A covering tour approach to the location of satellite distribution centers to supply humanitarian aid

This article concerns the location of satellite distribution centers (SDCs) to supply humanitarian aid to the affected people throughout a disaster area. In such situations, it is not possible for the relief teams to visit every single home. Instead, the people are required to go to a satellite distribution center in order to obtain survival goods, provided that these centers are not too far from their homes. The SDCs are usually within walking distance. However, these SDCs need to be supplied from a central depot, using a heterogeneous and capacitated fleet of vehicles. We model this situation as a generalization of the covering tour problem, introduce the idea of split delivery, and propose an efficient heuristic approach to solve it. Numerical experiments on randomly-generated data show that, first, only very small instances can be solved efficiently using the mathematical model and, second, our heuristic produces high-quality solutions and solves real-size instances in a reasonable computing 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 new tabu search algorithm for the vehicle routing problem with backhauls

In the distribution of goods from a central depot to geographically dispersed customers happens quite frequently that some customers, called linehauls, receive goods from that depot while others, named backhauls, send goods to it. This situation is described and studied by the vehicle routing problem with backhauls. In this paper we present a new tabu search algorithm that starting from pseudo-lower bounds was able to match almost all the best published solutions and to find many new best solutions, for a large set of benchmark problems.     

Comparing backhauling strategies in vehicle routing using Ant Colony Optimization

In the Vehicle Routing Problem with Backhauls and Time Windows (VRPBTW) customers either receive goods from the depot or send goods to the depot and pickup or delivery at a customer has to occur within a pre-specified time window. The main objective is to minimize the total required fleet size for serving all customers. Secondary objectives are to minimize the total distance travelled or to minimize the total route duration of all vehicles. In this paper we consider a variant of the mixed VRPBTW where backhauls may be served before linehauls on any given route. Besides the modelling aspect of this variant we will study its performance implications when compared to the standard VRPBTW using a heuristic algorithm based on Ant Colony Optimization.     

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.     

A specialized column generation approach for a vehicle routing problem with demand allocation

Motivated by logistical operations for a food bank, this paper addresses a class of vehicle routing problems with demand allocation considerations over a network of partner agencies locations and candidate delivery sites. Any delivery tour starts at a central depot operated by the food bank and selected delivery sites are sequentially visited in order to supply goods to a set of partner agencies who travel from their respective locations to their assigned delivery sites. The problem is modelled as a mixed-integer programme with the objective of minimizing a weighted average of the distances travelled by delivery vehicles and partner agencies, and is tackled via two heuristics. First, a relax-and-fix heuristic is presented for the proposed model and is computationally enhanced using two symmetry-defeating strategies. Second, the problem is reformulated as a set partitioning model with side packing constraints that prompts a specialized column generation approach. Computational experience is provided using realistic data instances to demonstrate the usefulness of the proposed heuristics and the importance of integrated solution techniques for this class of problems.     

A unified heuristic for a large class of Vehicle Routing Problems with Backhauls

The Vehicle Routing Problem with Backhauls is a generalization of the ordinary capacitated vehicle routing problem where goods are delivered from the depot to the linehaul customers, and additional goods are brought back to the depot from the backhaul customers. Numerous ways of modeling the backhaul constraints have been proposed in the literature, each imposing different restrictions on the handling of backhaul customers. A survey of these models is presented, and a unified model is developed that is capable of handling most variants of the problem from the literature. The unified model can be seen as a Rich Pickup and Delivery Problem with Time Windows, which can be solved through an improved version of the large neighborhood search heuristic proposed by Ropke and Pisinger [An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows, Technical Report, DIKU, University of Copenhagen, 2004]. The results obtained in this way are comparable to or improve on similar results found by state of the art heuristics for the various variants of the problem. The heuristic has been tested on 338 problems from the literature and it has improved the best known solution for 227 of these. An additional benefit of the unified modeling and solution method is that it allows the dispatcher to mix various variants of the Vehicle Routing Problem with Backhauls for the individual customers or vehicles.     

Approximative solutions to the bicriterion Vehicle Routing Problem with Time Windows

The Vehicle Routing Problem with Time Windows (VRPTW) is a combinatorial optimization problem. It deals with route planning and the distribution of goods from a depot to geographically dispersed customers by a fleet of vehicles with constrained capacities. The customers’ demands are known and each customer has a time window in which it has to be supplied. The time windows are assumed to be soft, that means, violations of the time windows are allowed, but associated with penalties. The problem is to organize the vehicle routes optimally, i.e. to minimize the total costs, consisting of the number of used vehicles and the total distance, and the penalties simultaneously. Thus, the problem is formulated as a bicriterion minimization problem and heuristic methods are used to calculate approximations of the Pareto optimal solutions. Experimental results show that in certain cases the allowance of penalties leads to significant savings of the total costs.     

