带软时间窗的同时取送货车辆路径问题研究

考虑软时间窗下的车辆路径问题,客户点常伴有同时取送货的双重需求。针对此类问题,通过对软时间窗、车辆在途前后时间关系及二者融合问题进行刻画,同时将车辆行驶距离、车辆使用数、违反软时间窗总时间、客户满意度等纳入综合考量,构建相应混合整数非线性规划(mixed integer nonlinear programming, MINLP)模型。设计相应多目标优化求解算法,运用理想点法对目标函数进行转化,将多目标优化问题转化为单目标优化问题。结合相应算例集,运用LINGO 17.0全局求解程序求得每组算例的全局最优解。结果表明,针对带软时间窗的同时取送货车辆路径问题(vehicle routing problem with simultaneous pick-up and delivery and soft time windows, VRPSPDSTW),所建模型及算法是有效且可行的。     

Integrated planning of loaded and empty container movements

Efficiently planning drayage operations is an important task for transportation companies since these operations constitute a large part of the cost of an intermodal transport. In this paper, a full truckload vehicle routing problem for transporting loaded and empty containers in drayage operations is studied. For empty container transports, either the origin or the destination is not predefined. The problem is formulated as an asymmetric multiple vehicle Travelling Salesman Problem with Time Windows (am-TSPTW). Two solution approaches are proposed: a sequential and an integrated approach. For both approaches, a single- and a two-phase deterministic annealing algorithm are presented. Results show that the proposed algorithms are able to find good quality solutions in a small amount of computation time. The integrated approach clearly outperforms the sequential one and the results confirm the advantage of using a two-phase algorithm for vehicle routing problems with hierarchical objectives. Finally, it is shown that the proposed integrated solution method improves previous results on a similar problem.     

Research on Vehicle Routing Problem with Soft Time Windows Based on Hybrid Tabu Search and Scatter Search Algorithm

With the expansion of the application scope of social computing problems, many path problems in real life have evolved from pure path optimization problems to social computing problems that take into account various social attributes, cultures, and the emotional needs of customers. The actual soft time window vehicle routing problem, speeding up the response of customer needs, improving distribution efficiency, and reducing operating costs is the focus of current social computing problems. Therefore, designing fast and effective algorithms to solve this problem has certain theoretical and practical significance. In this paper, considering the time delay problem of customer demand, the compensation problem is given, and the mathematical model of vehicle path problem with soft time window is given. This paper proposes a hybrid tabu search (TS) & scatter search (SS) algorithm for vehicle routing problem with soft time windows (VRPSTW), which mainly embeds the TS dynamic tabu mechanism into the SS algorithm framework. TS uses the scattering of SS to avoid the dependence on the quality of the initial solution, and SS uses the climbing ability of TS improves the ability of optimizing, so that the quality of search for the optimal solution can be significantly improved. The hybrid algorithm is still based on the basic framework of SS. In particular, TS is mainly used for solution improvement and combination to generate new solutions. In the solution process, both the quality and the dispersion of the solution are considered. A simulation experiments verify the influence of the number of vehicles and maximum value of tabu length on solution, parameters’ control over the degree of convergence, and the influence of the number of diverse solutions on algorithm performance. Based on the determined parameters, simulation experiment is carried out in this paper to further prove the algorithm feasibility and effectiveness. The results of this paper provide further ideas for solving vehicle routing problems with time windows and improving the efficiency of vehicle routing problems and have strong applicability.     

The bi-objective two-dimensional loading vehicle routing problem with partial conflicts

The two-dimensional loading vehicle routing problem with partial conflicts combines two NP-hard problems: the classical vehicle routing problem and the two-dimensional bin-packing problem with partial conflicts. This new variant of transportation problems is inspired from hazardous materials classification and compatibilities, where some materials can be partially conflicting. In this case, they can be loaded together but an additional constraint on the distance separating them must be respected. We propose in this paper an NSGA-II algorithm to perform a bi-objective study in which the minimization of the total cost of transportation as well as the load balancing between different routes in terms of used area of vehicles are the considered objectives. The first results for this new problem are presented, using benchmarks available in the literature that have been adapted to deal with the problem. Moreover, the adding value of path relinking is proved with different statistical measurements.     

