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Modelling and comparison of stability metrics for a re-optimisation approach of the Inventory Routing Problem under demand uncertainty 需求不确定性下库存路径问题再优化方法的稳定性指标建模与比较
IF 2.4 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2021-01-01 DOI: 10.1016/j.ejtl.2021.100050
Faycal A. Touzout, Anne-Laure Ladier, Khaled Hadj-Hamou

The inventory routing problem (IRP) is an optimisation problem that integrates transportation and inventory management decisions. When subjected to unexpected events such as demand changes, the a posteriori approach consists in re-optimising including the data related to this event; the challenge is to ensure that the obtained solution does not deviate too much from the original one, lest that creates important organisational issues. Therefore, a stability metric is needed when re-optimising IRP models. This article proposes a panel of stability metrics adapted from the scheduling, routing and inventory management literature to fit the requirements of the IRP and proposes mathematical formulations for the most relevant ones. A framework of comparison is proposed to validate and compare these metrics over a benchmark of 3000 instances generated from the literature. A strong correlation between the metrics is observed. Moreover, the results show that ensuring the stability of the re-optimised solutions has little impact on the initial objective, the total cost.

库存路径问题(IRP)是一个综合了运输和库存管理决策的优化问题。当受到诸如需求变化等意外事件的影响时,后验方法包括重新优化包括与该事件相关的数据;挑战在于确保获得的解决方案不会与最初的解决方案偏离太多,以免造成重大的组织问题。因此,在重新优化IRP模型时需要一个稳定性度量。本文提出了一组适应调度、路由和库存管理文献的稳定性指标,以适应IRP的要求,并提出了最相关的数学公式。本文提出了一个比较框架,通过从文献中生成的3000个实例的基准来验证和比较这些指标。我们观察到这些指标之间存在很强的相关性。此外,结果表明,确保重新优化解的稳定性对初始目标,总成本的影响很小。
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引用次数: 2
Axle Weights in combined Vehicle Routing and Container Loading Problems 组合车辆路线和集装箱装载问题中的轴重
IF 2.4 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2021-01-01 DOI: 10.1016/j.ejtl.2021.100043
Corinna Krebs , Jan Fabian Ehmke

Overloaded axles not only lead to increased erosion on the road surface, but also to an increased braking distance and more serious accidents due to higher impact energy. Therefore, the load on axles should be already considered during the planning phase and thus before loading the truck in order to prevent overloading. Hereby, a detailed 2D or 3D planning of the vehicle cargo space is required. We model the Axle Weight Constraint for trucks with and without trailers based on the Science of Statics and provide flexible formulas for different axle configurations of trucks. We include the Axle Weight Constraint into the combined Vehicle Routing and Container Loading Problem (“2L-CVRP” and “3L-CVRP”). A hybrid heuristic approach is used where an outer Adaptive Large Neighbourhood Search tackles the routing problem and an inner Deepest-Bottom-Left-Fill algorithm solves the packing problem. Moreover, to ensure feasibility, we show that the Axle Weight Constraint must be checked after each placement of an item. The impact of the Axle Weight Constraint is also evaluated.

超载的车轴不仅会增加对路面的侵蚀,而且由于冲击能量的增加,制动距离也会增加,事故也会更加严重。因此,在规划阶段,在装载卡车之前,应该已经考虑到轴上的负载,以防止超载。因此,需要对车辆货物空间进行详细的二维或三维规划。基于静力学原理,建立了带挂车和不带挂车的货车车轴重约束模型,并针对不同的货车车轴构型给出了灵活的计算公式。我们将轴重约束引入到车辆路径和集装箱装载问题(“2L-CVRP”和“3L-CVRP”)中。采用一种混合启发式方法,其中外部自适应大邻域搜索解决路由问题,内部最深底左填充算法解决打包问题。此外,为了确保可行性,我们表明在每次放置物品后必须检查轴重约束。还对轴重约束的影响进行了评价。
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引用次数: 13
The Baggage Belt Assignment Problem 行李带分配问题
IF 2.4 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2021-01-01 DOI: 10.1016/j.ejtl.2021.100041
David Pisinger , Rosario Scatamacchia

We consider the problem of assigning flights to baggage belts in the baggage reclaim area of an airport. The problem is originated by a real-life application in Copenhagen airport. The objective is to construct a robust schedule taking passenger and airline preferences into account. We consider a number of business and fairness constraints, avoiding congestion, and ensuring a good passenger flow. Robustness of the solutions is achieved by matching the delivery time with the expected arrival time of passengers, and by adding sufficient buffer time between two flights scheduled on the same belt. We denote this problem as the Baggage Belt Assignment Problem (BBAP). We first derive a general Integer Linear Programming (ILP) formulation for the problem. Then, we propose a Branch-and-Price (B&P) algorithm based on a reformulation of the ILP model tackled by Column Generation. Our approach relies on an effective dynamic programming algorithm for handling the pricing problems. We tested the proposed algorithm on a set of real-life data from Copenhagen airport as well as on a set of instances inspired by the real data. Our B&P scheme outperforms a commercial solver launched on the ILP formulation of the problem and is effective in delivering high quality solutions in limited computational times, making it possible to use the solution approach in daily operations in medium-sized and large airports.

