A tabu search algorithm for the periodic vehicle routing problem with multiple vehicle trips and accessibility restrictions

In this paper, we consider a periodic vehicle routing problem that includes, in addition to the classical constraints, the possibility of a vehicle doing more than one route per day, as long as the maximum daily operation time for the vehicle is not exceeded. In addition, some constraints relating to accessibility of the vehicles to the customers, in the sense that not every vehicle can visit every customer, must be observed. We refer to the problem we consider here as the site-dependent multi-trip periodic vehicle routing problem. An algorithm based on tabu search is presented for the problem and computational results presented on randomly generated test problems that are made publicly available. Our algorithm is also tested on a number of routing problems from the literature that constitute particular cases of the proposed problem. Specifically we consider the periodic vehicle routing problem; the site-dependent vehicle routing problem; the multi-trip vehicle routing problem; and the classical vehicle routing problem. Computational results for our tabu search algorithm on test problems taken from the literature for all of these problems are presented.     

A rich vehicle routing problem dealing with perishable food: a case study

This paper presents a successful application of operations research techniques in guiding the decision making process to achieve a superior operational efficiency in core activities. We focus on a rich vehicle routing problem faced by a Portuguese food distribution company on a daily basis. This problem can be described as a heterogeneous fleet site dependent vehicle routing problem with multiple time windows. We use the adaptative large neighbourhood search framework, which has proven to be effective to solve a variety of different vehicle routing problems. Our plans are compared against those of the company and the impact that the proposed decision support tool may have in terms of cost savings is shown. The algorithm converges quickly giving the planner considerably more time to focus on value-added tasks, rather than manually correct the routing schedule. Moreover, contrarily to the necessary adaptation time of the planner, the tool is quite flexible in following market changes, such as the introduction of new customers or new products.     

A priori policy evaluation and cyclic-order-based simulated annealing for the multi-compartment vehicle routing problem with stochastic demands

We develop methods to estimate and exactly calculate the expected cost of a priori policies for the multi-compartment vehicle routing problem with stochastic demands, an extension of the classical vehicle routing problem where customer demands are uncertain and products must be transported in separate partitions. We incorporate our estimation procedure into a cyclic-order-based simulated annealing algorithm, significantly improving the best-known solution values for a set of benchmark problems. We also extend the updating procedure for a cyclic order’s candidate route set to duration-constrained a priori policies.     

A Lagrangean relaxation heuristic for vehicle routing

This paper presents a new heuristic algorithm for the vehicle routing problem (VRP) which makes use of Lagrangean relaxation to transform the VRP into a modified m-traveling salesman problem. Application of the proposed algorithm to test problems from the literature has produced new best-known solutions.     

The single vehicle routing problem with toll-by-weight scheme: A branch-and-bound approach

Expressways in China make use of the toll-by-weight scheme, in which expressway tolls are collected based on the weight and traveling distance of the vehicle. Most vehicle routing models assume that the cost of traversing each edge is equivalent to edge length or some constant; as a result, such models cannot be practically applied to the Chinese expressway transportation system. This study addresses a new single vehicle routing problem that takes the vehicle’s (laden and unladen) weight into account. To solve this problem exactly, we provide a branch-and-bound algorithm with a provably valid lower bound measure, along with five dominance checkers for additional pruning. We analyze our algorithm using instances generated from standard TSP test cases, as well as two new sets of test cases based on real expressway information from the Gansu and Jiangxi provinces in China. The algorithm can be applied to any toll scheme in which the toll per unit distance monotonically increases with weight, even if the toll function is non-linear.     

A Branch-and-Cut-and-Price Approach for the Capacitated m-Ring-Star Problem

The Capacitated m-ring-star Problem is a variant of the classical one-depot capacitated vehicle routing problem in which a customer is either on a route or is connected to another customer or to some Steiner point present in a route. We develop a new exact algorithm for this problem using a branch-and-cut-and-price approach and compare its performance with that of a branch-and-cut algorithm proposed earlier in the literature. Computational results show that the new algorithm outperforms the branch-and-cut one in many instance classes.     

A period vehicle routing case study

The period vehicle routing problem is a multilevel problem assembling two classical problems: the assignment problem and the vehicle routing problem. Collection days have to be assigned to each customer and vehicle routes have to be designed for each day of the period (time horizon) so that the total distribution cost is minimised. The interaction between the temporal and spatial aspects turns the problem into one of the most challenging variations of vehicle routing. In this paper, we present the study of a real period vehicle routing system: the collection of recycling paper containers in the City Council of Almada, Portugal.     

