Vehicle routing problem with stochastic travel times including soft time windows and service costs

This paper studies a vehicle routing problem with soft time windows and stochastic travel times. A model is developed that considers both transportation costs (total distance traveled, number of vehicles used and drivers' total expected overtime) and service costs (early and late arrivals). We propose a Tabu Search method to solve this model. An initialization algorithm is developed to construct feasible routes by taking into account the travel time stochasticity. Solutions provided by the Tabu Search algorithm are further improved by a post-optimization method. We conduct our computational experiments for well-known problem instances. Results show that our Tabu Search method performs well by obtaining very good final solutions in a reasonable amount of time.     

Vehicle routing and scheduling with dynamic travel times

The field of dynamic vehicle routing and scheduling is growing at a fast pace nowadays, due to many potential applications in courier services, emergency services, truckload and less-than-truckload trucking, and many others. In this paper, a dynamic vehicle routing and scheduling problem with time windows is described where both real-time customer requests and dynamic travel times are considered. Different reactive dispatching strategies are defined and compared through the setting of a single “tolerance” parameter. The results show that some tolerance to deviations with the current planned solution usually leads to better solutions.     

The dynamic multiperiod vehicle routing problem with probabilistic information

This paper introduces the Dynamic Multiperiod Vehicle Routing Problem with Probabilistic Information, an extension of the Dynamic Multiperiod Vehicle Routing Problem in which, at each time period, the set of customers requiring a service in later time periods is unknown, but its probability distribution is available. Requests for service must be satisfied within a given time window that comprises several time periods of the planning horizon. We propose an adaptive service policy that aims at estimating the best time period to serve each request within its associated time window in order to reduce distribution costs. The effectiveness of this policy is compared with that of two alternative basic policies through a series of computational experiments.     

Production scheduling and vehicle routing with time windows for perishable food products

We propose a nonlinear mathematical model to consider production scheduling and vehicle routing with time windows for perishable food products in the same framework. The demands at retailers are assumed stochastic and perishable goods will deteriorate once they were produced. Thus the revenue of the supplier is uncertain and depends on the value and the transaction quantity of perishable products when they are carried to retailers. The objective of this model is to maximize the expected total profit of the supplier. The optimal production quantities, the time to start producing and the vehicle routes can be determined in the model simultaneously. Furthermore, we elaborate a solution algorithm composed of the constrained Nelder–Mead method and a heuristic for the vehicle routing with time windows to solve the complex problem. Computational results indicate our algorithm is effective and efficient.     

A note on the time travel approach for handling time windows in vehicle routing problems

In this paper, we identify two cases in which the proposition for calculating time window penalties presented in Nagata, Y., Bräysy, O. and Dullaert, W. A penalty-based edge assembly memetic algorithm for the vehicle routing problem with time windows, Computers & Operations Research 2010;37(4): 724–37 yields incorrect results. We derive the corrected proposition and use numerical studies to show that a significant proportion of the evaluations performed by a Tabu Search for VRPTW falls under the two incorrect cases. Moreover, we demonstrate that the incorrect time window handling has a significant negative impact on the solution quality of the Tabu Search.     

The robust vehicle routing problem with time windows

This paper addresses the robust vehicle routing problem with time windows. We are motivated by a problem that arises in maritime transportation where delays are frequent and should be taken into account. Our model only allows routes that are feasible for all values of the travel times in a predetermined uncertainty polytope, which yields a robust optimization problem. We propose two new formulations for the robust problem, each based on a different robust approach. The first formulation extends the well-known resource inequalities formulation by employing adjustable robust optimization. We propose two techniques, which, using the structure of the problem, allow to reduce significantly the number of extreme points of the uncertainty polytope. The second formulation generalizes a path inequalities formulation to the uncertain context. The uncertainty appears implicitly in this formulation, so that we develop a new cutting plane technique for robust combinatorial optimization problems with complicated constraints. In particular, efficient separation procedures are discussed. We compare the two formulations on a test bed composed of maritime transportation instances. These results show that the solution times are similar for both formulations while being significantly faster than the solutions times of a layered formulation recently proposed for the problem.     

