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。     

A tabu search heuristic for the vehicle routing problem with private fleet and common carrier

This paper describes a tabu search heuristic for a vehicle routing problem where the owner of a private fleet can either visit a customer with one of his vehicles or assign the customer to a common carrier. The owner’s objective is to minimize the variable and fixed costs for operating his fleet plus the total costs charged by the common carrier. The proposed tabu search is shown to outperform the best approach reported in the literature on 34 benchmark instances with a homogeneous fleet.     

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.     

Target aiming Pareto search and its application to the vehicle routing problem with route balancing

In this paper, we present a solution method for a bi-objective vehicle routing problem, called the vehicle routing problem with route balancing (VRPRB), in which the total length and balance of the route lengths are the objectives under consideration. The method, called Target Aiming Pareto Search, is defined to hybridize a multi-objective genetic algorithm for the VRPRB using local searches. The method is based on repeated local searches with their own appropriate goals. We also propose an implementation of the Target Aiming Pareto Search using tabu searches, which are efficient meta-heuristics for the vehicle routing problem. Assessments with standard metrics on classical benchmarks demonstrate the importance of hybridization as well as the efficiency of the Target Aiming Pareto Search.     

A sweep-based algorithm for the fleet size and mix vehicle routing problem

This paper presents a new sweep-based heuristic for the fleet size and mix vehicle routing problem. This problem involves two kinds of decisions: the selection of a mix of vehicles among the available vehicle types and the routing of the selected fleet. The proposed algorithm first generates a large number of routes that are serviced by one or two vehicles. The selection of routes and vehicles to be used is then made by solving to optimality, in polynomial time, a set-partitioning problem having a special structure. Results on a set of benchmark test problems show that the proposed heuristic produces excellent solutions in short computing times. Having a fast but good solution method is needed for transportation companies that rent a significant part of their fleet and consequently can take advantage of frequent changes in fleet composition. Finally, the proposed heuristic produced new best-known solutions for three of the test problems; these solutions are reported.     

Tabu search with ejection chains for the vehicle routing problem with private fleet and common carrier

The problem reported in this paper is a variant of the classical vehicle routing problem, where customer requests for a transportation company can be served either by its private fleet of vehicles or assigned to an external common carrier. The latter case occurs if the demand exceeds the total capacity of the private fleet or if it is more economical to do so. Accordingly, the objective is to minimize the variable and fixed costs of the private fleet plus the costs charged by the common carrier. A tabu search heuristic with a neighbourhood structure based on ejection chains is proposed to solve this problem. It is empirically demonstrated that this algorithm outperforms the best approaches reported in the literature on a set of benchmark instances with both homogeneous and heterogeneous fleets.     

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.     

A perturbation metaheuristic for the vehicle routing problem with private fleet and common carriers

The purpose of this article is to propose a perturbation metaheuristic for the vehicle routing problem with private fleet and common carrier (VRPPC). This problem consists of serving all customers in such a way that (1) each customer is served exactly once either by a private fleet vehicle or by a common carrier vehicle, (2) all routes associated with the private fleet start and end at the depot, (3) each private fleet vehicle performs only one route, (4) the total demand of any route does not exceed the capacity of the vehicle assigned to it, and (5) the total cost is minimized. This article describes a new metaheuristic for the VRPPC, which uses a perturbation procedure in the construction and improvement phases and also performs exchanges between the sets of customers served by the private fleet and the common carrier. Extensive computational results show the superiority of the proposed metaheuristic over previous methods.     

Matheuristics for solving a multi-attribute collection problem for a charity organisation

This paper studies a real-life multi-attribute profit collecting vehicle routing problem, arising in the collection operations of a charity organisation in the United Kingdom. The problem involves a heterogeneous fleet of vehicles of different capacities, mandatory visits to a subset of vertices, time windows, rest requirements associated with maximum driving and working times, and partial collection. A mixed integer programming formulation of the problem is described, along with three matheuristics based on Tabu Search and Large Neighbourhood Search. Computational results on instances derived from the case study are presented, and insights are given from a practical implementation.     

A General Vehicle Routing Problem

In this paper, we study a rich vehicle routing problem incorporating various complexities found in real-life applications. The General Vehicle Routing Problem (GVRP) is a combined load acceptance and generalised vehicle routing problem. Among the real-life requirements are time window restrictions, a heterogeneous vehicle fleet with different travel times, travel costs and capacity, multi-dimensional capacity constraints, order/vehicle compatibility constraints, orders with multiple pickup, delivery and service locations, different start and end locations for vehicles, and route restrictions for vehicles. The GVRP is highly constrained and the search space is likely to contain many solutions such that it is impossible to go from one solution to another using a single neighbourhood structure. Therefore, we propose iterative improvement approaches based on the idea of changing the neighbourhood structure during the search.     

A practical solution approach for the cyclic inventory routing problem

Vendor managed inventory (VMI) is an example of effective cooperation and partnering practices between up- and downstream stages in a supply chain. In VMI, the supplier takes the responsibility for replenishing his customers’ inventories based on their consumption data, with the aim of optimizing the over all distribution and inventory costs throughout the supply chain. This paper discusses the challenging optimization problem that arises in this context, known as the inventory routing problem (IRP). The objective of this IRP problem is to determine a distribution plan that minimizes average distribution and inventory costs without causing any stock-out at the customers. Deterministic constant customer demand rates are assumed and therefore, a long-term cyclical approach is adopted, integrating fleet sizing, vehicle routing, and inventory management. Further, realistic side-constraints such as limited storage capacities, driving time restrictions and constant replenishment intervals are taken into account. A heuristic solution approach is proposed, analyzed and evaluated against a comparable state-of-the-art heuristic.     