A coordinated algorithm for integrated production scheduling and vehicle routing problem

In this paper, the integrated production scheduling and vehicle routing problem is considered for a Make-to-Order manufacturer, who has a single machine for production and limited vehicles with capacity constraints for transportation. The objective is to determine production scheduling and vehicle routing, which are two interacted decisions, to minimise the maximum order delivery time. A property on optimal production sequence is proposed first, based on which backward and forward batching methods are developed and are embedded into a proposed genetic algorithm. The proposed genetic algorithm is capable of providing high-quality solutions by determining the two decisions simultaneously. For comparison purpose, a two-stage algorithm is developed, which decomposes the overall problem into two successively solved sub-problems. The experiments show that the proposed genetic algorithm can provide higher quality solutions than the proposed two-stage algorithm and two published algorithms studying related problems.     

A vehicle routing problem with time windows and stochastic demands

Abstract

This study presents an approach for considering a vehicle routing problem where customers’ pickup demands are uncertain and require serving within some settled time windows. Customers’ demands are assumed to follow given discrete probability distributions. This study proposes a nonlinear stochastic integer program with recourse to formulate the vehicle routing problem with stochastic demands and time windows (VRPTW‐SD, for short). The objective of the VRPTW‐SD is to minimize the total cost of the first‐stage solution and expected recourse cost of the second‐stage solution. The total cost of the first‐stage problem includes the total travel cost for all links and the total waiting cost at all nodes. When a vehicle capacity is attained or exceeded, recourse actions are needed and recourse costs incurred in order to finish the planned route schedules. Two categories of schedule failure are introduced in this work; the recourse costs derive from the variations in travel time travel time, waiting time, and penalties of late arrival for time windows. In addition, an optimization algorithm is developed for solving the VRPTW‐SD, according to the framework of the L‐shaped method. Numerical results are given to demonstrate its validity.     

集装箱车辆调度问题的变邻域禁忌搜索算法

研究一类带工作时间约束的集装箱专用车辆调度问题的混合禁忌搜索算法.此问题可分解为车辆路线设定和车辆分配两个组合优化问题,但是两个问题的分开求解最优解的组合却并不一定是总问题的最优解.首先对问题给出数学描述,之后通过引入一个变邻域搜索策略,提出一个解决该问题的混合禁忌搜索算法.该算法使用两行向量进行编码,采用随机扩大禁忌步长,并设计三种邻域变换定义,采用变邻域策略来扩大搜索空间.最后通过对6个不同规模算例求解验证该算法在解决此类问题的有效性.     

Mathematical formulation and heuristic algorithms for optimisation of auto-part milk-run logistics network considering forward and reverse flow of pallets

The operational planning of distribution network for automotive industry is complex with many conditions to consider, including heterogeneous fleet, enforcing the feasibility of 3D-packing of pallets into vehicles to address the vehicle's capacity in terms of weight and volume, compatibility of orders in a vehicle, returning empty pallets from assembly-plants backwards to suppliers, and delivery time windows. A mathematical model (MILP) is proposed that takes account of these conditions to minimise total transportation costs. The network structure can be a combination of direct shipment and milk-run for both forward and reverse flow of pallets. The model is solved optimally for small-size problems. For solving larger problems, a heuristic algorithm (in two versions) is proposed that uses a similarity measure to generate a reasonable list of orders. Best/first-fit strategies are employed to generate a feasible solution with the aid of a relaxed version of the proposed MILP. Improvement heuristics are also designed. Unlike most of existing constructive heuristics, our aim for developing the heuristic approach is to force routing decision, with all of its considerations, being made optimal. We also use the proposed best-fit strategy in the body of grouping evolution strategy (GES) algorithm to attain an effective meta-heuristic approach. The effectiveness of heuristics is tested on generated instances which demonstrates they are optimal for small-size problems. They are also tested on the data of daily auto-parts shipments gathered from the largest Iranian automobile company. Results demonstrate there exists a significant potential for cost saving through milk-run strategy compared with the direct shipping strategy.     

Operational planning models for distribution networks

The design and optimisation of a logistic network deals with a wide set of decisions, e.g. the determination of the best location and capacity of the different logistic facilities (production plants, distribution centres, transit points, wholesalers, etc.), the allocation of the product demand coming from customers in presence (or absence) of fractionable flows of material, the determination of the best transportation mode (truck, rail, etc.) as well as loading and routing of vehicles. These decisions involve multiple stages of a distribution network: customers-regional distribution centres (RDC), RDCs-central distribution centres (CDC) and CDCs-production plants and sources, in presence of multiple products and the variable time (i.e. time-dependent product demand and flows of material). This paper presents a top-down methodology that joins the strategic planning, the tactical planning and the operational planning of distribution networks with a special focus on the development of effective heuristic methods to face the vehicle routing problem. Original models and heuristic algorithms for the operational planning are illustrated. The impact of the strategic and tactical decisions on the performance of the operational planning is evaluated by the application of the proposed hierarchical approach to two realistic case studies. Obtained results are illustrated in a what-if experimental analysis conducted on multiple problem settings and realistic scenarios.     

