Applications of the vehicle routing problem with trailers and transshipments

The vehicle routing problem with trailers and transshipments (VRPTT) is a recent and challenging extension of the well-known vehicle routing problem. The VRPTT constitutes an archetypal representative of the class of vehicle routing problems with multiple synchronization constraints (VRPMSs). In addition to the usual task covering constraints, VRPMSs require further synchronization between vehicles, concerning spatial, temporal, and load aspects. VRPMSs possess considerable practical relevance, but limited coverage in the scientific literature. The purpose of the present paper is to describe how several important types of VRPMSs, such as multi-echelon location-routing problems and simultaneous vehicle and crew routing problems, can be modelled as VRPTTs.     

A primal-dual approximation algorithm for a two depot heterogeneous traveling salesman problem

Surveillance applications require a collection of heterogeneous vehicles to visit a set of targets. We consider a fundamental routing problem that arises in these applications involving two vehicles. Specifically, we consider a routing problem where there are two heterogeneous vehicles that start from distinct initial locations and a set of targets. The objective is to find a tour for each vehicle such that each of the targets is visited at least once by a vehicle and the sum of the distances traveled by the vehicles is minimal. We consider an important special case of this routing problem where the travel costs satisfy the triangle inequality and the following monotonicity property: the first vehicle’s cost of traveling between any two targets is at most equal to the second vehicle’s cost of traveling between the same targets. We present a primal-dual algorithm for this case that provides an approximation ratio of 2.     

A new mixed integer linear model for a rich vehicle routing problem with docking constraints

In this paper we address a rich vehicle routing problem that arises in real-life applications. Among other aspects we consider time windows, simultaneous delivery and pick-up at customer locations and multiple use of vehicles. To guarantee a coordinated material flow at the depot, we include the timed allocation of vehicles to loading bays at which the loading and unloading activities can occur. The resulting vehicle routing problem is formulated as a two-index vehicle-flow model which integrates the routing under real-life conditions and the assignment of vehicles to loading bays at the depot. We use CPLEX 11.0 to solve medium-sized instances that are derived from the extended Solomon test set. The selective implementation of preprocessing techniques and cutting planes improves the solver performance significantly.     

Solving routing problems with pairwise synchronization constraints

Pairwise route synchronization constraints are commonly encountered in the field of service technician routing and scheduling and in the area of mobile care. Pairwise route synchronization refers to constraints that require that two technicians or home care workers visit the same location at exactly the same time. We consider constraints of this type in the context of the well-known vehicle routing problem with time windows and a generic service technician routing and scheduling problem. Different approaches for dealing with the problem of pairwise route synchronization are compared and several ways of integrating a synchronization component into a metaheuristic algorithm tailored to the original problems are analyzed. When applied to benchmark instances from the literature, our algorithm matches almost all available optimal values and it produces several new best results for the remaining instances.

     

A greedy look-ahead heuristic for the vehicle routing problem with time windows

In this paper we consider the problem of physically distributing finished goods from a central facility to geographically dispersed customers, which pose daily demands for items produced in the facility and act as sales points for consumers. The management of the facility is responsible for satisfying all demand, and promises deliveries to the customers within fixed time intervals that represent the earliest and latest times during the day that a delivery can take place. We formulate a comprehensive mathematical model to capture all aspects of the problem, and incorporate in the model all critical practical concerns such as vehicle capacity, delivery time intervals and all relevant costs. The model, which is a case of the vehicle routing problem with time windows, is solved using a new heuristic technique. Our solution method, which is based upon Atkinson's greedy look-ahead heuristic, enhances traditional vehicle routing approaches, and provides surprisingly good performance results with respect to a set of standard test problems from the literature. The approach is used to determine the vehicle fleet size and the daily route of each vehicle in an industrial example from the food industry. This actual problem, with approximately two thousand customers, is presented and solved by our heuristic, using an interface to a Geographical Information System to determine inter-customer and depot–customer distances. The results indicate that the method is well suited for determining the required number of vehicles and the delivery schedules on a daily basis, in real life applications.     

New mixed integer-programming model for the pickup-and-delivery problem with transshipment

In recent years, many important real-world applications are studied as “rich” vehicle routing problems that are variants and generalizations of the well-known vehicle routing problem. In this paper we address the pickup-and-delivery version of this problem and consider further generalization by allowing transshipment in the network. Moreover, we allow heterogenous vehicles and flexible fleet size. We describe mixed integer-programming formulations for the problem with and without time windows for services. The number of constraints and variables in the models are bounded by polynomial size of the problem. We discuss several problem variants that are either captured by our models or can be easily captured through simple modifications. Computational work gave promising results and confirms that transshipment in network can indeed enhance optimization.     

