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.     

Polyhedral study of the capacitated vehicle routing problem

The capacitated vehicle routing problem (CVRP) considered in this paper occurs when goods must be delivered from a central depot to clients with known demands, usingk vehicles of fixed capacity. Each client must be assigned to exactly one of the vehicles. The set of clients assigned to each vehicle must satisfy the capacity constraint. The goal is to minimize the total distance traveled. When the capacity of the vehicles is large enough, this problem reduces to the famous traveling salesman problem (TSP). A variant of the problem in which each client is visited by at least one vehicle, called the graphical vehicle routing problem (GVRP), is also considered in this paper and used as a relaxation of CVRP. Our approach for CVRP and GVRP is to extend the polyhedral results known for TSP. For example, the subtour elimination constraints can be generalized to facets of both CVRP and GVRP. Interesting classes of facets arise as a generalization of the comb inequalities, depending on whether the depot is in a handle, a tooth, both or neither. We report on the optimal solution of two problem instances by a cutting plane algorithm that only uses inequalities from the above classes.This work was supported in part by NSF grant DDM-8901495.     

The capacitated general windy routing problem with turn penalties

In this paper we present the capacitated general windy routing problem with turn penalties. This new problem subsumes many important and well-known arc and node routing problems, and it takes into account turn penalties and forbidden turns, which are crucial in many real-life applications, particularly in downtown areas and for large vehicles. We provide a way to solve this problem both optimally and heuristically by transforming it into a generalized vehicle routing problem.     

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.     

Designing vehicle routes for a mix of different request types,under time windows and loading constraints

This article introduces and solves a new rich routing problem integrated with practical operational constraints. The problem examined calls for the determination of the optimal routes for a vehicle fleet to satisfy a mix of two different request types. Firstly, vehicles must transport three-dimensional, rectangular and stackable boxes from a depot to a set of predetermined customers. In addition, vehicles must also transfer products between pairs of pick-up and delivery locations. Service of both request types is subject to hard time window constraints. In addition, feasible palletization patterns must be identified for the transported products. A practical application of the problem arises in the transportation systems of chain stores, where vehicles replenish the retail points by delivering products stored at a central depot, while they are also responsible for transferring stock between pairs of the retailer network. To solve this very complex combinatorial optimization problem, our major objective was to develop an efficient methodology whose required computational effort is kept within reasonable limits. To this end, we propose a local search-based framework for optimizing vehicle routes, in which feasible loading arrangements are identified via a simple-structured packing heuristic. The algorithmic framework is enhanced with various memory components which store and retrieve useful information gathered through the search process, in order to avoid any duplicate unnecessary calculations. The proposed solution approach is assessed on newly introduced benchmark instances.     

A new tabu search heuristic for the open vehicle routing problem

In this paper, another version of the vehicle routing problem (VRP)—the open vehicle routing problem (OVRP) is studied, in which the vehicles are not required to return to the depot, but if they do, it must be by revisiting the customers assigned to them in the reverse order. By exploiting the special structure of this type of problem, we present a new tabu search heuristic for finding the routes that minimize two objectives while satisfying three constraints. The computational results are provided and compared with two other methods in the literature.     

Open vehicle routing problem with driver nodes and time deadlines

In this paper, we consider a variant of the open vehicle routing problem in which vehicles depart from the depot, visit a set of customers, and end their routes at special nodes called driver nodes. A driver node can be the home of the driver or a parking lot where the vehicle will stay overnight. The resulting problem is referred to as the open vehicle routing problem with driver nodes (OVRP-d). We consider three classes of OVRP-d: with no time constraints, with a maximum route duration, and with both a maximum route duration as well as time deadlines for visiting customers. For the solution of these problems, which are not addressed previously in the literature, we develop a new tabu search heuristic. Computational results on randomly generated instances indicate that the new heuristic exhibits a good performance both in terms of the solution quality and computation time.     

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.     

A variable neighbourhood search algorithm for the open vehicle routing problem

In the open vehicle routing problem (OVRP), the objective is to minimise the number of vehicles and then minimise the total distance (or time) travelled. Each route starts at the depot and ends at a customer, visiting a number of customers, each once, en route, without returning to the depot. The demand of each customer must be completely fulfilled by a single vehicle. The total demand serviced by each vehicle must not exceed vehicle capacity. Additionally, in one variant of the problem, the travel time of each vehicle should not exceed an upper limit.     