Manufacturing cells' design in consideration of various production factors

A cell formation problem is introduced that incorporates various real-life production factors such as the alternative process routing, operation sequence, operation time, production volume of parts, machine capacity, machine investment cost, machine overload, multiple machines available for machine types and part process routing redesigning cost. None of the cell formation models in the literature has considered these factors simultaneously. A similarity coefficient is developed that incorporates alternative process routing, operation sequence, operation time and production volume factors. Although very few studies have considered the machine capacity violated issue under the alternative process routing environment, owing to the difficulties of the issue discussed here, these studies fail to deal with the issue because they depend on some unrealistic assumptions. Five solutions have been proposed here and are used to cope with this difficulty. A heuristic algorithm that consists of two stages is developed. The developed similarity coefficient is used in stage 1 to obtain basic machine cells. Stage 2 solves the machine-capacity violated issue, assigns parts to cells, selects process routing for each part and refines the final cell formation solution. Some numerical examples are used to compare with other related approaches in the literature and two large size problems are also solved to test the computational performance of the developed algorithm. The computational results suggest that the approach is reliable and efficient in either the quality or the speed for solving cell formation problems.     

Indirect search for the vehicle routing problem with pickup and delivery and time windows

The vehicle routing problem with pickup and delivery and time windows (VRPPDTW) is one of the prominent members studied in the class of rich vehicle routing problems and it has become one of the challenges for developing heuristics which are accurate and fast at the same time. Indirect local search heuristics are ideally suited to flexibly handle complex constraints as those occurring in rich combinatorial optimization problems by separating the problem of securing feasibility of solutions from the objective-driven metaheuristic search process using simple encodings and appropriate decoders. In this paper we show that the approach of indirect local search with greedy decoding (GIST) is not only flexible and simple but when applied to the VRPPDTW it also gives results which are competitive with state-of-the-art VRPPDTW-methods by Li and Lim, as well as Pankratz.     

Solving the heterogeneous fixed fleet open vehicle routing problem by a combined metaheuristic algorithm

The vehicle routing problem (VRP) is a well-known combinatorial optimisation problem and holds a central place in logistics management. Many exact, heuristic and metaheuristic approaches have been proposed to solve VRP. An important variant of the VRP arises when a ?eet of vehicles is fixed and characterised by different capacities for distribution activities. The problem is known as the heterogeneous fixed fleet VRP (HFFVRP). The HFFVRP is a natural generalisation of the VRP with several vehicle types, each type being defined by a capacity, a fixed cost and a cost per distance unit, and can cover more practical situations in transportation. This problem consists of determining a set of vehicle trips of minimum total length in which a set of customers is to be satisfied in the demand constraints using identical vehicles with limited capacity. If open routes instead of closed ones are considered in the HFFVRP, the problem becomes a heterogeneous fixed fleet Open VRP (HFFOVRP) which has numerous applications in industrial and service problems. In this paper, a bone route algorithm which uses the tabu search as an improved procedure is utilised to solve the HFFOVRP. The proposed algorithm was tested empirically on a 24 of generated VRPs, and compared with elite ant system and ant colony system. In all cases, the proposed algorithm finds the best-known solutions within a reasonable time.     

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。     

Models and algorithms for the heterogeneous dial-a-ride problem with driver-related constraints

This paper introduces models and algorithms for a static dial-a-ride problem arising in the transportation of patients by non-profit organizations such as the Austrian Red Cross. This problem is characterized by the presence of heterogeneous vehicles and patients. In our problem, two types of vehicles are used, each providing a different capacity for four different modes of transportation. Patients may request to be transported either seated, on a stretcher or in a wheelchair. In addition, some may require accompanying persons. The problem is to construct a minimum-cost routing plan satisfying service-related criteria, expressed in terms of time windows, as well as driver-related constraints expressed in terms of maximum route duration limits and mandatory lunch breaks. We introduce both a three-index and a set-partitioning formulation of the problem. The linear programming relaxation of the latter is solved by a column generation algorithm. We also propose a variable neighborhood search heuristic. Finally, we integrate the heuristic and the column generation approach into a collaborative framework. The column generation algorithm and the collaborative framework provide tight lower bounds on the optimal solution values for small-to-medium-sized instances. The variable neighborhood search algorithm yields high-quality solutions for realistic test instances.     

