A planning model and solution algorithm for multi-trip split-delivery vehicle routing and scheduling problems with time windows

This study proposes a daily vehicle routing model for minimizing the total cost of replenishing inventory within a supply chain. The first major contribution of this research is to allow multiple use of vehicles in a split delivery vehicle routing problem with time windows (SDVRPTW), which is more realistic for various real-life applications. The multi-trip SDVRPTW (MTSDVRPTW) is formulated using the time–space network technique, which provides greater flexibility for formulating the complicated interactions between vehicles and products when multi-trip, split delivery, and delivery time windows are simultaneously considered. The resulting formulation of the MTSDVRPTW can be categorized as an integer multi-commodity network flow problem with side constraints. A two-step solution algorithm is proposed to solve this NP-hard problem, which is the second major contribution of this research. Finally, a real-world scale numerical example is performed to demonstrate and to test the methodology. The results indicate that these vehicle routing problems can be solved effectively and efficiently and that the proposed methodology has great potential for inventory replenishment scheduling where split deliveries and multiple trips for a single vehicle are allowed and time window constraints are imposed.     

A model and a solution algorithm for the car pooling problem with pre-matching information

Most past car pooling studies have focused on the to-work problem (from different origins to a common destination) or the return-from-work problem (from the same origin to different destinations). Pre-matching information, including the carpool partners and the route/schedule for each previously participating vehicle, have rarely been considered. As a result, there has not yet been a suitable method/model developed for solving practical many-to-many car pooling problem with multiple vehicle and person types, as well as pre-matching information, that occur in real-world. In this study we strive to make up this lack by employing a time–space network flow technique to develop a model for this type of car pooling problem with pre-matching information (CPPPMI). The model is formulated as an integer multiple commodity network flow problem. A solution algorithm, based on Lagrangian relaxation and a heuristic for the upper bound solution, is developed to solve the model. To test how well the model and the solution algorithm may be applied to real-world, numerical tests are performed with several problem instances randomly generated based upon data reported from a past study carried out in northern Taiwan. The test results show the effectiveness of the proposed model and solution algorithm.     

A parallel evolutionary algorithm for the vehicle routing problem with heterogeneous fleet

Nowadays genetic algorithms stand as a trend to solve NP-complete and NP-hard problems. In this paper, we present a new hybrid metaheuristic which uses parallel genetic algorithms and scatter search coupled with a decomposition-into-petals procedure for solving a class of vehicle routing and scheduling problems. The parallel genetic algorithm presented is based on the island model and its performance is evaluated for a heterogeneous fleet problem, which is considered a problem much harder to solve than the homogeneous vehicle routing problem.     

有时间窗车辆路径问题的捕食搜索算法

有时间窗车辆路径问题是当前物流配送系统研究中的热点问题,该问题具有NP难性质。难以求得最优解或满意解,在建立有时间窗车辆路径问题数学模型的基础上。设计了一种模仿动物捕食策略的捕食搜索算法．该算法利用控制搜索空间的限制大小来实现算法的局域搜索和全局搜索,具有良好的局部集中搜索和跳出局部最优的能力．通过实例计算,并与相关启发式算法比较．取得了满意的结果．     

An improved model for vehicle routing problem with time constraint based on genetic algorithm

A vehicle routing problem (VRP) with time constraint is one of the important problems in distribution and transportation. Thus the generic VRP and its practical extensions are discussed in great detail in the literatures. In the VRP, the service of a customer must start and finish within a given time interval. The objective of this problem is to minimize the cost of servicing the set of customers without being tardy or exceeding the capacity or travel time of the vehicles. In this research we concentrated on developing a GA–TSP model by improving the genetic algorithm (GA) operators and the initial population. For the computational purpose, we developed a GUI (graphic user interface)-type computer program according to the proposed method. The computational results show that the proposed method is very effective on a set of standard test problems and it can be potentially useful in solving the VRPs.     

A decomposition based memetic algorithm for multi-objective vehicle routing problem with time windows

Multi-objective evolutionary algorithm based on decomposition (MOEA/D) provides an excellent algorithmic framework for solving multi-objective optimization problems. It decomposes a target problem into a set of scalar sub-problems and optimizes them simultaneously. Due to its simplicity and outstanding performance, MOEA/D has been widely studied and applied. However, for solving the multi-objective vehicle routing problem with time windows (MO-VRPTW), MOEA/D faces a difficulty that many sub-problems have duplicated best solutions. It is well-known that MO-VRPTW is a challenging problem and has very few Pareto optimal solutions. To address this problem, a novel selection operator is designed in this work to enhance the original MOEA/D for dealing with MO-VRPTW. Moreover, three local search methods are introduced into the enhanced algorithm. Experimental results indicate that the proposed algorithm can obtain highly competitive results on Solomon׳s benchmark problems. Especially for instances with long time windows, the proposed algorithm can obtain more diverse set of non-dominated solutions than the other algorithms. The effectiveness of the proposed selection operator is also demonstrated by further analysis.     

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.     