A stochastic dynamic traveling salesman problem with hard time windows

Just-in-time (JIT) trucking service, i.e., arriving at customers within specified time windows, has become the norm for freight carriers in all stages of supply chains. In this paper, a JIT pickup/delivery problem is formulated as a stochastic dynamic traveling salesman problem with time windows (SDTSPTW). At a customer location, the vehicle either picks up goods for or delivers goods from the depot, but does not provide moving service to transfer goods from one location to another. Such routing problems are NP-hard in deterministic settings, and in our context, complicated further by the stochastic, dynamic nature of the problem. This paper develops an efficient heuristic for the SDTSPTW with hard time windows. The heuristic is shown to be useful both in controlled numerical experiments and in applying to a real-life trucking problem.     

A hybrid tabu search based heuristic for the periodic distribution inventory problem with perishable goods

Most of the research on integrated inventory and routing problems ignores the case when products are perishable. However, considering the integrated problem with perishable goods is crucial since any discrepancy between the routing and inventory cost can double down the risk of higher obsolescence costs due to the limited shelf-life of the products. In this paper, we consider a distribution problem involving a depot, a set of customers and a homogeneous fleet of capacitated vehicles. Perishable goods are transported from the depot to customers in such a way that out-of-stock situations never occur. The objective is to simultaneously determine the inventory and routing decisions over a given time horizon such that total transportation cost is minimized. We present a new “arc-based formulation” for the problem which is deemed more suitable for our new tabu search based approach for solving the problem. We perform a thorough sensitivity analysis for each of the tabu search parameters individually and use the obtained gaps to fine-tune the parameter values that are used in solving larger sized instances of the problem. We solve different sizes of randomly generated instances and compare the results obtained using the tabu search algorithm to those obtained by solving the problem using CPLEX and a recently published column generation algorithm. Our computational experiments demonstrate that the tabu search algorithm is capable of obtaining a near-optimal solution in less computational time than the time required to solve the problem to optimality using CPLEX, and outperforms the column generation algorithm for solving the “path flow formulation” of the problem in terms of solution quality in almost all of the considered instances.     

Disrupted capacitated vehicle routing problem with order release delay

With the popularity of the just-in-time system, more and more companies are operating with little or no inventories, which make them highly vulnerable to delays on supply. This paper discusses a situation when the supply of the commodity does not arrive at the depot on time, so that not enough of the commodity is available to be loaded on all vehicles at the start of the delivery period. New routing plans need to be developed in such a case to reduce the impact the delay of supply may have on the distribution company. The resulting vehicle routing problem is different from other types of vehicle routing problems as it involves waiting and multiple trips. Two approaches have been developed to solve the order release delay problem, both of which involve a Tabu Search algorithm. Computational results show the proposed approaches can largely reduce the disruption costs that are caused by the delayed supply and they are especially effective when the length of delay is long.     

计及客户满意度的电动汽车物流配送路径规划与充放电管理

物流配送作为一种盈利型社会服务性行业,配送服务时间对客户满意度具有重要影响。论文考虑电动汽车(electric vehicle, EV)在配送途中和回到配送中心两个阶段,以物流配送成本最低和客户平均满意度最高为目标,构建了一种EV在换电模式下计及客户满意度的物流配送路径规划与充放电管理多目标优化模型,其中物流配送成本包括换电成本、车辆损耗成本以及慢速充放电成本。最后,以A-n29节点VRP基准测试系统插入四座换电站节点为例进行数值仿真,采用非支配排序遗传算法(Non-dominated sorting genetic algorithm, NSGA-II)对所提多目标优化模型进行求解,结果验证了所提方法的可行性和有效性。此外,论文进一步考查了EV慢速充放电管理对配电系统的影响,并对EV发车时间作了参数灵敏度分析,为管理者提供一些参考。     

Designing multi-vehicle delivery tours in a grid-cell format

This paper presents a methodology to be used in the design of multi-delivery tours associated with the servicing of a heterogeneous region, where the density of visiting points and the amount of cargo vary over the served area. Both vehicle cycle time and vehicle load are treated probabilistically. The region under analysis is partitioned into a number of sectors, rings, and districts, with the polar coordinates centered at the depot. We assume a rectangular grid structure for the representation of the spatial variables. This division is intended to attain a quasi-homogeneous distribution effort (approximate equal number of vehicles) in each partition. The optimization model seeks the best fleet of vehicles that minimizes total daily transport costs. As an example, the model is applied to a parcel delivery problem in the city of São Paulo, Brazil.     

