Multi-depot vehicle routing problem with time windows under shared depot resources

A new variant of multi-depot vehicle routing problem with time windows is studied. In the new variant, the depot where the vehicle ends is flexible, namely, it is not entirely the same as the depot that it starts from. An integer programming model is formulated with the minimum total traveling cost under the constrains of time window, capacity and route duration of the vehicle, the fleet size and the number of parking spaces of each depot. As the problem is an NP-Hard problem, a hybrid genetic algorithm with adaptive local search is proposed to solve it. Finally, the computational results show that the proposed method is competitive in terms of solution quality. Compared with the classic MDVRPTW, allowing flexible choice of the stop depot can further reduce total traveling cost.     

有模糊时间窗的车辆调度组合干扰管理研究

研究带有模糊时间窗的车辆调度组合干扰管理模型及其混合遗传算法.采用时间窗模糊化处理方法,定义客户满意度函数,根据干扰管理思想对车辆调度中组合性干扰事件进行分析,从配送路径、配送成本和客户满意度三个方面进行干扰辨识与度量,建立基于模糊时间窗的车辆调度组合干扰管理模型;构造模型求解的混合遗传算法,将最佳客户插入规则与遗传算法结合,同时在算法中嵌入模糊优化程序以处理问题的模糊特征;进行数值实验,实验结果验证了模型与算法的有效性.     

An investigation into the vehicle routing problem with time windows and link capacity constraints

In this work, we investigate a new, yet practical, variant of the vehicle routing problem called the vehicle routing problem with time windows and link capacity constraints (VRPTWLC). The problem considers new constraints imposed on road links with regard to vehicle passing tonnage, which is motivated by a business project with a Hong Kong transportation company that transports hazardous materials (hazmats) across the city and between Hong Kong and mainland China. In order to solve this computationally challenging problem, we develop a tabu search heuristic with an adaptive penalty mechanism (TSAP) to help manage the company's vehicle fleet. A new data set and its generation scheme are also presented to help validate our solutions. Extensive computational experiments are conducted, showing the effectiveness of the proposed solution approach.     

Two approaches to solving the multi-depot vehicle routing problem with time windows in a time-based logistics environment

This paper presents a two-phase heuristic method that can be used to efficiently solve the intractable multi-depot vehicle routing problem with time windows. The waiting time that was ignored by previous researchers is considered in this study. The necessity of this consideration is verified through an initial experiment. The results indicate that the waiting time has a significant impact on the total distribution time and the number of vehicles used when solving test problems with narrow time windows. In addition, to fairly evaluate the performance of the proposed heuristic method, a meta-heuristic method, which extends the unified tabu search of Cordeau et al., is proposed. The results of a second experiment reveal that the proposed heuristic method can obtain a better solution in the case of narrow time windows and a low capacity ratio, while the proposed meta-heuristic method outperforms the proposed heuristic method, provided that wide time windows and a high capacity ratio are assumed. Finally, a well-known logistics company in Taiwan is used to demonstrate the method, and a comparison is made, which shows that the proposed heuristic method is superior to the current method adopted by the case company.     

Integrated Ant Colony and Tabu Search approach for time dependent vehicle routing problems with simultaneous pickup and delivery

Today manufacturers have become much more concerned with the coordination of both manufacturing (of new products) and recycling (of reusable resources) operations. This requires simultaneous scheduling of both forward and reverse flows of goods over a supply chain network. This paper studies time dependent vehicle routing problems with simultaneous pickup and delivery (TD-VRPSPD). We formulate this problem as a mixed integer programming model, where the time step function is used to calculate the travel time. To efficiently solve this complex problem, we develop a hybrid algorithm that integrates both Ant Colony System (ACS) and Tabu Search (TS) algorithms. Our algorithm uses the pheromones, travel time and vehicle residual loading capacity as a factor structure according to the characteristics of TD-VRPSPD. In our computational experiments, 56 groups of benchmark instances are used to evaluate the performance of our hybrid algorithm. In addition, we compare the performance of our hybrid algorithm with those of individual ACS and TS algorithms. The computational results suggest that our hybrid algorithm outperform stand-alone ACS and the TS algorithms.     

