problem (MC-VRP) consists of designing transportation routes to satisfy the demands of a set of customers for several products that, because of incompatibility constraints, must be loaded in independent vehicle compartments. Despite its wide practical applicability the MC-VRP has not received much attention in the literature, and the few existing methods assume perfect knowledge of the customer demands, regardless of their stochastic nature. This paper extends the MC-VRP by introducing uncertainty on what it is known as the MC-VRP with stochastic demands (MC-VRPSD). The MC-VRPSD is modeled as a stochastic program with recourse and solved by means of a memetic algorithm. The proposed memetic algorithm couples genetic operators and local search procedures proven to be effective on deterministic routing problems with a novel individual evaluation and reparation strategy that accounts for the stochastic nature of the problem. The algorithm was tested on instances of up to 484 customers, and its results were compared to those obtained by a savings-based heuristic and a memetic algorithm (MA/SCS) for the MC-VRP that uses a spare capacity strategy to handle demand fluctuations. In addition to effectively solve the MC-VRPSD, the proposed MA/SCS also improved 14 best known solutions in a 40-problem testbed for the MC-VRP.     

A branch-and-cut approach for the vehicle routing problem with loading constraints

In this paper we describe a branch-and-cut algorithm for the vehicle routing problem with unloading constraints. The problem is to determine a set of routes with minimum total cost, each route leaving a depot, such that all clients are visited exactly once. Each client has a demand, given by a set of items, that are initially stored in a depot. We consider the versions of the problem with two and tri dimensional parallelepiped items. For each route in a solution, we also need to construct a feasible packing for all the items of the clients in this route. As it would be too expensive to rearrange the vehicle cargo when removing the items of a client, it is important to perform this task without moving the other client items. Such packings are said to satisfy unloading constraints.In this paper we describe a branch-and-cut algorithm that uses several techniques to prune the branch-and-cut enumeration tree. The presented algorithm uses several packing routines with different algorithmic approaches, such as branch-and-bound, constraint programming and metaheuristics. The careful combination of these routines showed that the presented algorithm is competitive, and could obtain optimum solutions within significantly smaller computational times for most of the instances presented in the literature.     

A record-to-record travel algorithm for solving the heterogeneous fleet vehicle routing problem

In the heterogeneous fleet vehicle routing problem (HVRP), several different types of vehicles can be used to service the customers. The types of vehicles differ with respect to capacity, fixed cost, and variable cost. We assume that the number of vehicles of each type is fixed and equal to a constant. We must decide how to make the best use of the fixed fleet of heterogeneous vehicles.     

A reactive simheuristic using online data for a real‐life inventory routing problem with stochastic demands

In the context of a supply chain for the animal‐feed industry, this paper focuses on optimizing replenishment strategies for silos in multiple farms. Assuming that a supply chain is essentially a value chain, our work aims at narrowing this chasm and putting analytics into practice by identifying and quantifying improvements on specific stages of an animal‐feed supply chain. Motivated by a real‐life case, the paper analyses a rich multi‐period inventory routing problem with homogeneous fleet, stochastic demands, and maximum route length. After describing the problem and reviewing the related literature, we introduce a reactive heuristic, which is then extended into a biased‐randomized simheuristic. Our reactive approach is validated and tested using a series of adapted instances to explore the gap between the solutions it provides and the ones generated by existing nonreactive approaches.     

A combined multistart random constructive heuristic and set partitioning based formulation for the vehicle routing problem with time dependent travel times

Although the Vehicle Routing Problem (VRP) has been broadly addressed in the literature, most of the works consider constant travel times. This is a strong simplification that does not allow to correctly model real world applications. In fact, nowadays, travel times sensibly change, across the day, due to congestion phenomena. Therefore, to actually represent the reality, it is necessary to consider time dependent travel times. In this paper, the VRP with Time Dependent Travel Times, service times at nodes, and limit on the maximum route duration, is addressed. The objective function consists into minimizing the total travel time. A Multistart Random Constructive Heuristic, (MRCH), in which congestion level is considered, is proposed. The routes obtained by the MRCH are then used as columns in a Set Partitioning formulation. Computational results, carried out on instances derived by VRP instances taken from the literature, show the efficiency and effectiveness of the proposed approach.     

随机需求车辆路径问题的价值逼近在线决策

随着高效实时物流的发展,不确定车辆路径问题面临着兼顾决策精度和实时响应能力的新挑战.本文以应用最为广泛的随机需求车辆路径问题为例,研究提出一种有效的在线决策方法.首先,考虑多车辆同时在线,以总旅行成本最小化为目标,建立马尔科夫决策模型,并引入可信度约束和邻域半径减少策略缩小行动空间,提高求解效率.其次,设计强化学习中的...     

A maritime inventory routing problem with stochastic sailing and port times

This paper describes a stochastic short sea shipping problem where a company is responsible for both the distribution of oil products between islands and the inventory management of those products at consumption storage tanks located at ports. In general, ship routing and scheduling is associated with uncertainty in weather conditions and unpredictable waiting times at ports. In this work, both sailing times and port times are considered to be stochastic parameters. A two-stage stochastic programming model with recourse is presented where the first stage consists of routing, loading and unloading decisions, and the second stage consists of scheduling and inventory decisions. The model is solved using a decomposition approach similar to an L-shaped algorithm where optimality cuts are added dynamically, and this solution process is embedded within the sample average approximation method. A computational study based on real-world instances is presented.     

A hybrid approach for the vehicle routing problem with three-dimensional loading constraints

This paper addresses a recently practical combinatorial problem named Three-Dimensional Loading Capacitated Vehicle Routing Problem, which combines three-dimensional loading problem and vehicle routing problem in distribution logistics. The problem requires a combinatorial optimization of a feasible loading and successive routing of vehicles to satisfy customer demands, where all vehicles must start and finish at a central depot. The goal of this combinatorial problem is to minimize the total transportation cost while serving customers. Despite its clearly practical significance in the real world distribution management, for its high combinatorial complexity, published papers on this problem in literature are very limited.     

A branch-and-price approach for a multi-period vehicle routing problem

In this paper, we consider tactical planning for a class of multi-period vehicle routing problems (MPVRP). This problem involves optimizing daily product collections from several production locations over a given planning horizon. In this context, a single routing plan for the whole horizon must be prepared, and the seasonal variations in the producers’ supplies must be taken into account. Production variations over the horizon are approximated using a sequence of periods, each corresponding to a production season, while the intra-period variations are neglected. We propose a mathematical model that is based on the two-stage a priori optimization paradigm. The first stage corresponds to the design of a plan which, in the second stage, takes the different periods into account. The proposed set partitioning-based formulation is solved using a branch-and-price approach. The subproblem is a multi-period elementary shortest path problem with resource constraints (MPESPPRC), for which we propose an adaptation of the dynamic-programming-based label-correcting algorithm. Computational results show that this approach is able to solve instances with up to 60 producers and five periods.