Packing first,routing second—a heuristic for the vehicle routing and loading problem

The Vehicle Routing and Loading Problem (VRLP) results by combining vehicle routing, possibly with time windows, and three-dimensional loading. Some packing constraints of high practical relevance, among them an unloading sequence constraint and a support constraint, are also part of the VRLP. Different formulations of the VRLP are considered and the issue is discussed under which circumstances routing and packing should be tackled as a combined task. A two-stage heuristic is presented following a “packing first, routing second” approach, i.e. the packing of goods and the routing of vehicles is done in two strictly separated stages. High quality results are achieved in short computation times for the 46 VRLP instances recently introduced by Moura and Oliveira. Moreover 120 new large benchmark instances including up to 1000 customers and 50,000 boxes are introduced and results for these instances are also reported.     

A Road Timetable to aid vehicle routing and scheduling

Both within and between urban conurbations, the time of a journey and the corresponding shortest path in a road network from an origin to a destination may depend on the time of the day, the day of the week and the season of the year. Significant journey time differences occur mainly due to recurring instances and variations in levels of traffic congestion throughout the year. This paper examines the issues involved in constructing a database of road times for a road network that uses time-dependent data on the travel times for individual roads in the network to provide the expected times and distances between locations for journeys starting at different times. The benefits of time-dependent vehicle routing and scheduling systems are demonstrated by using real-world data for the road network in the north west of England.     

Exact and heuristic algorithms for the vehicle routing problem with multiple interdependent time windows

In this paper a model and several solution procedures for a novel type of vehicle routing problems where time windows for the pickup of perishable goods depend on the dispatching policy used in the solution process are presented. This problem is referred to as Vehicle Routing Problem with multiple interdependent time windows (VRPmiTW) and is motivated by a project carried out with the Austrian Red Cross blood program to assist their logistics department. Several variants of a heuristic constructive procedure as well as a branch-and-bound based algorithm for this problem were developed and implemented. Besides finding the expected reduction in costs when compared with the current procedures of the Austrian Red Cross, the results show that the heuristic algorithms find solutions reasonably close to the optimum in fractions of a second. Another important finding is that increasing the number of pickups at selected customers beyond the theoretical minimum number of pickups yields significantly greater potential for cost reductions.     

A model for aeromedical routing and scheduling

The Aeromedical Airlift Wing of the United States Air Force is responsible for the transportation of military personnel in need of specialized medical treatment to and from various military hospitals. Over eight million active and retired personnel, spouses and dependents benefit from the system. The system operates under a variety of regulations to ensure timely service and safe operation of the aircraft. This paper presents a model of the system to assist the route planners in generating solutions minimizing patient inconvenience. This is achieved by assigning patients to sequences of aircraft while minimizing layovers.     

A knowledge-based evolutionary algorithm for the multiobjective vehicle routing problem with time windows

This paper addresses the multiobjective vehicle routing problem with time windows (MOVRPTW). The objectives are to minimize the number of vehicles and the total distance simultaneously. Our approach is based on an evolutionary algorithm and aims to find the set of Pareto optimal solutions. We incorporate problem-specific knowledge into the genetic operators. The crossover operator exchanges one of the best routes, which has the shortest average distance, the relocation mutation operator relocates a large number of customers in non-decreasing order of the length of the time window, and the split mutation operator breaks the longest-distance link in the routes. Our algorithm is compared with 10 existing algorithms by standard 100-customer and 200-customer problem instances. It shows competitive performance and updates more than 1/3 of the net set of the non-dominated solutions.     

具有同时集送货需求车辆路径问题的混沌量子进化算法研究

针对量子进化算法中旋转角取值的离散性使其解空间的搜索具有跳跃性,提出了基于混沌理论的精英均值计算旋转角算法,并将其应用于具有同时集送货需求车辆路径问题的求解.在理论上分析了解的强可行和弱可行条件的基础上,使用启发式算子对解进行改进.通过仿真实验与其他算法进行了比较,仿真结果表明所提出算法是求解此类问题的有效方法.     

A two-phase metaheuristic for the cumulative capacitated vehicle routing problem

The cumulative capacitated vehicle routing problem, which aims to minimize the total arrival time at customers, is a relatively new variant of vehicle routing problem. It can be used to model many real-world applications, e.g., the important application arisen from the humanitarian aid after a natural disaster. In this paper, an approach, called two-phase metaheuristic, is proposed to deal with this problem. This algorithm starts from a solution. At each iteration, two interdependent phases use different perturbation and local search operators for solution improvement. The effectiveness of the proposed algorithm is empirically investigated. The comparison results show that the proposed algorithm is promising. Moreover, for nine benchmark instances, the two-phase metaheuristic can find better solutions than those reported in the previous literature.     