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.     

A path relinking algorithm for a multi-depot periodic vehicle routing problem

In this paper, we consider a multi-depot periodic vehicle routing problem which is characterized by the presence of a homogeneous fleet of vehicles, multiple depots, multiple periods, and two types of constraints that are often found in reality, i.e., vehicle capacity and route duration constraints. The objective is to minimize total travel costs. To tackle the problem, we propose an efficient path relinking algorithm whose exploration and exploitation strategies enable the algorithm to address the problem in two different settings: (1) As a stand-alone algorithm, and (2) As a part of a co-operative search algorithm called integrative co-operative search. The performance of the proposed path relinking algorithm is evaluated, in each of the above ways, based on standard benchmark instances. The computational results show that the developed PRA performs well, in both solution quality and computational efficiency.     

Scatter search for the fleet size and mix vehicle routing problem with time windows

This work proposes a scatter search (SS) approach to solve the fleet size and mix vehicle routing problem with time windows (FSMVRPTW). In the FSMVRPTW the customers need to be serviced in their time windows at minimal costs by a heterogeneous fleet. Computational results on 168 benchmark problems are reported. Computational testing revealed that our algorithm presented better results compared to other methods published in the literature.     

A heuristic for vehicle fleet mix problem using tabu search and set partitioning

The vehicle fleet mix problem is a special case of the vehicle routing problem where customers are served by a heterogeneous fleet of vehicles with various capacities. An efficient heuristic for determining the composition of a vehicle fleet and travelling routes was developed using tabu search and by solving set partitioning problems. Two kinds of problems have appeared in the literature, concerning fixed cost and variable cost, and these were tested for evaluation. Initial solutions were found using the modified sweeping method. Whenever a new solution in an iteration of the tabu search was obtained, optimal vehicle allocation was performed for the set of routes, which are constructed from the current solution by making a giant tour. Experiments were performed for the benchmark problems that appeared in the literature and new best-known solutions were found.     

A worst-case analysis for the split delivery vehicle routing problem with minimum delivery amounts

In the vehicle routing problem (VRP), a fleet of vehicles must service the demands of customers in a least-cost way. In the split delivery vehicle routing problem (SDVRP), multiple vehicles can service the same customer by splitting the deliveries. By allowing split deliveries, savings in travel costs of up to 50 % are possible, and this bound is tight. Recently, a variant of the SDVRP, the split delivery vehicle routing problem with minimum delivery amounts (SDVRP-MDA), has been introduced. In the SDVRP-MDA, split deliveries are allowed only if at least a minimum fraction of a customer’s demand is delivered by each visiting vehicle. We perform a worst-case analysis on the SDVRP-MDA to determine tight bounds on the maximum possible savings.     

A meta-heuristic algorithm for heterogeneous fleet vehicle routing problems with two-dimensional loading constraints

The two-dimensional loading heterogeneous fleet vehicle routing problem (2L-HFVRP) is a variant of the classical vehicle routing problem in which customers are served by a heterogeneous fleet of vehicles. These vehicles have different capacities, fixed and variable operating costs, length and width in dimension, and two-dimensional loading constraints. The objective of this problem is to minimize transportation cost of designed routes, according to which vehicles are used, to satisfy the customer demand. In this study, we proposed a simulated annealing with heuristic local search (SA_HLS) to solve the problem and the search was then extended with a collection of packing heuristics to solve the loading constraints in 2L-HFVRP. To speed up the search process, a data structure was used to record the information related to loading feasibility. The effectiveness of SA_HLS was tested on benchmark instances derived from the two-dimensional loading vehicle routing problem (2L-CVRP). In addition, the performance of SA_HLS was also compared with three other 2L-CVRP models and four HFVRP methods found in the literature.     

Minimizing fleet operating costs for a container transportation company

This paper focuses on a fleet management problem that arises in container trucking industry. From the container transportation company perspective, the present and future operating costs to minimize can be divided in three components: the routing costs, the resource (i.e., driver and truck) assignment costs and the container repositioning costs (i.e., the costs of restoring a given container fleet distribution over the serviced territory, as requested by the shippers that own the containers).This real-world problem has been modeled as an integer programming problem. The proposed solution approach is based on the decomposition of this problem in three simpler sub-problems associated to each of the costs considered above.Numerical experiments on randomly generated instances, as well as on a real-world data set of an Italian container trucking company, are presented.     

A complementary tool to enhance the effectiveness of existing methods for heterogeneous fixed fleet vehicle routing problem

The heterogeneous fixed fleet vehicle routing problem (HFFVRP) is a variant of the standard vehicle routing problem (VRP), in which the vertices have to be served using a fixed number of vehicles that could be different in size and fixed or variable costs. In this article, we propose an integer linear programming-based heuristic approach in order to solve the HFFVRP that could be used as a complementary tool to improve the performance of the existing methods of solving this problem. Computational results show the effectiveness of the proposed method.     

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.