Solving the dynamic capacitated location-routing problem with fuzzy demands by hybrid heuristic algorithm

In this paper, the dynamic capacitated location-routing problem with fuzzy demands (DCLRP-FD) is considered. In the DCLRP-FD, facility location problem and vehicle routing problem are solved on a time horizon. Decisions concerning facility locations are permitted to be made only in the first time period of the planning horizon but, the routing decisions may be changed in each time period. Furthermore, the vehicles and depots have a predefined capacity to serve the customers with altering demands during the time horizon. It is assumed that the demands of customers are fuzzy variables. To model the DCLRP-FD, a fuzzy chance-constrained programming is designed based upon the fuzzy credibility theory. To solve this problem, a hybrid heuristic algorithm (HHA) with four phases including the stochastic simulation and a local search method are proposed. To achieve the best value of two parameters of the model, the dispatcher preference index (DPI) and the assignment preference index (API), and to analyze their influences on the final solution, numerical experiments are carried out. Moreover, the efficiency of the HHA is demonstrated via comparing with the lower bound of solutions and by using a standard benchmark set of test problems. The numerical examples show that the proposed algorithm is robust and could be used in real world problems.     

A vehicle routing problem with multi-trips and time windows for circular items

This article presents a vehicle routing problem with time windows, multiple trips, a limited number of vehicles and loading constraints for circular objects. This is a real problem experienced by a home delivery service company. A linear model is proposed to handle small problems and a two-step heuristic method to solve real size instances: the first step builds an initial solution through the modification of the Solomon I1 sequential insertion heuristic, and the second step improves the initial solution through the Tabu search algorithm proposed; in both steps, the problems related to circle packing with different sizes and bin packing are solved jointly with the use of heuristics. Finally, the computing results for two different sets of instances are presented.     

Solving multiobjective vehicle routing problem with stochastic demand via evolutionary computation

This paper considers the routing of vehicles with limited capacity from a central depot to a set of geographically dispersed customers where actual demand is revealed only when the vehicle arrives at the customer. The solution to this vehicle routing problem with stochastic demand (VRPSD) involves the optimization of complete routing schedules with minimum travel distance, driver remuneration, and number of vehicles, subject to a number of constraints such as time windows and vehicle capacity. To solve such a multiobjective and multi-modal combinatorial optimization problem, this paper presents a multiobjective evolutionary algorithm that incorporates two VRPSD-specific heuristics for local exploitation and a route simulation method to evaluate the fitness of solutions. A new way of assessing the quality of solutions to the VRPSD on top of comparing their expected costs is also proposed. It is shown that the algorithm is capable of finding useful tradeoff solutions for the VRPSD and the solutions are robust to the stochastic nature of the problem. The developed algorithm is further validated on a few VRPSD instances adapted from Solomon’s vehicle routing problem with time windows (VRPTW) benchmark problems.     

基于交通流的多模糊时间窗车辆路径优化

研究了基于交通流的多模糊时间窗车辆路径问题,考虑了实际中不断变化的交通流以及客户具有多个模糊时间窗的情况,以最小化配送总成本和最大化客户满意度为目标,构建基于交通流的多模糊时间窗车辆路径模型。根据伊藤算法的基本原理,设计了求解该模型的改进伊藤算法,结合仿真算例进行了模拟计算,并与蚁群算法的计算结果进行了对比分析,结果表明,利用改进伊藤算法求解基于交通流的多模糊时间窗车辆路径问题,迭代次数小,效率更高,能够在较短的时间内收敛到全局最优解,可以有效的求解多模糊时间窗车辆路径问题。     

A heuristic solution method for node routing based solid waste collection problems

This paper considers a real world waste collection problem in which glass, metal, plastics, or paper is brought to certain waste collection points by the citizens of a certain region. The collection of this waste from the collection points is therefore a node routing problem. The waste is delivered to special sites, so called intermediate facilities (IF), that are typically not identical with the vehicle depot. Since most waste collection points need not be visited every day, a planning period of several days has to be considered. In this context three related planning problems are considered. First, the periodic vehicle routing problem with intermediate facilities (PVRP-IF) is considered and an exact problem formulation is proposed. A set of benchmark instances is developed and an efficient hybrid solution method based on variable neighborhood search and dynamic programming is presented. Second, in a real world application the PVRP-IF is modified by permitting the return of partly loaded vehicles to the depots and by considering capacity limits at the IF. An average improvement of 25% in the routing cost is obtained compared to the current solution. Finally, a different but related problem, the so called multi-depot vehicle routing problem with inter-depot routes (MDVRPI) is considered. In this problem class just a single day is considered and the depots can act as an intermediate facility only at the end of a tour. For this problem several instances and benchmark solutions are available. It is shown that the algorithm outperforms all previously published metaheuristics for this problem class and finds the best solutions for all available benchmark instances.     

A branch-and-cut algorithm for the capacitated open vehicle routing problem

In open vehicle routing problems, the vehicles are not required to return to the depot after completing service. In this paper, we present the first exact optimization algorithm for the open version of the well-known capacitated vehicle routing problem (CVRP). The algorithm is based on branch-and-cut. We show that, even though the open CVRP initially looks like a minor variation of the standard CVRP, the integer programming formulation and cutting planes need to be modified in subtle ways. Computational results are given for several standard test instances, which enables us for the first time to assess the quality of existing heuristic methods, and to compare the relative difficulty of open and closed versions of the same problem.     

改进蚁群算法在应急VRP问题中的应用研究

提出一种改进的蚁群算法优化应急物流配送车辆路径问题算法,设计了应急物流配送车辆路径问题的数学模型,并利用计算机进行了仿真实验.实验结果表明,方法能有效解决应急物流配送车辆路径问题,具有一定的理论价值和实际意义.     