Customer satisfaction in dynamic vehicle routing problem with time windows

The dynamic vehicle routing and scheduling problem is a well-known complex combinatorial optimization problem that drew significant attention over the past few years. This paper presents a novel algorithm introducing a new strategy to integrate anticipated future visit requests during plan generation, aimed at explicitly improving customer satisfaction. An evaluation of the proposed strategy is performed using a hybrid genetic algorithm previously designed for the dynamic vehicle problem with time windows that we modified to capture customer satisfaction over multiple visits. Simulations compare the value of the revisited algorithm exploiting the new strategy, clearly demonstrating its impact on customer satisfaction level.     

A multi-objective dynamic vehicle routing problem with fuzzy time windows: Model,solution and application

In this paper, a multi-objective dynamic vehicle routing problem with fuzzy time windows (DVRPFTW) is presented. In this problem, unlike most of the work where all the data are known in advance, a set of real time requests arrives randomly over time and the dispatcher does not have any deterministic or probabilistic information on the location and size of them until they arrive. Moreover, this model involves routing vehicles according to customer-specific time windows, which are highly relevant to the customers’ satisfaction level. This preference information of customers can be represented as a convex fuzzy number with respect to the satisfaction for a service time. This paper uses a direct interpretation of the DVRPFTW as a multi-objective problem where the total required fleet size, overall total traveling distance and waiting time imposed on vehicles are minimized and the overall customers’ preferences for service is maximized. A solving strategy based on the genetic algorithm (GA) and three basic modules are proposed, in which the state of the system including information of vehicles and customers is checked in a management module each time. The strategy module tries to organize the information reported by the management module and construct an efficient structure for solving in the subsequent module. The performance of the proposed approach is evaluated in different steps on various test problems generalized from a set of static instances in the literature. In the first step, the performance of the proposed approach is checked in static conditions and then the other assumptions and developments are added gradually and changes are examined. The computational experiments on data sets illustrate the efficiency and effectiveness of the proposed approach.     

考虑时间窗与随机航行时间的船舶航线规划

良好的航线设计是船运公司降低运营成本,提高服务质量的关键。船舶运输中存在航行时间不确定,码头资源稀缺等特点,基于此将其航线问题抽象为考虑时间窗与随机旅行时间的多重流动旅行商问题。针对航行时间的随机性,设计了线性近似方法,提出了虚拟时间窗的概念,构建了初始模型与修正模型;给出了该问题的一个算例,验证了模型与算法的有效性和合理性。     

Formulations and exact algorithms for the vehicle routing problem with time windows

In this paper we review the exact algorithms proposed in the last three decades for the solution of the vehicle routing problem with time windows (VRPTW). The exact algorithms for the VRPTW are in many aspects inherited from work on the traveling salesman problem (TSP). In recognition of this fact this paper is structured relative to four seminal papers concerning the formulation and exact solution of the TSP, i.e. the arc formulation, the arc-node formulation, the spanning tree formulation, and the path formulation. We give a detailed analysis of the formulations of the VRPTW and a review of the literature related to the different formulations. There are two main lines of development in relation to the exact algorithms for the VRPTW. One is concerned with the general decomposition approach and the solution to certain dual problems associated with the VRPTW. Another more recent direction is concerned with the analysis of the polyhedral structure of the VRPTW. We conclude by examining possible future lines of research in the area of the VRPTW.     

A dynamic vehicle routing problem with time-dependent travel times

In this paper we present a formulation for the dynamic vehicle routing problem with time-dependent travel times. We also present a genetic algorithm to solve the problem. The problem is a pick-up or delivery vehicle routing problem with soft time windows in which we consider multiple vehicles with different capacities, real-time service requests, and real-time variations in travel times between demand nodes.The performance of the genetic algorithm is evaluated by comparing its results with exact solutions and lower bounds for randomly generated test problems. For small size problems with up to 10 demands, the genetic algorithm provides almost the same results as the exact solutions, while its computation time is less than 10% of the time required to produce the exact solutions. For the problems with 30 demand nodes, the genetic algorithm results have less than 8% gap with lower bounds.This research also shows that as the uncertainty in the travel time information increases, a dynamic routing strategy that takes the real-time traffic information into account becomes increasingly superior to a static one. This is clear when we compare the static and dynamic routing strategies in problem scenarios that have different levels of uncertainty in travel time information. In additional tests on a simulated network, the proposed algorithm works well in dealing with situations in which accidents cause significant congestion in some part of the transportation network.     

