Notes on the single route lateral transhipment problem

Previous research has analyzed deterministic and stochastic models of lateral transhipments between different retailers in a supply chain. In these models the analysis assumes given fixed transhipment costs and determines under which situations (magnitudes of excess supply and demand at various retailers) the transhipment is profitable. However, in reality, these depend on aspects like the distance between retailers or the transportation mode chosen. In many situations, combining the transhipments may save transportation costs. For instance, one or more vehicle routes may be used to redistribute the inventory of the potential pickup and delivery stations. This can be done in any sequence as long as the vehicle capacity is not violated and there is enough load on the vehicle to satisfy demand. The corresponding problem is an extension of the one-commodity pickup and delivery traveling salesman and the pickup and delivery vehicle routing problem. When ignoring the routing aspect and assuming given fixed costs, transhipment is only profitable if the quantities are higher than a certain threshold. In contrast to that, the selection of visited retailers is dependent on the transportation costs of the tour and therefore the selected retailers are interrelated. Hence the problem also has aspects of a (team) orienteering problem. The main contribution is the discussion of the tour planning aspects for lateral transhipments which may be valuable for in-house planning but also for price negotiations with external contractors. A mixed integer linear program for the single route and single commodity version is presented and an improved LNS framework to heuristically solve the problem is introduced. Furthermore, the effect of very small load capacity on the structure of optimal solutions is discussed.     

Heuristic solution approaches for the cumulative capacitated vehicle routing problem

Cumulative capacitated vehicle routing problem (CCVRP) is an extension of the well-known capacitated vehicle routing problem, where the objective is minimization of sum of the arrival times at nodes instead of minimizing the total tour cost. This type of routing problem arises when a priority is given to customer needs or dispatching vital goods supply after a natural disaster. This paper focuses on comparing the performances of neighbourhood and population-based approaches for the new problem CCVRP. Genetic algorithm (GA), an evolutionary algorithm using particle swarm optimization mechanism with GA operators, and tabu search (TS) are compared in terms of required CPU time and obtained objective values. In addition, a nearest neighbourhood-based initial solution technique is also proposed within the paper. To the best of authors’ knowledge, this paper constitutes a base for comparisons along with GA, and TS for further possible publications on the new problem CCVRP.     

A Queueing Framework for Routing Problems with Time-dependent Travel Times

Assigning and scheduling vehicle routes in a dynamic environment is a crucial management problem. Despite numerous publications dealing with efficient scheduling methods for vehicle routing, very few addressed the inherent stochastic and dynamic nature of travel times. In this paper, a vehicle routing problem with time-dependent travel times due to potential traffic congestion is considered. The approach developed introduces the traffic congestion component based on queueing theory. This is an innovative modelling scheme to capture the stochastic behavior of travel times as it generates an analytical expression for the expected travel times as well as for the variance of the travel times. Routing solutions that perform well in the face of the extra complications due to congestion are developed. These more realistic solutions have the potential to reduce real operating costs for a broad range of industries which daily face routing problems. A number of datasets are used to illustrate the appropriateness of the novel approach. Moreover it is shown that static (or time-independent) solutions are often infeasible within a congested traffic environment which is generally the case on European road networks. Finally, the effect of travel time variability (obtained via the queueing approach) is quantified for the different datasets.      

Vehicle routing with dynamic travel times: A queueing approach

Transportation is an important component of supply chain competitiveness since it plays a major role in the inbound, inter-facility, and outbound logistics. In this context, assigning and scheduling vehicle routes is a crucial management problem. In this paper, a vehicle routing problem with dynamic travel times due to potential traffic congestion is considered. The approach developed introduces mainly the traffic congestion component based on queueing theory. This is an innovative modeling scheme to capture travel times. The queueing approach is compared with other approaches and its potential benefits are described and quantified. Moreover, the optimization of the starting times of a route at the distribution center is evaluated. Finally, the trade-off between solution quality and calculation time is discussed. Numerous test instances are used, both to illustrate the appropriateness of the approach as well as to show that time-independent solutions are often unrealistic within a congested traffic environment, which is usually the case on European road networks.     