第三方库存-路线问题的模型及混合遗传算法设计

根据第三方库存-路线问题的特点,以车辆租赁费用和运行费用之和为目标函数,不限制客户每次的配送量小于车辆容量,建立了满载运输和非满载运输混合的整数规划模型.针对第三方库存-路线问题的复杂性,本文设计嵌入禁忌搜索的遗传算法来同时决策库存和路线问题.首先对配送间隔进行编码,然后用禁忌搜索法计算每天需要配送的车辆路线问题.最后与其下界值进行比较,结果表明该算法是一个有效的算法,不但第三方能取得较低的运营总成本和较高的车辆利用率,而且也能为客户节约库存空间.     

Dynamic system optimal performances of shared autonomous and human vehicle system for heterogeneous travellers

ABSTRACT

Autonomous vehicles (AV) can solve vehicle relocation problems faced by traditional one-way vehicle-sharing systems. This paper explores the deterministic time-dependent system optimum of mixed shared AVs (SAV) and human vehicles (SHV) system to provide the benchmark for the situation of mixed vehicle flows. In such a system, the system planner determines vehicle-traveller assignment and optimal vehicle routing in transportation networks to serve predetermined travel demand of heterogeneous travellers. Due to large number of vehicles involved, travel time is considered endogenous with congestion. Using link transmission model (LTM) as a traffic flow model, the deterministic time-dependent system optimum is formulated as linear programming (LP) model to minimize the comprehensive cost including travellers’ travel time cost, waiting time cost and empty vehicle repositioning time cost. Numerical examples are conducted to show system performances and model effectiveness.     

Multi-objective metaheuristics for a location-routing problem with multiple use of vehicles on real data and simulated data

We address an integrated logistic system where decisions on location of depot, vehicle routing and assignment of routes to vehicles are considered simultaneously. Total cost and workload balance are common criteria influencing decision-making. Literature on location-routing problems addressed the location and vehicle routing decisions with a common assumption of assigning one route to one vehicle. However, the cost of acquiring vehicles (and crew) is often more significant than the routing cost. This notion of assigning several routes to a vehicle during the routing procedure is explored in our integrated model. We apply metaheuristics of tabu search and simulated annealing on real data and simulated data, to compare their performances under two versions: simultaneous or sequential routes assignment to vehicles. A new statistical procedure is proposed to compare two algorithms on the strength of their multi-objective solutions. Results show that the simultaneous versions have advantage over the sequential versions in problems where routes are capacity-constrained, but not in the time dimension. The simultaneous versions are also more effective in generating non-dominated solutions than the sequential versions.     

An integrated approach for collection network design,capacity planning and vehicle routing in reverse logistics

This study considers network design, capacity planning and vehicle routing for collection systems in reverse logistics. The network design and capacity planning problems are to determine the static locations and capacities of collection points as well as the dynamic allocations of demand points to the opened collection points over a planning horizon, and the vehicle routing problem is to determine the number and routes of vehicles in such a way that each collection point must be visited exactly once by one vehicle starting and terminating at the depot while satisfying the return demands at collection points and the vehicle capacity. The objective is to minimize the sum of fixed costs to open collection points and to acquire vehicles as well as variable costs to transport returns at demand points to the opened collection points and travel the opened collection points by vehicles. Unlike the location-routing problems, the integrated problem considered in this study has several features: multi-period dynamic model, capacity planning for collection points, maximum allowable collection distances, etc. To solve the integrated problem, two types of tabu search algorithms, hierarchical and integrated ones, are suggested, and their test results are reported. In particular, the efficiency of the integrated approach is shown by comparing the two algorithm types.     