Polynomial time approximation schemes for minimum disk cover problems

The following planar minimum disk cover problem is considered in this paper: given a set D\mathcal{D} of n disks and a set ℘ of m points in the Euclidean plane, where each disk covers a subset of points in ℘, to compute a subset of disks with minimum cardinality covering ℘. This problem is known to be NP-hard and an algorithm which approximates the optimal disk cover within a factor of (1+ε) in O(mn^{O(\frac1e2log2\frac1e)})\mathcal{O}(mn^{\mathcal{O}(\frac{1}{\epsilon^{2}}\log^{2}\frac{1}{\epsilon})}) time is proposed in this paper. This work presents the first polynomial time approximation scheme for the minimum disk cover problem where the best known algorithm can approximate the optimal solution with a large constant factor. Further, several variants of the minimum disk cover problem such as the incongruent disk cover problem and the weighted disk cover problem are considered and approximation schemes are designed.     

基于矩阵变换的车辆路径问题仿真优化方法

针对车辆路径问题这一求解难题,提出基于启发式变换的仿真优化原理和求解方法,建立了基于邻接矩阵的车辆路径问题的数学模型;利用启发式运行规则对仿真运行的参数进行了分析,通过矩阵变换改进优化搜索策略并找出最优解或满意解.算例求解表明,基于矩阵变换的仿真优化方法具有良好的稳定性和求解效率.该项研究为求解车辆路径问题这一难题提供了新思路.     

A visual interactive approach to classical and mixed vehicle routing problems with backhauls

In this paper a new visual interactive approach for the classical vehicle routing problem with backhauls (VRPB) and its extensions is presented. The classical VRPB is the problem of designing minimum cost routes from a single depot to two type customers that are known as Backhaul (pickup) and Linehaul (delivery) customers where deliveries after pickups are not allowed. The mixed VRPB is an extension of the classical VRPB where deliveries after pickups are allowed.     

Local search algorithms for multiple-depot vehicle routing and for multiple traveling salesman problems with proved performance guarantees

We consider two related problems: the multiple-depot vehicle routing problem (MDVRP) and the Multiple traveling salesman problem (mTSP). In both of them, given is the complete graph on n vertices \(G = (V,E)\) with nonnegative edge lengths that form a metric on V. Also given is a positive integer k. In typical applications, V represents locations of customers and k represents the number of available vehicles. In MDVPR, we are also given a set of k depots \(\{O_1,\ldots ,O_k\} \subseteq V\) , and the goal is to find a minimum-length cycle cover of G of size k, that is, a collection of k (possibly empty) cycles such that each \(v \in V\) is in exactly one cycle, and each cycle in the cover contains exactly one depot. In mTSP, no depots are given, so the goal is to find (any) minimum-length cycle cover of G of size k. We present local search algorithms for both problems, and we prove that their approximation ratio is 2.     

大规模邻域搜索算法求解时变车辆调度问题

对时变网络车辆调度问题提出一种满足先入先出准则的时变处理方法,并建立相应的数学模型,提出一种基于大规模邻域搜索技术的智能优化算法进行求解,算法顶层采用动态规划算法搜索环状交换邻域以得到每辆车的最佳服务顾客集合;底层设计动态搜索算法用以安排每辆车的最佳服务路线.在此基础上提出顶层加入虚拟顾客和底层嵌入insert两类改进策略.通过实验仿真比较,验证了所提算法的有效性.     

Approximation schemes for two-machine flow shop scheduling with two agents

In this paper we consider two-machine flow shop scheduling with two agents. Two models are investigated. One is the weighted-sum optimization model and the other is the constrained optimization model. For the former, we show that it is weakly NP-hard and propose a fully polynomial time approximation scheme. For the latter, we also show the problem is weakly NP-hard. With violating the constraint a factor of ?? a fully polynomial time approximation scheme is provided.     

A metaheuristic for the delivery man problem with time windows

Journal of Combinatorial Optimization - The Delivery Man Problem with Time Windows (DMPTW) is an extension of the Delivery Man Problem. The objective of DMPTW is to minimize the sum of...     