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 self-tuning heuristic for a multi-objective vehicle routing problem

In this study, a heuristic free from parameter tuning is introduced to solve the vehicle routing problem (VRP) with two conflicting objectives. The problem which has been presented is the designing of optimal routes: minimizing both the number of vehicles and the maximum route length. This problem, even in the case of its single objective form, is NP-hard. The proposed self-tuning heuristic (STH) is based on local search and has two parameters which are updated dynamically throughout the search process. The most important advantage of the algorithm is the application convenience for the end-users. STH is tested on the instances of a multi-objective problem in school bus routing and classical vehicle routing. Computational experiments, when compared with the prior approaches proposed for the multi-objective routing of school buses problem, confirm the effectiveness of STH. STH also finds high-quality solutions for multi-objective VRPs.     

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.     

An adaptive memory algorithm for the split delivery vehicle routing problem

The split delivery vehicle routing problem (SDVRP) relaxes routing restrictions forcing unique deliveries to customers and allows multiple vehicles to satisfy customer demand. Split deliveries are used to reduce total fleet cost to meet those customer demands. We provide a detailed survey of the SDVRP literature and define a new constructive algorithm for the SDVRP based on a novel concept called the route angle control measure. We extend this constructive approach to an iterative approach using adaptive memory concepts, and then add a variable neighborhood descent process. These three new approaches are compared to exact and heuristic approaches by solving the available SDVRP benchmark problem sets. Our approaches are found to compare favorably with existing approaches and we find 16 new best solutions for a recent 21 problem benchmark set.     

成品油配送多车舱车辆指派及路径优化问题研究

针对成品油配送中多车型、多车舱的车辆优化调度难题,综合考虑多车型车辆指派、多车舱车辆装载及路径安排等决策,以派车成本与油耗成本之和的总成本最小为目标,建立了多车型多车舱的车辆优化调度模型。为降低模型求解的复杂性,本文提出一种基于C-W节约算法的“需求拆分→合并装载”的车辆装载策略,并综合利用Relocate和Exchange算子进行并行邻域搜索改进,获得优化的成品油配送方案。最后,通过算例验证了本文提出的模型与算法用于求解大规模成品油配送问题的有效性。并通过数据实验揭示了以下规律:1)多车舱车辆相对于单车舱车辆在运营成本上具有优越性;2)大型车辆适合远距离配送,小型车辆适合近距离配送;3)多车型车辆混合配送相对于单车型车辆配送在运营成本上具有优越性。这些规律可为成品油配送公司的车辆配置提供决策参考。     

Single vehicle routing with a predefined customer sequence and multiple depot returns

The optimal routing of a single vehicle with limited capacity that delivers one product to n clients according to a predefined client sequence can be determined using dynamic programming. In the present paper we propose and investigate three practical variations of this problem: (i) the case of multiple-product deliveries when each product is stored in its own compartment in the vehicle, (ii) the case of multiple-product deliveries when all products are stored together in the vehicle’s single compartment, and (iii) the case in which the vehicle picks up from and delivers a single product to each customer. Suitable dynamic programming algorithms that find the optimal routing of the vehicle are developed for each case. The efficiency of the algorithms is studied by solving large problem sets.     

Solving a real-world vehicle routing problem with multiple use of tractors and trailers and EU-regulations for drivers arising in air cargo road feeder services

In this paper we present two approaches for solving a real-world vehicle routing problem arising in the air cargo road feeder service business. The problem is to combine transportation tasks from a given timetable to trips which have to be assigned to tractors and which can be operated by tractor drivers respecting the restrictive rules on driving times from EC Regulation No. 561/2006. Tractor trips which start and end at the hub can be combined to multiple-trips which are operated by the same tractor. Also, to each trip a trailer has to be assigned which is compatible with all tasks in the trip. The primary objective is to minimize the number of required tractors, i.e. the number of multiple-trips. The methods developed are currently applied in practice.     

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.     

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.     