Optimizing the periodic pick-up of raw materials for a manufacturer of auto parts

We describe a solution procedure for a special case of the periodic vehicle routing problem (PVRP). Operation managers at an auto parts manufacturer in the north of Spain described the optimization problem to the authors. The manufacturer must pick up parts (raw material) from geographically dispersed locations. The parts are picked up periodically at scheduled times. The problem consists of assigning a pickup schedule to each of its supplier’s locations and also establishing daily routes in order to minimize total transportation costs. The time horizon under consideration may be as long as 90 days. The resulting PVRP is such that the critical decision is the assignment of locations to schedules, because once this is done, the daily routing of vehicles is relatively straightforward. Through extensive computational experiments, we show that the metaheuristic procedure described in this paper is capable of finding high-quality solutions within a reasonable amount of computer time. Our main contribution is the development of a procedure that is more effective at handling PVRP instances with long planning horizons when compared to those proposed in the literature.     

Improved load balancing and resource utilization for the Skill Vehicle Routing Problem

The Skill Vehicle Routing Problem (Skill VRP) considers vehicle routing under the assumption of skill requirements given on demand nodes. These requirements have to be met by the serving vehicles. No further constraints, like capacity or cost restrictions, are imposed. Skill VRP solutions may show a tendency to have a bad load balancing and resource utilization. In a majority of solutions only a subset of vehicles is active. Moreover, a considerable share of demand nodes is served by vehicles that have a skill higher than necessary. A reason for that solution behavior lies in the model itself. As no resource restrictions are imposed, the Skill VRP tends to produce TSP-like solutions. To obtain better balanced solutions, we introduce two new approaches. First we propose a minmax model that aims at minimizing the maximal vehicle tour length. Second we suggest a two-step method combining the minmax approach with a distance constrained model. Our experiments illustrate that these approaches lead to improvements in load balancing and resource utilization, but, with different impact on routing costs.     

An interactive GRAMPS algorithm for the heterogeneous fixed fleet vehicle routing problem with and without backhauls

In this article, a visual interactive approach based on a new greedy randomised adaptive memory programming search (GRAMPS) algorithm is proposed to solve the heterogeneous fixed fleet vehicle routing problem (HFFVRP) and a new extension of the HFFVRP, which is called heterogeneous fixed fleet vehicle routing problem with backhauls (HFFVRPB). This problem involves two different sets of customers. Backhaul customers are pickup points and linehaul customers are delivery points that are to be serviced from a single depot by a heterogeneous fixed fleet of vehicles, each of which is restricted in the capacity it can carry, with different variable travelling costs.     

The open vehicle routing problem with time windows

In this paper, we consider the open vehicle routing problem with time windows (OVRPTW). The OVRPTW seeks to find a set of non-depot returning vehicle routes, for a fleet of capacitated vehicles, to satisfy customers’ requirements, within fixed time intervals that represent the earliest and latest times during the day that customers’ service can take place. We formulate a comprehensive mathematical model to capture all aspects of the problem, and incorporate in the model all critical practical concerns. The model is solved using a greedy look-ahead route construction heuristic algorithm, which utilizes time windows related information via composite customer selection and route-insertion criteria. These criteria exploit the interrelationships between customers, introduced by time windows, that dictate the sequence in which vehicles must visit customers. Computational results on a set of benchmark problems from the literature provide very good results and indicate the applicability of the methodology in real-life routing applications.     

The coordination of transportation and batching scheduling

We study a coordinated scheduling problem of production and transportation in which each job is transported to a single batching machine for further processing. There are m vehicles that transport jobs from the holding area to the batching machine. Each vehicle can transport only one job at a time. The batching machine can process a batch of jobs simultaneously where there is an upper limit on the batch size. Each batch to be processed occurs a processing cost. The problem is to find a joint schedule of production and transportation such that the sum of the total completion time and the total processing cost is optimized. For a special case of the problem where the job assignment to the vehicles is predetermined, we provide a polynomial time algorithm. For the general problem, we prove that it is NP-hard (in the ordinary sense) and present a pseudo-polynomial time algorithm. A fully polynomial time approximation scheme for the general problem is obtained by converting an especially designed pseudo-polynomial dynamic programming algorithm.     

Combined vehicle routing and scheduling with temporal precedence and synchronization constraints

We present a mathematical programming model for the combined vehicle routing and scheduling problem with time windows and additional temporal constraints. The temporal constraints allow for imposing pairwise synchronization and pairwise temporal precedence between customer visits, independently of the vehicles. We describe some real world problems where in the literature the temporal constraints are usually remarkably simplified in the solution process, even though these constraints may significantly improve the solution quality and/or usefulness. We also propose an optimization based heuristic to solve real size instances. The results of numerical experiments substantiate the importance of the temporal constraints in the solution approach. We also make a computational study by comparing a direct use of a commercial solver against the proposed heuristic, where the latter approach can find high quality solutions within specific time limits.     