我们考虑在机场行李提取区将航班分配给行李带的问题。这个问题源于哥本哈根机场的一个实际应用。目标是构建一个考虑到乘客和航空公司偏好的稳健时间表。我们考虑了一些商业和公平约束,避免拥堵,并确保良好的客流。解决方案的鲁棒性是通过将交付时间与乘客的预期到达时间相匹配,以及在同一条带上安排的两个航班之间增加足够的缓冲时间来实现的。我们把这个问题称为行李带分配问题(BBAP)。我们首先推导出该问题的一般整数线性规划(ILP)公式。然后,我们提出了一种基于列生成解决的ILP模型的重新表述的Branch-and-Price (B&P)算法。我们的方法依赖于一个有效的动态规划算法来处理定价问题。我们在哥本哈根机场的一组真实数据以及一组受真实数据启发的实例上测试了所提出的算法。我们的B&P方案优于基于问题的ILP公式推出的商业求解器,并且在有限的计算时间内有效地提供高质量的解决方案,使解决方案方法可以在大中型机场的日常运营中使用。
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引用次数: 2
Hybridizing large neighborhood search and exact methods for generalized vehicle routing problems with time windows 带时间窗的广义车辆路径问题的大邻域搜索与精确方法
IF 2.4 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2021-01-01 DOI: 10.1016/j.ejtl.2021.100040
Dorian Dumez , Christian Tilk , Stefan Irnich , Fabien Lehuédé , Olivier Péton

Delivery options are at the heart of the generalized vehicle routing problem with time windows (GVRPTW) allowing that customer requests are shipped to alternative delivery locations which can also have different time windows. Recently, the vehicle routing problem with delivery options was introduced into the scientific literature. It extends the GVRPTW by capacities of shared locations and by specifying service-level constraints defined by the customers’ preferences for delivery options. The vehicle routing problem with delivery options also generalizes the vehicle routing problem with home roaming delivery locations and the vehicle routing problem with multiple time windows. For all these GVRPTW variants, we present a widely applicable matheuristic that relies on a large neighborhood search (LNS) employing several problem-tailored destruction operators. Most of the time, the LNS performs relatively small and fast moves, but when the solution has not been improved for many iterations, a larger destruction move is applied to arrive in a different region of the search space. Moreover, an adaptive layer of the LNS embeds two exact components: First, a set-partitioning formulation is used to combine previously found routes to new solutions. Second, the Balas-Simonetti neighborhood is adapted to further improve already good solutions. These new components are in the focus of our work and we perform an exhaustive computational study to evaluate four configurations of the new matheuristic on several benchmark instances of the above-mentioned variants. On all the benchmark sets, our matheuristic is competitive with the previous state-of-the-art methods. In summary, the four configurations provide 81 new best-known solutions.

配送选项是带时间窗口的广义车辆路线问题(GVRPTW)的核心,该问题允许将客户请求运送到具有不同时间窗口的备选配送地点。近年来,具有配送选项的车辆路线问题被引入科学文献。它通过共享位置的容量和指定由客户的交付选项首选项定义的服务级别约束来扩展GVRPTW。具有送货选项的车辆路线问题也推广了具有家庭漫游送货地点的车辆路线问题和具有多个时间窗口的车辆路线问题。对于所有这些GVRPTW变体,我们提出了一种广泛适用的数学方法,该方法依赖于使用几个针对问题的销毁算子的大邻域搜索(LNS)。大多数情况下,LNS执行相对较小和快速的移动,但是当解决方案在许多迭代中没有得到改进时,应用更大的破坏移动来到达搜索空间的不同区域。此外,LNS的自适应层嵌入了两个精确的组件:首先,使用集合划分公式将先前找到的路由组合为新的解决方案。第二,对Balas-Simonetti社区进行了调整,以进一步改善已经很好的解决方案。这些新组件是我们工作的重点,我们执行了详尽的计算研究,以在上述变体的几个基准实例上评估新数学的四种配置。在所有基准集上,我们的数学方法与以前最先进的方法具有竞争力。总之,这四种配置提供了81种新的知名解决方案。
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引用次数: 10
The vehicle routing problem with relaxed priority rules 放宽优先规则下的车辆路径问题
IF 2.4 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2021-01-01 DOI: 10.1016/j.ejtl.2021.100039
Thanh Tan Doan , Nathalie Bostel , Minh Hoàng Hà