Adaptive granular local search heuristic for a dynamic vehicle routing problem

The advance of communication and information technologies based on satellite and wireless networks have allowed transportation companies to benefit from real-time information for dynamic vehicle routing with time windows. During daily operations, we consider the case in which customers can place requests such that their demand and location are stochastic variables. The time windows at customer locations can be violated although lateness costs are incurred. The objective is to define a set of vehicle routes which are dynamically updated to accommodate new customers in order to maximize the expected profit. This is the difference between the total revenue and the sum of lateness costs and costs associated with the total distance traveled. The solution approach makes use of a new constructive heuristic that scatters vehicles in the service area and an adaptive granular local search procedure. The strategies of letting a vehicle wait, positioning a vehicle in a region where customers are likely to appear, and diverting a vehicle away from its current destination are integrated within a granular local search heuristic. The performance of the proposed approach is assessed in test problems based on real-life Brazilian transportation companies.     

A planning model and solution algorithm for multi-trip split-delivery vehicle routing and scheduling problems with time windows

This study proposes a daily vehicle routing model for minimizing the total cost of replenishing inventory within a supply chain. The first major contribution of this research is to allow multiple use of vehicles in a split delivery vehicle routing problem with time windows (SDVRPTW), which is more realistic for various real-life applications. The multi-trip SDVRPTW (MTSDVRPTW) is formulated using the time–space network technique, which provides greater flexibility for formulating the complicated interactions between vehicles and products when multi-trip, split delivery, and delivery time windows are simultaneously considered. The resulting formulation of the MTSDVRPTW can be categorized as an integer multi-commodity network flow problem with side constraints. A two-step solution algorithm is proposed to solve this NP-hard problem, which is the second major contribution of this research. Finally, a real-world scale numerical example is performed to demonstrate and to test the methodology. The results indicate that these vehicle routing problems can be solved effectively and efficiently and that the proposed methodology has great potential for inventory replenishment scheduling where split deliveries and multiple trips for a single vehicle are allowed and time window constraints are imposed.     

On solving periodic re-optimization dynamic vehicle routing problems

The Vehicle Routing Problem (VRP) is a complex and high-level set of routing problems. One of its important variants is the Dynamic Vehicle Routing Problem (DVRP) in which not all customers are known in advance, but are revealed as the system progresses. DVRP is a Dynamic Optimization Problem (DOP) that has become a challenging research topic in the past two decades. In DOPs, at least one part of the problem changes as time passes. For DVRP, customers change as a system progresses. Consequently, DVRP applications are seen to operate on a dynamic basis in various real-life systems. To date, a time-based evaluation approach has been used to evaluate periodic re-optimized DVRP systems, which are evaluated by solving while using a specific time budget. In this paper, we solve DVRP while using an enhanced Genetic Algorithm (GA) that tries to increase both diversity and the capability to escape from local optima. Also, we propose a fair weighted fitness evaluation approach as an alternative for the biased time-based approach, regardless of the specifications and power of the running system. The proposed enhanced GA outperformed the previously published algorithms based on both the time-based and weighted fitness evaluation approaches.     

A genetic algorithm for vehicle routing with backhauling

In this paper, a greedy route construction heuristic for a vehicle routing problem with backhauling is described. This heuristic inserts customers one by one into the routes using a fixed a priori ordering of customers. Then, a genetic algorithm is used to identify an ordering that produces good routes. Numerical comparisons are provided with an exact algorithm and with other heuristic approaches.     

