Opportunistic planning for a fleet of transportation robots

The Dynamic Transportation-Planning Problem (DTPP) embodies a class of real-world applications that involve the reactive routing and scheduling of a fleet of vehicles in response to dynamically changing transportation demands. Examples include mobile robots in a warehouse, taxis in an urban road network, or aeroplanes for medical evacuation. In contrast with the Vehicle Routing Problem, for which a plethora of techniques is available, few approaches exist that permit the efficient deployment of a large number of vehicles in a changing environment. This paper highlights the characteristic features of the problem, reviews possible approaches and existing techniques, and proposes a heuristic solution to the DTPP using a Blackboard-based approach. The resulting application is an intelligent transportation planning system (ITPS) for a fleet of automated robot taxis, based on the generic assumption-based truth maintained Blackboard shell (GATMBS) and comprising traffic simulation models as well as various monitoring and problem-solving strategies for assignment and routing. The Blackboard architecture supports the dynamic alteration of planned routes in response to changes in traffic conditions and passenger requests. A prototype of the ITPS has been validated in simulation using a small fleet of robot taxis with randomly generated road networks, background traffic load, and passenger requests.     

The green vehicle routing problem: A heuristic based exact solution approach

This paper develops a simulated annealing heuristic based exact solution approach to solve the green vehicle routing problem (G-VRP) which extends the classical vehicle routing problem by considering a limited driving range of vehicles in conjunction with limited refueling infrastructure. The problem particularly arises for companies and agencies that employ a fleet of alternative energy powered vehicles on transportation systems for urban areas or for goods distribution. Exact algorithm is based on the branch-and-cut algorithm which combines several valid inequalities derived from the literature to improve lower bounds and introduces a heuristic algorithm based on simulated annealing to obtain upper bounds. Solution approach is evaluated in terms of the number of test instances solved to optimality, bound quality and computation time to reach the best solution of the various test problems. Computational results show that 22 of 40 instances with 20 customers can be solved optimally within reasonable computation time.     

A multistart adaptive memory-based tabu search algorithm for the heterogeneous fixed fleet open vehicle routing problem

This paper addressed the heterogeneous fixed fleet open vehicle routing problem (HFFOVRP), in which the demands of customers are fulfilled by a fleet of fixed number of vehicles with various capacities and related costs. Moreover, the vehicles start at the depot and terminate at one of the customers. This problem is an important variant of the classical vehicle routing problem and can cover more practical situations in transportation and logistics. We propose a multistart adaptive memory programming metaheuristic with modified tabu search algorithm to solve this new vehicle routing problem. The algorithmic efficiency and effectiveness are experimentally evaluated on a set of generated instances.     

A column‐generation‐based approach to fleet design problems mixing owned and hired vehicles

We look at the problem of choosing a fleet of vehicles to carry out delivery tasks across a long time horizon. The delivery quantities may vary significantly from day to day, and from season to season, and the underlying routing problem may have rich constraints, for example, time windows, multiple compartments, multiple commodities, and compatibility constraints. We consider the option of hiring extra vehicles from external carriers in order to efficiently carry out the day‐to‐day operations while containing the costs of owning the fleet. The goal is to design a fleet so as to minimize the sum of costs of routing the fleet every day of the horizon, the acquisition costs, the maintenance costs, and the costs of hiring external vehicles. In the literature, there is no previous work on fleet design for a long time horizon, which also considers the hiring options. We propose to tackle the problem using column generation and develop three different heuristics. The methods proposed are tested and compared on a set of real‐world problems. It is also shown how introducing the possibility of hiring helps reducing the overall cost and the number of idle vehicles over the planning horizon.     

A multilevel approach for modelling vehicle routing problem with uncertain travelling time

Vehicle routing problem is concerned with finding optimal collection or delivery routes in a transportation network, beginning and ending at a central depot, for a fleet of vehicles to serve a set of customers under some constraints. Assuming the travel times between two customers are uncertain variables, this paper proposes an uncertain multilevel programming model for a vehicle routing problem, of which the leader’s object is to minimize the total waiting times of the customers, and the followers’ objects are to minimize the waiting times of the vehicles for the beginning moments of the customers’ time windows. The uncertain multilevel programming model is transformed into a determinacy programming model, and an intelligent algorithm is designed for solving the crisp model.     