Exact algorithms for routing problems under vehicle capacity constraints

The solution of a vehicle routing problem calls for the determination of a set of routes, each performed by a single vehicle which starts and ends at its own depot, such that all the requirements of the customers are fulfilled and the global transportation cost is minimized. The routes have to satisfy several operational constraints which depend on the nature of the transported goods, on the quality of the service level, and on the characteristics of the customers and of the vehicles. One of the most common operational constraint addressed in the scientific literature is that the vehicle fleet is capacitated and the total load transported by a vehicle cannot exceed its capacity.     

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.     

A list based threshold accepting metaheuristic for the heterogeneous fixed fleet vehicle routing problem

In real life situations most companies that deliver or collect goods own a heterogeneous fleet of vehicles. Their goal is to find a set of vehicle routes, each starting and ending at a depot, making the best possible use of the given vehicle fleet such that total cost is minimized. The specific problem can be formulated as the Heterogeneous Fixed Fleet Vehicle Routing Problem (HFFVRP), which is a variant of the classical Vehicle Routing Problem. This paper describes a variant of the threshold accepting heuristic for the HFFVRP. The proposed metaheuristic has a remarkably simple structure, it is lean and parsimonious and it produces high quality solutions over a set of published benchmark instances. Improvement over several of previous best solutions also demonstrates the capabilities of the method and is encouraging for further research.     

具有学习效应的三层供应链排序问题

研究了具有学习效应的三层供应链排序问题. 多个客户分布在不同位置,每个客户都有订 单需要制造商进行生产. 制造商需要针对每一个不同订单的客户从不同的地方进购对应的原材料进行生产,生产完工后需要利用有限的车辆将工件运输到相应客户处. 要求每辆运输车装载尽可 能多的货物才开始运输. 利用动态规划算法研究了最大流程时间、总流程时间以及最大延迟三个目标函数.     

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.     

Emergency Logistics Planning in Natural Disasters

Logistics planning in emergency situations involves dispatching commodities (e.g., medical materials and personnel, specialised rescue equipment and rescue teams, food, etc.) to distribution centres in affected areas as soon as possible so that relief operations are accelerated. In this study, a planning model that is to be integrated into a natural disaster logistics Decision Support System is developed. The model addresses the dynamic time-dependent transportation problem that needs to be solved repetitively at given time intervals during ongoing aid delivery. The model regenerates plans incorporating new requests for aid materials, new supplies and transportation means that become available during the current planning time horizon. The plan indicates the optimal mixed pick up and delivery schedules for vehicles within the considered planning time horizon as well as the optimal quantities and types of loads picked up and delivered on these routes. In emergency logistics context, supply is available in limited quantities at the current time period and on specified future dates. Commodity demand is known with certainty at the current date, but can be forecasted for future dates. Unlike commercial environments, vehicles do not have to return to depots, because the next time the plan is re-generated, a node receiving commodities may become a depot or a former depot may have no supplies at all. As a result, there are no closed loop tours, and vehicles wait at their last stop until they receive the next order from the logistics coordination centre. Hence, dispatch orders for vehicles consist of sets of “broken” routes that are generated in response to time-dependent supply/demand. The mathematical model describes a setting that is considerably different than the conventional vehicle routing problem. In fact, the problem is a hybrid that integrates the multi-commodity network flow problem and the vehicle routing problem. In this setting, vehicles are also treated as commodities. The model is readily decomposed into two multi-commodity network flow problems, the first one being linear (for conventional commodities) and the second integer (for vehicle flows). In the solution approach, these sub-models are coupled with relaxed arc capacity constraints using Lagrangean relaxation. The convergence of the proposed algorithm is tested on small test instances as well as on an earthquake scenario of realistic size.     

Optimised crossover genetic algorithm for capacitated vehicle routing problem

This paper presents a genetic algorithm for solving capacitated vehicle routing problem, which is mainly characterised by using vehicles of the same capacity based at a central depot that will be optimally routed to supply customers with known demands. The proposed algorithm uses an optimised crossover operator designed by a complete undirected bipartite graph to find an optimal set of delivery routes satisfying the requirements and giving minimal total cost. We tested our algorithm with benchmark instances and compared it with some other heuristics in the literature. Computational results showed that the proposed algorithm is competitive in terms of the quality of the solutions found.