Stochastic single vehicle routing problem with delivery and pick up and a predefined customer sequence

In this paper we study the routing of a single vehicle that delivers products and picks up items with stochastic demand. The vehicle follows a predefined customer sequence and is allowed to return to the depot for loading/unloading as needed. A suitable dynamic programming algorithm is proposed to determine the minimum expected routing cost. Furthermore, the optimal routing policy to be followed by the vehicle’s driver is derived by proposing an appropriate theorem. The efficiency of the algorithm is studied by solving large problem sets.     

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.     

Recent advances in vehicle routing exact algorithms

The capacitated vehicle routing problem (CVRP) is the problem in which a set of identical vehicles located at a central depot is to be optimally routed to supply customers with known demands subject to vehicle capacity constraints. This paper provides a review of the most recent developments that had a major impact in the current state-of-the-art of exact algorithms for the CVRP. The most important mathematical formulations for the problem together with various CVRP relaxations are reviewed. The paper also describes the recent exact methods for the CVRP and reports a comparison of their computational performances.      

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。     

Optimising passing bay locations and vehicle schedules in underground mines

In many underground mines, haulage vehicles carry ore from underground loading stations to the surface. Vehicles travel in narrow tunnels with occasional passing bays that allow descending empty vehicles to pull off the main path and wait for ascending laden vehicles to pass. The number of passing bays and their locations influence the delays to descending vehicles, and hence the haulage productivity of the mine. We formulate and solve a mixed integer programming (MIP) model to determine the optimal locations of passing bays to maximise haulage productivity for given numbers of vehicles and passing bays. The MIP also generates the corresponding vehicle schedule. Previous studies have only examined the placement of equally spaced bays. The results obtained from the MIP show that this is not always optimal. Furthermore, we observe that the best locations of passing bays are those that allow interleaving of vehicles without delays at bays.     

The multi-trip vehicle routing problem

The basic vehicle routing problem is concerned with the design of a set of routes to serve a given number of customers, minimising the total distance travelled. In that problem, each vehicle is assumed to be used only once during a planning period, which is typically a day, and therefore is unrepresentative of many practical situations, where a vehicle makes several journeys during a day. The present authors have previously published an algorithm which outperformed an experienced load planner working on the complex, real-life problems of Burton's Biscuits, where vehicles make more than one trip each day. This present paper uses a simplified version of that general algorithm, in order to compare it with a recently published heuristic specially designed for the theoretical multi-trip vehicle routing problem.     

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.     

A heuristic method for the open vehicle routing problem

The open vehicle routing problem (OVRP) differs from the classic vehicle routing problem (VRP) because the vehicles either are not required to return to the depot, or they have to return by revisiting the customers assigned to them in the reverse order. Therefore, the vehicle routes are not closed paths but open ones. A heuristic method for solving this new problem, based on a minimum spanning tree with penalties procedure, is presented. Computational results are provided.     

A heuristic method for the capacitated arc routing problem with refill points and multiple loads

We describe a solution procedure for a capacitated arc routing problem with refill points and multiple loads. This problem stems from the road network marking in Quebec, Canada. Two different types of vehicles are used: the first type (called servicing vehicle—SV) with a finite capacity to service the arcs and the other (called refilling vehicle—RV) to refill the SV vehicle.The RV can deliver multiple loads, which means that it meets the SV several times before returning to the depot. The problem consists of simultaneously determining the vehicle routes that minimize the total cost of the two vehicles.We present an integer formulation and a route first-cluster second heuristic procedure. Computational results are provided.     

Dynamic scheduling of recreational rental vehicles with revenue management extensions

The rental fleet scheduling problem (RFSP) arises in vehicle-rental operations that offer a wide variety of vehicle types to customers, and allow a rented vehicle to ‘migrate’ to a setdown depot other than the pickup depot.When there is a shortage of vehicles of a particular type at a depot, vehicles may be relocated to that depot, or vehicles of similar types may be substituted.The RFSP involves assigning vehicles to rentals so as to minimise the costs of these operations, and arises in both static and online contexts. The authors have adapted a well-known assignment algorithm for application in the online context. In addition, a network-flow algorithm with more comprehensive coverage of problem conditions is used to investigate the determination of rental pricing using revenue management principles. The paper concludes with an outline of the algorithms’ use in supporting the operations of a large recreational vehicle rental company.     

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.