A hybrid multi-objective evolutionary algorithm for solving truck and trailer vehicle routing problems

This paper considers a transportation problem for moving empty or laden containers for a logistic company. Owing to the limited resource of its vehicles (trucks and trailers), the company often needs to sub-contract certain job orders to outsourced companies. A model for this truck and trailer vehicle routing problem (TTVRP) is first constructed in the paper. The solution to the TTVRP consists of finding a complete routing schedule for serving the jobs with minimum routing distance and number of trucks, subject to a number of constraints such as time windows and availability of trailers. To solve such a multi-objective and multi-modal combinatorial optimization problem, a hybrid multi-objective evolutionary algorithm (HMOEA) featured with specialized genetic operators, variable-length representation and local search heuristic is applied to find the Pareto optimal routing solutions for the TTVRP. Detailed analysis is performed to extract useful decision-making information from the multi-objective optimization results as well as to examine the correlations among different variables, such as the number of trucks and trailers, the trailer exchange points, and the utilization of trucks in the routing solutions. It has been shown that the HMOEA is effective in solving multi-objective combinatorial optimization problems, such as finding useful trade-off solutions for the TTVRP routing problem.     

An exact algorithm for a vehicle routing problem with time windows and multiple use of vehicles

The vehicle routing problem with multiple use of vehicles is a variant of the classical vehicle routing problem. It arises when each vehicle performs several routes during the workday due to strict time limits on route duration (e.g., when perishable goods are transported). The routes are defined over customers with a revenue, a demand and a time window. Given a fixed-size fleet of vehicles, it might not be possible to serve all customers. Thus, the customers must be chosen based on their associated revenue minus the traveling cost to reach them. We introduce a branch-and-price approach to address this problem where lower bounds are computed by solving the linear programming relaxation of a set packing formulation, using column generation. The pricing subproblems are elementary shortest path problems with resource constraints. Computational results are reported on euclidean problems derived from well-known benchmark instances for the vehicle routing problem with time windows.     

Managing pharmaceuticals delivery service using a hybrid particle swarm intelligence approach

Medicines or drugs have unique characteristics of short life cycle, small size, light weight, restrictive distribution time and the need of temperature and humidity control (selected items only). Thus, logistics companies often use different types of vehicles with different carrying capacities, and considering fixed and variable costs in service delivery, which make the vehicle assignment and route optimization more complicated. In this study, we formulate the problem to a multi-type vehicle assignment and mixed integer programming route optimization model with fixed fleet size under the constraints of distribution time and carrying capacity. Given non-deterministic polynomial hard and optimal algorithm can only be used to solve small-size problem, a hybrid particle swarm intelligence (PSI) heuristic approach, which adopts the crossover and mutation operators from genetic algorithm and 2-opt local search strategy, is proposed to solve the problem. We also adapt a principle based on cost network and Dijkstra’s algorithm for vehicle scheduling to balance the distribution time limit and the high loading rate. We verify the relative performance of the proposed method against several known optimal or heuristic solutions using a standard data set for heterogeneous fleet vehicle routing problem. Additionally, we compare the relative performance of our proposed Hybrid PSI algorithm with two intelligent-based algorithms, Hybrid Population Heuristic algorithm and Improved Genetic Algorithm, using a real-world data set to illustrate the practical and validity of the model and algorithm.

     

An approximation algorithm for the pickup and delivery vehicle routing problem on trees

This paper presents an approximation algorithm for a vehicle routing problem on a tree-shaped network with a single depot where there are two types of demands, pickup demand and delivery demand. Customers are located on nodes of the tree, and each customer has a positive demand of pickup and/or delivery.Demands of customers are served by a fleet of identical vehicles with unit capacity. Each vehicle can serve pickup and delivery demands. It is assumed that the demand of a customer is splittable, i.e., it can be served by more than one vehicle. The problem we are concerned with in this paper asks to find a set of tours of the vehicles with minimum total lengths. In each tour, a vehicle begins at the depot with certain amount of goods for delivery, visits a subset of the customers in order to deliver and pick up goods and returns to the depot. At any time during the tour, a vehicle must always satisfy the capacity constraint, i.e., at any time the sum of goods to be delivered and that of goods that have been picked up is not allowed to exceed the vehicle capacity. We propose a 2-approximation algorithm for the problem.