基于博弈论的内河港口作业车辆协同选路方法

针对以汽车运输为主且吞吐量较大的内河港口的交通拥堵问题,提出一种基于博弈论的内河港口作业车辆协同选路方法。首先,基于港口路网特征与车辆作业特点,将同时请求路径规划的作业车辆间的交互建模为不完全信息博弈,采用满足均衡（SE）的概念来分析该博弈。假设每个车辆对选路效用都有一个预期,当所有车辆都得到满足时博弈即达到均衡。然后,提出了一种车辆协同选路算法,算法中每个车辆首先按照贪心策略初始选路,之后将所有车辆按规则分组,组内车辆根据历史选路结果进行适应性学习并完成博弈。实验结果表明,当港区同时作业车辆数为286时,协同选路算法的车辆平均行驶时间分别比Dijkstra算法和自适应学习算法（SALA）少50.8%和16.3%,系统收益分别比Dijkstra算法和SALA提高51.7%和24.5%。所提算法能够有效减少车辆平均行驶时间,提高系统收益,更适用于内河港口车辆选路问题。     

Vehicle capacity planning system: a case study on vehicle routing problem with time windows

In this paper, we consider a local logistic company that provides transportation service for moving empty and laden containers within Singapore. Due to the limited capacity of its own fleet of vehicles, the company cannot handle all the job orders and have to outsource some orders to other smaller local transportation companies. The current operation of assigning jobs for outsourcing goes through two steps. In the first step, a certain percentage of jobs will be preselected for outsourcing according to some simple rules. Then at the second step, the rest of the jobs will be put into an in-house computer system which assigns jobs to its internal fleet of vehicles according to some greedy rules and the remaining jobs that cannot be served by the internal fleet of vehicles will be outsourced. This paper presents a vehicle capacity planning system (VCPS), which models the problem as a vehicle routing problem with time window constraints (VRPTW) and tabu search (TS) is applied to find a solution for the problem. From the simulation results, some new rules on how to assign jobs for outsourcing are derived, which are shown to be about 8% better than existing rules currently adopted by the company.     

An integrated inventory problem with transportation in a divergent supply chain under service level constraint

This study investigates an integrated inventory problem with transportation in a single-vendor and multi-buyer divergent supply chain. The vendor manufactures a product and delivers the product to the buyers located in different locations by a fleet of vehicles of identical capacity. The external demands per unit time on the buyers are independent and normally distributed. The lead time components of the buyers, excluding transportation time, can be reduced at an added crash cost. A model has been formulated to minimize the total expected cost of the system associated with the production, inventory, transportation and lead time reduction to find the optimal production, inventory and routing decisions while satisfying the service level constraint of the buyers. We propose a coordinated two-phase iterative approach to solve the model, which has been illustrated through a numerical example.     

Agent-based modeling and evolutionary computation for disseminating public advisories about hazardous material emergencies

In the event of a large-scale disaster, an important aspect of humanitarian logistics is the distribution of information or warnings to the affected population. This research develops the problem formulation and solution approach for a specific routing for relief problem, in which warnings should be disseminated to an affected community, using public announcement systems mounted on emergency vehicles. The problem statement is formulated to maximize the number of individuals of a community who are protected. An evolutionary algorithm framework is developed by coupling an agent-based model with a variable-length genetic algorithm to route emergency vehicles. The dynamics of interactions among consumers, emergency vehicles, and the spatiotemporal trajectory of the hazard are simulated using an agent-based modeling approach, and a variable-length genetic algorithm approach selects routes to warn a maximum number of consumers before they are affected by the emergency. The example that is explored in this research is contamination of a water distribution network. A fleet of emergency vehicles is equipped with public address systems and is deployed to warn consumers to stop using contaminated water. The framework is demonstrated for an illustrative virtual city, Mesopolis. The results of the evolutionary algorithm framework are compared with two conventional routing optimization approaches, including a covering tour problem approach and a manual routing approach, for four contamination scenarios. The evolutionary algorithm can be applied to route emergency service vehicles to broadcast information for other emergencies, such as flash flooding, hazardous materials incidents, and severe weather.     