A genetic algorithm based approach to vehicle routing problem with simultaneous pick-up and deliveries

The vehicle routing problem with simultaneous pick-up and deliveries, which considers simultaneous distribution and collection of goods to/from customers, is an extension of the capacitated vehicle routing problem. There are various real cases, where fleet of vehicles originated in a depot serves customers with pick-up and deliveries from/to their locations. Increasing importance of reverse logistics activities make it necessary to determine efficient and effective vehicle routes for simultaneous pick-up and delivery activities. The vehicle routing problem with simultaneous pick-up and deliveries is also NP-hard as a capacitated vehicle routing problem and this study proposes a genetic algorithm based approach to this problem. Computational example is presented with parameter settings in order to illustrate the proposed approach. Moreover, performance of the proposed approach is evaluated by solving several test problems.     

A heuristic method for the vehicle routing problem with backhauls and inventory

The purpose of this paper is to determine the route of the vehicle routing problem with backhauls (VRPB), delivering new items and picking up the reused items or wastes, and resolve the inventory control decision problem simultaneously since the regular VRPB does not. Both the vehicle routing decision for delivery and pickup, and the inventory control decision affect each other and must be considered together. Hence, a mathematical model of vehicle routing problem with backhauls and inventory (VRPBI) is proposed. Since finding the optimal solution(s) for VRPBI is a NP-hard problem, this paper proposes a heuristic method, variable neighborhood tabu search (VNTS), adopting six neighborhood searching approaches to obtain the optimal solution. Moreover, this paper compares the proposed heuristic method with two other existing heuristic methods. The experimental results indicate that the proposed method is better than the two other methods in terms of average logistic cost (transportation cost and inventory cost).     

An improved multi-objective evolutionary algorithm for the vehicle routing problem with time windows

The vehicle routing problem with time windows is a complex combinatorial problem with many real-world applications in transportation and distribution logistics. Its main objective is to find the lowest distance set of routes to deliver goods, using a fleet of identical vehicles with restricted capacity, to customers with service time windows. However, there are other objectives, and having a range of solutions representing the trade-offs between objectives is crucial for many applications. Although previous research has used evolutionary methods for solving this problem, it has rarely concentrated on the optimization of more than one objective, and hardly ever explicitly considered the diversity of solutions. This paper proposes and analyzes a novel multi-objective evolutionary algorithm, which incorporates methods for measuring the similarity of solutions, to solve the multi-objective problem. The algorithm is applied to a standard benchmark problem set, showing that when the similarity measure is used appropriately, the diversity and quality of solutions is higher than when it is not used, and the algorithm achieves highly competitive results compared with previously published studies and those from a popular evolutionary multi-objective optimizer.     

Solving a vehicle routing problem with time windows by a decomposition technique and a genetic algorithm

The present study investigates the cost concerns of distribution centers and formulates a vehicle routing problem with time window constraints accordingly. Based on the embedded structure of the original problem, a decomposition technique is employed to decompose the original problems to a clustering problem (main problem) and a set of traveling salesman problems (sub-problems) with time window constraints. This decomposition not only reduces the problem size but also enable the use of simpler solution procedures. A genetic algorithm is developed to solve the clustering problem, while a simple heuristic algorithm is formulated to solve the set of traveling salesman problems. The solution of the original problem is obtained through iterative interactions between the main problem and the set of sub-problems. The performance of the proposed approach is compared with the well-known insertion method and a manual scheduling of a distribution center.     

A hybrid large-neighborhood search algorithm for the cumulative capacitated vehicle routing problem with time-window constraints

This paper introduces a special vehicle routing problem, i.e. the cumulative capacitated vehicle routing problem with time-window constraints (Cum-CVRPTW). The problem can be defined as designing least-cost delivery routes from a depot to a set of geographically-scattered customers, subject to the constraint that each customer has to be served within a time window; accordingly, the objective costs are computed as the sum of arrival times at all the customers. The Cum-CVRPTW finds practical utility in many situations, e.g. the provision of humanitarian aids in the context of natural disasters. The Cum-CVRPTW can be viewed as a combination of two NP-hard problems, i.e. the vehicle routing problem with time windows and the cumulative vehicle routing problem. To effectively address this problem, an effective algorithm is designed, which is based on the frameworks of Large Neighborhood Search Algorithm and hybridizes with Genetic Algorithm. The proposed algorithm adopts a constraint-relaxation scheme to extend the search space, enabling the iterative exploration of both the feasible and infeasible neighborhood solutions of an incumbent solution. Furthermore, some speed-up techniques are designed to reduce the computational complexity. To elucidate its effectiveness, the proposed algorithm is examined on the benchmark instances from the literature. The resultant numerical findings show that the algorithm is able to improve and obtain some best-known solutions found by existing state-of-the-art methods.     

A tabu search algorithm for the vehicle routing problem with simultaneous pick-up and delivery service

The vehicle routing problem with simultaneous pick-up and delivery (VRP_SPD) is a variant of the classical vehicle routing problem (VRP) where clients require simultaneous pick-up and delivery service. Deliveries are supplied from a single depot at the beginning of the vehicle's service, while pick-up loads are taken to the same depot at the conclusion of the service. One important characteristic of this problem is that a vehicle's load in any given route is a mix of pick-up and delivery loads.