面向电商终端物流配送的电动车配置与路径集成优化

在电子商务终端物流配送方面,存在能力与需求的矛盾。一方面,电动车存在货物容量约束和电池电量约束,配送能力有限;另一方面,一个物流配送点需要为众多的消费者进行门到门的配送,配送任务繁重。针对电子商务环境下终端物流配送规模大、电动车货物容量和行驶里程有限的问题,建立电商终端物流配送的电动车配置与路径规划集成优化模型,并提出一种基于临近城市列表的双策略蚁群算法,实现物流配送电动车辆配置与配送路径集成优化。该模型以电动车辆数最少和总路径最短为目标,以电动车货物容量和电池续航里程为约束,是带容量的车辆路径问题的进一步扩展,属于双容量约束路径规划问题。双策略蚁群算法在货物容量和续航里程的约束下,将蚁群搜索策略分为两类,即基于临近城市列表的局部搜索策略和全局搜索策略,在提高搜索效率的同时防止陷入局部优化。最后,通过阿里巴巴旗下菜鸟网络科技有限公司在上海的30组真实配送数据进行了测试,验证双策略蚁群算法显著优于一般蚁群算法。     

An approximate dynamic programming approach for the vehicle routing problem with stochastic demands

This paper examines approximate dynamic programming algorithms for the single-vehicle routing problem with stochastic demands from a dynamic or reoptimization perspective. The methods extend the rollout algorithm by implementing different base sequences (i.e. a priori solutions), look-ahead policies, and pruning schemes. The paper also considers computing the cost-to-go with Monte Carlo simulation in addition to direct approaches. The best new method found is a two-step lookahead rollout started with a stochastic base sequence. The routing cost is about 4.8% less than the one-step rollout algorithm started with a deterministic sequence. Results also show that Monte Carlo cost-to-go estimation reduces computation time 65% in large instances with little or no loss in solution quality. Moreover, the paper compares results to the perfect information case from solving exact a posteriori solutions for sampled vehicle routing problems. The confidence interval for the overall mean difference is (3.56%, 4.11%).     

Stochastic single vehicle routing problem with delivery and pick up and a predefined customer sequence

In this paper we study the routing of a single vehicle that delivers products and picks up items with stochastic demand. The vehicle follows a predefined customer sequence and is allowed to return to the depot for loading/unloading as needed. A suitable dynamic programming algorithm is proposed to determine the minimum expected routing cost. Furthermore, the optimal routing policy to be followed by the vehicle’s driver is derived by proposing an appropriate theorem. The efficiency of the algorithm is studied by solving large problem sets.     

Implicit depot assignments and rotations in vehicle routing heuristics

Vehicle routing variants with multiple depots and mixed fleet present intricate combinatorial aspects related to sequencing choices, vehicle type choices, depot choices, and depots positioning. This paper introduces a dynamic programming methodology for efficiently evaluating compound neighborhoods combining sequence-based moves with an optimal choice of vehicle and depot, and an optimal determination of the first customer to be visited in the route, called rotation. The assignment choices, making the richness of the problem, are thus no more addressed in the solution structure, but implicitly determined during each move evaluation. Two meta-heuristics relying on these concepts, an iterated local search and a hybrid genetic algorithm, are presented. Extensive computational experiments demonstrate the remarkable performance of these methods on classic benchmark instances for multi-depot vehicle routing problems with and without fleet mix, as well as the notable contribution of the implicit depot choice and positioning methods to the search performance. New state-of-the-art results are obtained for multi-depot vehicle routing problems (MDVRP), and multi-depot vehicle fleet mix problems (MDVFMP) with unconstrained fleet size. The proposed concepts are fairly general, and widely applicable to many other vehicle routing variants.     

The multi-trip vehicle routing problem

The basic vehicle routing problem is concerned with the design of a set of routes to serve a given number of customers, minimising the total distance travelled. In that problem, each vehicle is assumed to be used only once during a planning period, which is typically a day, and therefore is unrepresentative of many practical situations, where a vehicle makes several journeys during a day. The present authors have previously published an algorithm which outperformed an experienced load planner working on the complex, real-life problems of Burton's Biscuits, where vehicles make more than one trip each day. This present paper uses a simplified version of that general algorithm, in order to compare it with a recently published heuristic specially designed for the theoretical multi-trip vehicle routing problem.     

Approximation results for a min-max location-routing problem

This paper studies a min-max location-routing problem, which aims to determine both the home depots and the tours for a set of vehicles to service all the customers in a given weighted graph, so that the maximum working time of the vehicles is minimized. The min-max objective is motivated by the needs of balancing or fairness in vehicle routing applications. We have proved that unless NP=P, it is impossible for the problem to have an approximation algorithm that achieves an approximation ratio of less than 4/3. Thus, we have developed the first constant ratio approximation algorithm for the problem. Moreover, we have developed new approximation algorithms for several variants, which improve the existing best approximation ratios in the previous literature.