A survey of models and algorithms for winter road maintenance. Part IV: Vehicle routing and fleet sizing for plowing and snow disposal

This is the last part of a four-part survey of optimization models and solution algorithms for winter road maintenance planning. The two first parts of the survey address system design problems for winter road maintenance. The third part concentrates mainly on vehicle routing problems for spreading operations. The aim of this paper is to provide a comprehensive survey of optimization models and solution methodologies for the routing of vehicles for plowing and snow disposal operations. We also review models for the fleet sizing and fleet replacement problems.     

A column generation approach to the heterogeneous fleet vehicle routing problem

We consider a vehicle routing problem with a heterogeneous fleet of vehicles having various capacities, fixed costs and variable costs. An approach based on column generation (CG) is applied for its solution, hitherto successful only in the vehicle routing problem with time windows. A tight integer programming model is presented, the linear programming relaxation of which is solved by the CG technique. A couple of dynamic programming schemes developed for the classical vehicle routing problem are emulated with some modifications to efficiently generate feasible columns. With the tight lower bounds thereby obtained, the branch-and-bound procedure is activated to obtain an integer solution. Computational experience with the benchmark test instances confirms that our approach outperforms all the existing algorithms both in terms of the quality of solutions generated and the solution time.     

An effective tabu search approach with improved loading algorithms for the 3L-CVRP

In this paper, we consider the Three-Dimensional Loading Capacitated Vehicle Routing Problem(3L-CVRP) which combines the routing of a fleet of vehicles and the loading of three-dimensional shaped goods into the vehicles while minimizing the total travel distance incurred. Apparently, 3L-CVRP is a combination of capacitated vehicle routing and three-dimensional bin packing problem and thus of high complexity. Different from most of previous works, we propose an innovative approach, called improved least waste heuristic for solving the loading subproblem, which is iteratively invoked by a simple tabu search algorithm for the routing. The good performance in terms of the solution quality and computational efficiency of our approach is shown through the numerical experiments on the benchmark instances from literature.     

Conflict-free container routing in mesh yard layouts

Container terminals play an important role in global cargo transportation and they have become an essential intermodal interface between the sea and the land. In the container terminal, the service area is often arranged into rectangular blocks, which leads to a mesh-like path topology. We present a mathematical model for general container routing in mesh yard layouts. Based on this model, a simple container routing algorithm guaranteeing freedom of conflicts is then presented. The algorithm works by carefully choosing suitable containers’ speeds such that the containers using the same junction will arrive at different points in time, and hence incur no conflicts; meanwhile, high routing performance can be achieved. The task completion time and the requirements on timing control during the container routing are also presented. Numerical results verify that our routing scheme has good performance and is free of conflicts.     

The fleet size and mix vehicle routing problem

In this paper, we address the problem of routing a fleet of vehicles from a central depot to customers with known demand. Routes originate and terminate at the central depot and obey vehicle capacity restrictions. Typically, researchers assume that all vehicles are identical. In this work, we relax the homogeneous fleet assumption. The objective is to determine optimal fleet size and mix by minimizing a total cost function which includes fixed cost and variable cost components. We describe several efficient heuristic solution procedures as well as techniques for generating a lower bound and an underestimate of the optimal solution. Finally, we present some encouraging computational results and suggestions for further study.     

Routing fleets with multiple driving ranges: Is it possible to use greener fleet configurations?