时间窗约束下的配送车辆调度问题研究

为解决时间窗约束下的物流配送车辆的多目标调度优化问题,给出了一种基于免疫计算的配送车辆调度优化方案。设计了配送车辆调度问题的数学模型和一种基于非劣邻域支配的多目标调度优化算法,在仿真环境下进行了实验。实验结果表明,算法能够有效地解决物流配送车辆调度问题,具有较好的应用价值。     

Dynamic vehicle routing using genetic algorithms

Many difficult combinatorial optimization problems have been modeled as static problems. However, in practice, many problems are dynamic and changing, while some decisions have to be made before all the design data are known. For example, in the Dynamic Vehicle Routing Problem (DVRP), new customer orders appear over time, and new routes must be reconfigured while executing the current solution. Montemanni et al. [1] considered a DVRP as an extension to the standard vehicle routing problem (VRP) by decomposing a DVRP as a sequence of static VRPs, and then solving them with an ant colony system (ACS) algorithm. This paper presents a genetic algorithm (GA) methodology for providing solutions for the DVRP model employed in [1]. The effectiveness of the proposed GA is evaluated using a set of benchmarks found in the literature. Compared with a tabu search approach implemented herein and the aforementioned ACS, the proposed GA methodology performs better in minimizing travel costs. Franklin T. Hanshar is currently a M.Sc. student in the Department of Computing and Information Science at the University of Guelph, Ontario, Canada. He received a B.Sc. degree in Computer Science from Brock University in 2005. His research interests include uncertain reasoning, optimization and evolutionary computation. Beatrice Ombuki-Berman is currently an Associate Professor in the Department of Computer Science at Brock University, Ontario, Canada. She obtained a PhD and ME in Information Engineering from University of The Ryukyus, Okinawa, Japan in 2001 and 1998, respectively. She received a B.Sc. in Mathematics and Computer Science from Jomo Kenyatta University, Nairobi, Kenya. Her primary research interest is evolutionary computation and applied optimization. Other research interests include neural networks, machine learning and ant colony optimization.     

带时间窗口动态车辆路径规划模型及其求解算法

基于事件触发,把带时间窗口动态车辆路径规划问题（DVRPTW）分解成一系列延迟快照,在快照基础上建立相应的动态数学模型,并提出双缓冲区改进大邻域搜索算法进行求解。利用算法的特点,实现新请求无缝插入。采用Solomon设计的56个100节点范例和Lackner相应的动态测试数据,经不同类型动态实例的实验表明,所建立的模型和给出的算法是有效的。     

A penalty-based edge assembly memetic algorithm for the vehicle routing problem with time windows

In this paper, we present an effective memetic algorithm for the vehicle routing problem with time windows (VRPTW). The paper builds upon an existing edge assembly crossover (EAX) developed for the capacitated VRP. The adjustments of the EAX operator and the introduction of a novel penalty function to eliminate violations of the time window constraint as well as the capacity constraint from offspring solutions generated by the EAX operator have proven essential to the heuristic's performance. Experimental results on Solomon's and Gehring and Homberger benchmarks demonstrate that our algorithm outperforms previous approaches and is able to improve 184 best-known solutions out of 356 instances.     

Job shop scheduling with setup times, deadlines and precedence constraints

In the last 15 years several procedures have been developed that can find solutions of acceptable quality in reasonable computing time to Job Shop Scheduling problems in environments that do not involve sequence-dependent setup times of the machines. The presence of the latter, however, changes the picture dramatically. In this paper we adapt one of the best known heuristics, the Shifting Bottleneck Procedure, to the case when sequence dependent setup times play an important role. This is done by treating the single machine scheduling problems that arise in the process as Traveling Salesman Problems with time windows, and solving the latter by an efficient dynamic programming algorithm. The model treated here also incorporates precedence constraints, release times and deadlines. Computational experience on a vast array of instances, mainly from the semiconductor industry, shows our procedure to advance substantially the state of the art. Paper presented in New York at MISTA 2005. E. Balas supported by the National Science Foundation through grant DMI-9802773 and by the Office of Naval Research through contract #N00014-97-1-0133.