时变单车路径优化模型及动态规划算法

车辆路径问题由于其广泛的应用领域及经济价值而成为学术研究热点。然而,在已有的研究文献中,车辆的速度时变与服务多任务特性很少被关注。本文讨论了具有这两个特性的单车路径优化问题。建立了以送货完成时间最早为优化目标的时变单车送货路径优化模型。由于很难获得该模型的精确解,本文提出了一种贪婪补货策略压缩原问题解空间,设计动态规划算法给出了车辆行驶时间满足FIFO规则的送货顺序近似最优解。数值算例验证了该算法所得到的解仅是原问题的近似最优解这一结论。算例同时表明优化配送时间随着车辆装载能力的增大而缩短,并在车辆装载能力超过所有客户配送总需求时实现最短配送时间,即,使用较大装载能力车辆能节约更多配送时间。     

Designing routes for WEEE collection: the vehicle routing problem with split loads and date windows

This paper presents an integer programming model and describes a GRASP based algorithm to solve a vehicle routing and scheduling problem for the collection of Waste of Electric and Electronic Equipment (WEEE). The difficulty of this problem arises from the fact that it is characterized by four variants of the vehicle routing problem that have been studied independently in the literature, but not together. The experimental analysis on a large set of randomly-generated instances shows the good performance of the proposed algorithm. Moreover, computational results using real data show that the method outperforms real existing approaches to reverse logistics.     

Solving the open vehicle routeing problem via a single parameter metaheuristic algorithm

In this paper, we consider the open vehicle routeing problem (OVRP), in which routes are not sequences of locations starting and ending at the depot but open paths. The problem is of particular importance for planning fleets of hired vehicles, a common practice in the distribution and service industry. In such cases, the travelling cost is a function of the vehicle open paths. To solve the problem, we employ a single-parameter metaheuristic method that exploits a list of threshold values to guide intelligently an advanced local search. Computational results on a set of benchmark problems show that the proposed method consistently outperforms previous approaches for the OVRP. A real-world example demonstrates the applicability of the method in practice, demonstrating that the approach can be used to solve actual problems of routing large vehicle fleets.     

Vehicle routing with stochastic demands and restricted failures

This paper considers a class of stochastic vehicle routing problems (SVRPs) with random demands, in which the number of potential failures per route is restricted either by the data or the problem constraints. These are realistic cases as it makes little sense to plan vehicle routes that systematically fail a large number of times. First, a chance constrained version of the problem is considered which can be solved to optimality by algorithms similar to those developed for the deterministic vehicle routing problem (VRP). Three classes of SVRP with recourse are then analyzed. In all cases, route failures can only occur at one of the lastk customers of the planned route. Since in general, SVRPs are considerably more intractable than the deterministic VRPs, it is interesting to note that these realistic stochastic problems can be solved as a sequence of deterministic traveling salesman problems (TSPs). In particular, whenk=1 the SVRP with recourse reduces to a single TSP.     

Disruption management of the vehicle routing problem with vehicle breakdown

This paper introduces a new class of problem, the disrupted vehicle routing problem (VRP), which deals with the disruptions that occur at the execution stage of a VRP plan. The paper then focuses on one type of such problem, in which a vehicle breaks down during the delivery and a new routing solution needs to be quickly generated to minimise the costs. Two Tabu Search algorithms are developed to solve the problem and are assessed in relation to an exact algorithm. A set of test problems has been generated and computational results from experiments using the heuristic algorithms are presented.     

Local search-based metaheuristics for the split delivery vehicle routing problem

The split delivery vehicle routing problem is a variant of the standard vehiclerouting problem where the single-visit assumption is waived and a customer mightbe served on more than one vehicle tour. In this article we report on a studywhere we have applied the standard local search-based metaheuristics usingadaptations of the most widely used inter-tour and intra-tour exchange operatorsfor solving the standard vehicle routing problem now allowing splitting andjoining of deliveries. As we will show we could find new best solutions for 51out of 57 benchmark instances, which have been defined for this problemclass.     

A tabu search algorithm for the multi-trip vehicle routing and scheduling problem

This paper describes a novel tabu search heuristic for the multi-trip vehicle routing and scheduling problem (MTVRSP). The method was developed to tackle real distribution problems, taking into account most of the constraints that appear in practice. In the MTVRSP, besides the constraints that are common to the basic vehicle routing problem, the following ones are present: during each day a vehicle can make more than one trip; the customers impose delivery time windows; the vehicles have different capacities considered in terms of both volume and weight; the access to some customers is restricted to some vehicles; the drivers' schedules must respect the maximum legal driving time per day and the legal time breaks; the unloading times are considered.