The Vehicle Routing Problem (VRP) is one of the most studied topics in Operations Research. Among the numerous variants of the VRP, this research addresses the VRP with relaxed priority rules (VRP-RPR) in which customers are assigned to several priority groups and customers with the highest priorities typically need to be served before lower priority ones. Additional rules are used to control the trade-off between priority and cost efficiency. We propose a Mixed Integer Linear Programming (MILP) model to formulate the problem and to solve small-sized instances. A metaheuristic based on the Adaptive Large Neighborhood Search (ALNS) algorithm with problem-tailored components is then designed to handle the problem at larger scales. The experimental results demonstrate the performance of our proposed algorithm. Remarkably, it outperforms a metaheuristic recently proposed to solve the Clustered Traveling Saleman Problem with d-relaxed priority rule (CTSP-d), a special case of VRP-RPR, in both solution quality and computational time.

车辆路径问题(VRP)是运筹学中研究最多的课题之一。在VRP的众多变体中,本文研究了具有放宽优先级规则的VRP (VRP- rpr),该规则将客户分配到多个优先级组,并且通常需要在低优先级组之前为最高优先级的客户提供服务。附加规则用于控制优先级和成本效率之间的权衡。我们提出了一个混合整数线性规划(MILP)模型来表述这个问题并解决小规模的实例。然后设计了一种基于自适应大邻域搜索(ALNS)算法的元启发式算法,并结合问题定制组件来处理更大规模的问题。实验结果证明了该算法的有效性。值得注意的是,它在求解质量和计算时间上都优于最近提出的一种基于d-放松优先级规则(CTSP-d)的聚类旅行推销员问题(VRP-RPR的一种特例)的元启发式算法。
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引用次数: 6
Erratum regarding missing Declaration of competing interest statements in previously published articles 关于先前发表的文章中缺少竞争利益声明的勘误表
IF 2.4 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2021-01-01 DOI: 10.1016/j.ejtl.2021.100031
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引用次数: 0
Integrating vehicle routing into intermodal service network design with stochastic transit times 基于随机运输时间的车辆路径与多式联运服务网络设计
IF 2.4 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2021-01-01 DOI: 10.1016/j.ejtl.2021.100046
Jan Philipp Müller , Ralf Elbert , Simon Emde

Service network design is an important optimization problem for intermodal freight transportation on a tactical level. It includes the decisions on choosing transportation modes and paths for commodities throughout the intermodal network. We present a stochastic service network design model with an integrated vehicle routing problem (SSND-VRP), which simultaneously covers transportation service choice and tour planning decisions for road transportation under consideration of uncertain transportation times. A sample average approximation approach is combined with an iterated local search in order to solve problem instances in a real-world case study for three intermodal road-rail networks in Central Europe. Results of the SSND-VRP are compared with its expected value model and a successive planning approach, demonstrating the possible cost reductions and the decrease in missed intermodal services that are achieved by the integrated stochastic model. In further parameter variation experiments we show that the attractiveness of rail transportation is highly sensitive to changes in intermodal costs, whereas the impact of delay reductions of the railway services is relatively low.

服务网络设计是多式联运的一个重要的战术优化问题。它包括在整个多式联运网络中选择商品的运输方式和路径的决策。提出了一种综合车辆路径问题的随机服务网络设计模型,该模型同时考虑了不确定运输时间下道路运输的运输服务选择和行程规划决策。为了解决中欧三个多式联运公路铁路网络的实际案例研究中的问题实例,将样本平均近似方法与迭代局部搜索相结合。将SSND-VRP的结果与其期望值模型和连续规划方法进行了比较,证明了综合随机模型可能实现的成本降低和多式联运服务错过的减少。在进一步的参数变化实验中,我们发现铁路运输的吸引力对多式联运成本的变化高度敏感,而铁路服务延迟减少的影响相对较低。
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引用次数: 5
Learning to handle parameter perturbations in Combinatorial Optimization: An application to facility location 学习处理组合优化中的参数扰动:在设施选址中的应用
IF 2.4 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2020-12-01 DOI: 10.1016/j.ejtl.2020.100023
Andrea Lodi , Luca Mossina , Emmanuel Rachelson

We present an approach to couple the resolution of Combinatorial Optimization problems with methods from Machine Learning. Specifically, our study is framed in the context where a reference discrete optimization problem is given and there exist data for many variations of such reference problem (historical or simulated) along with their optimal solution. Those variations can be originated by disruption but this is not necessarily the case. We study how one can exploit these to make predictions about an unseen new variation of the reference instance.

The methodology is composed by two steps. We demonstrate how a classifier can be built from these data to determine whether the solution to the reference problem still applies to a perturbed instance. In case the reference solution is only partially applicable, we build a regressor indicating the magnitude of the expected change, and conversely how much of it can be kept for the perturbed instance. This insight, derived from a priori information, is expressed via an additional constraint in the original mathematical programming formulation.