Vehicle routing and reverse logistics: The vehicle routing problem with simultaneous delivery and pick-up

Recently, the increasing focus on environmental protection has led to significant changes in logistics processes. In addition to the distribution process to the customers, re-usable packaging and goods to be recycled or remanufactured have to be transported in the reverse direction. If both tasks have to be performed simultaneously at the customers' locations which are serviced by a fleet of vehicles stationed in a depot or distribution/redistribution center, the vehicle routing problem with simultaneous delivery and pick-up arises. In this paper, the relation between this problem and other vehicle routing problems is investigated. A heuristic construction procedure is suggested. The proposed algorithm is successfully applied to a real-life problem as well as test instances introduced in the literature earlier. In addition, randomly generated instances are tackled in order to try to determine favorable settings for the parameters used in the solution approach.     

Generalisation of unidirectional loop layout problem and solution by a genetic algorithm

Unidirectional loop layouts (ULLs) are the preferred layouts in manufacturing systems owing to their relative low investment costs, high material handling elasticity and routing flexibility. Existing formulations of the unidirectional loop layout problem are concentrated on the arrangement of workstations under the assumption that the number and location of loading and unloading stations are known. In this study, the unidirectional loop layout problem is generalised by consideration of potentially attachable loading/unloading equipment to each workstation and releasing of the predetermined number of loading and unloading stations. Thus, more efficient and effective loop layout designs are allowed by eliminating some artificial restrictions. The present ULL model is generalised and a genetic algorithm is developed to solve the problem. Solutions obtained by the genetic algorithm outperformed those obtained by conventional methods. Additionally, comparisons of the generalised model with existing models on randomly generated test problems yielded encouraging results.     

Integrated production scheduling and vehicle routing problem with job splitting and delivery time windows

In this paper, we study a production scheduling and vehicle routing problem with job splitting and delivery time windows in a company working in the metal packaging industry. In this problem, a set of jobs has to be processed on unrelated parallel machines with job splitting and sequence-dependent setup time (cost). Then the finished products are delivered in batches to several customers with heterogeneous vehicles, subject to delivery time windows. The objective of production is to minimize the total setup cost and the objective of distribution is to minimize the transportation cost. We propose mathematical models for decentralized scheduling problems, where a production schedule and a distribution plan are built consecutively. We develop a two-phase iterative heuristic to solve the integrated scheduling problem. We evaluate the benefits of coordination through numerical experiments.     

Simulation-based optimisation approach for the stochastic two-echelon logistics problem

This work proposes a simulation-based optimisation approach for the two-echelon vehicle routing problem with stochastic demands (2E-VRPSD). In the proposed 2E-VRPSD, freight delivery from the depot to the customers is managed by shipping the freight through intermediate satellites, while each customer has a stochastic demand. The 2E-VRPSD is an extension of the famous capacitated vehicle routing problem with stochastic demands and the two-echelon vehicle routing problem (2E-VRP). A tabu search algorithm is designed to solve the 2E-VRPSD, in which Monte Carlo sampling is adopted to tackle the issue of stochastic demands. Modified two-echelon vehicle routing problem benchmark instances are used in the numerical experiments. The computational results show the advantage of the proposed simulation-based approach.     

混合智能算法在CVRPTW中的应用

考虑到遗传算法本身存在易"早熟收敛"的缺陷,提出将模拟退火算法中的Metropolis接受准则引入到遗传算法的群体更新策略中,并将其应用于物流管理中的带容量约束和时间窗的车辆路径问题(CVRPTW).针对Solomon提出的几个标准问题,从数值计算上探索了遗传算法和模拟退火算法融合后的优化能力,获得了满意的效果.     

共享电动车电池配送问题研究

共享电动车电池的配送方案关系到用户的切身体验和企业利益。为制定最优配送方案，真正打通人们出行的“最后一公里”，本文考虑企业对成本的要求和用户对时效性的要求，以总配送成本最小以及用户满意度最高为目标建立了一个带软时间窗的车辆路径问题模型，利用扫描法和基于最佳路径成本的交叉算子改进了传统遗传算法，用算例验证了模型与改进算法的有效性，并通过数值实验找出了种群大小、迭代次数与最优解之间的相关关系。