Combinatorial analysis for route first-cluster second vehicle routing

Two Route first-cluster second vehicle routing algorithms are contrasted in the first section of the paper. Next, the ‘large’ number of feasible solutions to a multiple travelling salesman problem is established given that each salesman can visit any number of customers in a stated range. An approximate expression is given for the ‘small’ fraction of this solution space searched by a route first-cluster second vehicle routing heuristic. Nevertheless, this heuristic is seen to be a very efficient means of searching its solution space.     

Capacitated vehicle routing problem on line with unsplittable demands

Journal of Combinatorial Optimization - In this paper we study the capacitated vehicle routing problem. An instance of capacitated vehicle routing problem consists of a set of vertices with demands...     

A branch-and-price algorithm for production routing problems with carbon cap-and-trade

This study presents a model for a pollution production-routing problem under carbon cap-and-trade. The aim is to incorporate carbon emissions into production inventory and routing decisions. The model is characterized by an additional flow-related cost structure, which generalizes models for pollution-routing problems and production inventory and routing problems. Correspondingly, we develop a branch-and-price heuristic by incorporating a column-generation formulation based on the Dantzig–Wolfe decomposition. In addition, we design an ad hoc label-setting algorithm to deal with time-slice networks in pricing subproblems. Computational results allow us to provide managerial insights concerning reduction of carbon emissions in supply chains. We prove that the model has the potential to reduce emission levels of carbon dioxide and operational costs.     

A heuristic algorithm for the period vehicle routing problem

In this paper we consider the period vehicle routing problem, which is the problem of designing routes for delivery vehicles to meet customer service level requirements (not all customers require delivery on every day in the period). A heuristic algorithm, based upon the daily vehicle routing algorithm of Fisher and Jaikumar, is presented and computational results are given for test problems drawn from the literature.     

Dynamic vehicle routing for online B2C delivery

Electronic commerce (EC) is increasingly popular in today's businesses. The business-to-consumer EC environment has voluminous, unpredictable, and dynamically changing customer orders. A major part of the delivery system of this environment is the dynamic vehicle routing (DVR) system. This study investigates several algorithms suitable for solving the DVR problem in business-to-consumer (B2C) EC environment. It designs the solution process into three phases: initial-routes formation, inter-routes improvement, and intra-route improvement. A computer program is created to demonstrate a system simulating vehicle routing process under the online B2C environment. The simulated system collects data for system performance indexes such as simulation time, travel distance, delivery time, and delay time. The results show that when orders are placed through the Internet in an online B2C environment, the Nearest algorithms can be used to find satisfactory routes during the first phase of a DVR delivery system. The three-phase solution process is proven to be significantly better in travel distance and delivery time than the conventional single-phase solution process.     

Route first—Cluster second methods for vehicle routing

In this paper we consider route first—cluster second methods for the vehicle routing problem. Extensions to the basic method both to improve its effectiveness and to enable it to cope with practical constraints are described. Computational results are given for the method applied to standard vehicle routing problems drawn from the literature.     

Approximation algorithms for connected facility location problems

We study Connected Facility Location problems. We are given a connected graph G=(V,E) with nonnegative edge cost c _e for each edge e∈E, a set of clients D⊆V such that each client j∈D has positive demand d _j and a set of facilities F⊆V each has nonnegative opening cost f _i and capacity to serve all client demands. The objective is to open a subset of facilities, say , to assign each client j∈D to exactly one open facility i(j) and to connect all open facilities by a Steiner tree T such that the cost is minimized for a given input parameter M≥1. We propose a LP-rounding based 8.29 approximation algorithm which improves the previous bound 8.55 (Swamy and Kumar in Algorithmica, 40:245–269, 2004). We also consider the problem when opening cost of all facilities are equal. In this case we give a 7.0 approximation algorithm.     

具有模糊预约时间的VRP混合遗传算法

在对具有模糊预约时间的多对多货物收发情况下的车辆路径问题进行简单描述的基础上,构建了该问题的多目标数学规划模型,提出了解决该问题的一种基于插入启发式算法、并用修正的推—碰—掷过程进行改进的混合遗传算法,最后,给出了该问题的一个计算实例,并与改进的Solomon插入启发式算法进行了比较.