We present the methodology through an application to the classical facility location problem and we provide an empirical evaluation and discuss the benefits, drawbacks and perspectives of such an approach.

Although it cannot be used in a black-box manner, i.e., it has to be adapted to the specific application at hand, we believe that the approach developed here is general and explores a new perspective on the exploitation of past experience in Combinatorial Optimization.

我们提出了一种将组合优化问题的解决与机器学习方法相结合的方法。具体来说,我们的研究是在给定参考离散优化问题的背景下进行的,并且存在此类参考问题(历史或模拟)的许多变化及其最优解的数据。这些变化可能源于颠覆,但事实并非如此。我们研究如何利用这些来预测参考实例的一个看不见的新变化。该方法由两个步骤组成。我们演示了如何从这些数据构建分类器,以确定引用问题的解决方案是否仍然适用于受干扰的实例。如果参考解决方案仅部分适用,我们建立一个回归量,指示预期变化的大小,反过来,对于受干扰的实例,它可以保留多少。这种从先验信息中获得的洞察力,通过原始数学规划公式中的附加约束来表达。我们将该方法应用于经典的设施选址问题,并提供了一个实证评估,并讨论了这种方法的优点、缺点和前景。虽然它不能以黑盒方式使用,也就是说,它必须适应手头的特定应用程序,但我们相信这里开发的方法是通用的,并且在利用组合优化中的过去经验方面探索了一个新的视角。
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引用次数: 21
Machine learning in airline crew pairing to construct initial clusters for dynamic constraint aggregation 航空机组配对中的机器学习构造初始聚类进行动态约束聚合
IF 2.4 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2020-12-01 DOI: 10.1016/j.ejtl.2020.100020
Yassine Yaakoubi , François Soumis , Simon Lacoste-Julien

The crew pairing problem (CPP) is generally modelled as a set partitioning problem where the flights have to be partitioned in pairings. A pairing is a sequence of flight legs separated by connection time and rest periods that starts and ends at the same base. Because of the extensive list of complex rules and regulations, determining whether a sequence of flights constitutes a feasible pairing can be quite difficult by itself, making CPP one of the hardest of the airline planning problems. In this paper, we first propose to improve the prototype Baseline solver of Desaulniers et al. (2020)2020) by adding dynamic control strategies to obtain an efficient solver for large-scale CPPs: Commercial-GENCOL-DCA. These solvers are designed to aggregate the flights covering constraints to reduce the size of the problem. Then, we use machine learning (ML) to produce clusters of flights having a high probability of being performed consecutively by the same crew. The solver combines several advanced Operations Research techniques to assemble and modify these clusters, when necessary, to produce a good solution. We show, on monthly CPPs with up to 50 ​000 flights, that Commercial-GENCOL-DCA with clusters produced by ML-based heuristics outperforms Baseline fed by initial clusters that are pairings of a solution obtained by rolling horizon with GENCOL. The reduction of solution cost averages between 6.8% and 8.52%, which is mainly due to the reduction in the cost of global constraints between 69.79% and 78.11%.

乘员配对问题(CPP)通常被建模为一个集合划分问题,其中航班必须成对划分。配对是由连接时间和休息时间分开的一系列飞行腿,在同一基地开始和结束。由于有大量复杂的规则和条例,确定一系列航班是否构成可行的配对本身就相当困难,这使得CPP成为航空公司规划问题中最难的问题之一。在本文中,我们首先提出通过添加动态控制策略来改进Desaulniers等(2020)2020)的原型基线求解器,从而获得大规模CPPs的高效求解器:Commercial-GENCOL-DCA。这些求解器的设计目的是聚合覆盖约束的航班,以减小问题的规模。然后,我们使用机器学习(ML)来生成高概率由同一机组人员连续执行的航班集群。求解器结合了几种先进的运筹学技术,在必要时组装和修改这些集群,以产生一个好的解决方案。我们表明,在每月多达5万次航班的CPPs中,基于ml的启发式算法生成的聚类Commercial-GENCOL-DCA优于由初始聚类提供的基线,这些聚类是通过滚动地平线与GENCOL获得的解决方案的配对。解决方案成本平均降低了6.8% - 8.52%,这主要是由于全球约束成本降低了69.79% - 78.11%。
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引用次数: 17
Introduction to the special issue on combining optimization and machine learning: Application in vehicle routing, network design and crew scheduling “优化与机器学习结合”专刊简介:在车辆路线、网络设计和乘员调度中的应用
IF 2.4 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2020-12-01 DOI: 10.1016/j.ejtl.2020.100024
Claudia Archetti , Jean-François Cordeau , Guy Desaulniers
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引用次数: 3
期刊
EURO Journal on Transportation and Logistics
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