This paper discusses the vehicle routing problem with multiple driving ranges (VRPMDR), an extension of the classical routing problem where the total distance each vehicle can travel is limited and is not necessarily the same for all vehicles – heterogeneous fleet with respect to maximum route lengths. The VRPMDR finds applications in routing electric and hybrid-electric vehicles, which can only cover limited distances depending on the running time of their batteries. Also, these vehicles require from long charging times, which in practice makes it difficult to consider en route recharging. The paper formally introduces the problem, describes an integer programming formulation and a multi-round heuristic algorithm that iteratively constructs a solution for the problem. Using a set of benchmarks adapted from the literature, the algorithm is then employed to analyze how distance-based costs are increased when considering ‘greener’ fleet configurations – i.e., when using electric vehicles with different degrees of autonomy.     

A mixed load capacitated rural school bus routing problem with heterogeneous fleet: Algorithms for the Brazilian context

A capacitated rural school bus routing problem featuring mixed loads, a heterogeneous fleet, and the same school starting time is here addressed. This is an important problem of the routing literature which has been attracting the attention of many researchers recently. The mixed load feature allows students from different schools to ride the same bus at the same time. Five meta-heuristic based algorithms were devised to solve the problem, and evaluated on solving four different datasets, one of them being based on a real case from Brazil. Four traditional local search neighborhood structures for vehicle routing problems were adapted and specialized to handle mixed loads and a heterogeneous fleet simultaneously. To the best of the authors knowledge, it is the first time that both features are treated jointly within an algorithm, and not as a post processing optimization step. The attained cost savings and reduction of fleet sizes suggest the suitability of a mixed load, heterogeneous fleet approach for sparsely populated rural areas. Moreover the devised framework has been embedded into a decision support system which is assisting several municipalities of the state of Minas Gerais, Brazil, to better plan their routes and reduce transportation costs.     

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.     

基于城市公共交通移动模型的协作延迟容忍网络路由策略

如何利用有限的传输机会可靠地传送车载服务感知信息是智能交通发展的“瓶颈”问题,利用公共交通中车辆的运动规律,提出基于节点之间机会接触来进行消息的逐跳转发策略,同时结合公共交通系统自身的特点,设计了一种基于公共交通移动模型的协作延迟容忍网络（DTN）路由算法TF。首先,根据公共交通移动模型自身的特点,将公交、长途客车等节点按其运动路径进行分组,提出一种基于固定运动路径分组的DTN路由算法;然后,将出租车、行人类节点定义为自由节点,并设计了一种基于转发因子控制的DTN路由策略作为分组路由机制的补充。仿真结果表明,与Epidemic、Prophet以及SAW路由算法相比,TF路由算法具有较高的消息投递率和较低的平均延迟。     

A heuristic based on multi-exchange techniques for a regional fleet assignment location-routing problem

We deal with a distribution network design problem that involves location, fleet assignment and routing decisions. Specifically, the distribution network under investigation is characterized by one central depot, a set of customers split into regions, and a heterogeneous fleet of vehicles. The goal is to locate one regional depot in each region, to assign some vehicles to each region, and to design the vehicles routes, each starting and ending at the central depot, in such a way that the regional depot is visited once by all vehicles assigned to the corresponding region, the vehicle capacities are not exceeded, the customer demands are satisfied and the overall distribution cost is minimized. The study has been motivated by a real life application related to a company operating in the North of Italy.     

A multi-start evolutionary local search for the two-dimensional loading capacitated vehicle routing problem

This paper addresses an extension of the capacitated vehicle routing problem where customer demand is composed of two-dimensional weighted items (2L-CVRP). The objective consists in designing a set of trips minimizing the total transportation cost with a homogenous fleet of vehicles based on a depot node. Items in each vehicle trip must satisfy the two-dimensional orthogonal packing constraints. A GRASP×ELS algorithm is proposed to compute solutions of a simpler problem in which the loading constraints are transformed into resource constrained project scheduling problem (RCPSP) constraints. We denote this relaxed problem RCPSP-CVRP. The optimization framework deals with RCPSP-CVRP and lastly RCPSP-CVRP solutions are transformed into 2L-CVRP solutions by solving a dedicated packing problem. The effectiveness of our approach is demonstrated through computational experiments including both classical CVRP and 2L-CVRP instances. Numerical experiments show that the GRASP×ELS approach outperforms all previously published methods.