Study of Solution Approach for Dynamic Vehicle Routing Problems with Real-Time Information

Dynamic vehicle routing problem (DVRP) with single depot has received increasing interest from engineers and scientists. Dynamic multi-depot vehicle routing problem (DMDVRP), an extension of DVRP, however, has not received much attention. In our paper, a distance-based clustering approach is introduced to simplify the DMDVRP by allocating each customer to its nearest depot. Thus, DMDVRP is decomposed to a sequence of DVRPs. An improved ant colony optimisation (IACO) with ant-weight strategy and mutation operation is presented to optimise vehicle routing problem (VRP) in this paper. Moreover, to satisfy the real-time feature of DMDVRP, the nearest addition approach is used to handle the new orders occurring during a time slice on the basis of VRP solution. Finally, the computational results for 17 benchmark problems are reported to validate that IACO with the distance-based clustering approach is more suitable for solving DMDVRP.

The Vehicle Routing Problem (VRP) is a complex and high-level set of routing problems. Two of its important variants are the Dynamic Vehicle Routing Problem (DVRP) and the Green Vehicle Routing Problem (GVRP). The first one has become a challenging research topic in the last two decades, in which not all informations are known in advance, but are revealed as the system progresses. The second one is seen as a new application and solution in new logistics patterns, more specifically, for finding routes of vehicles to serve a set of customers while minimizing the total amount of CO 2 emissions, by increasing the loading rate and reducing the number of empty trips could reduce from 10% to 40% km traveled and therefore CO 2 emissions [1]. In this paper, we combine these two variants (DVRP and GVRP), where we try to minimize, in the dynamic environment, the greenhouse gas especially the carbon dioxide CO 2 , which is the immediate consequence of the depletion of the ozone layer and time duration. We will call this combination the Dynamic Green Vehicle Routing Problem (DGVRP). To study this new problem, we present the technique employed to estimate the amount of CO 2 emissions, the emission matrix and integrate them into the DGVRP model, then we propose the hybridization based on Ant Colony Optimization (ACO) algorithm with a Large Neighborhood Search (LNS) algorithm to solve our problem. The effectiveness of this approach is tested on a set of the dynamic green problems instances, which are adopted in this work from the static GVRP benchmark datasets.

A dynamic vehicle routing problem with time-dependent travel times

Research on dynamic and stochastic vehicle routing problems received increasing interest in the last decade. It considers a novel problem class, aiming at an appropriate handling of dynamic events combined with the incorporation of stochastic information about possible future events. This survey summarises the recent literature in this area. Besides, the classification according to the available stochastic information, a new classification based on the point in time where substantial computational effort for determining decisions or decision policies arises, is introduced. Furthermore, the difference in solution quality is analysed between approaches which consider either purely dynamic or stochastic problems compared to those which consider both, stochastic and dynamic aspects. A graphical representation demonstrates the strength of the reviewed approaches incorporating dynamic and stochastic information. The survey also gives an overview on the intensity of research for the different problem classes and its benefit in recent years. Finally, guidelines and promising directions for further research are presented.

: In this paper we consider the dynamic routing of unmanned aerial vehicles (UAVs) currently in operational use with the US Air Force. Dynamic vehicle routing problems (VRP) have always been challenging, and the airborne version of the VRP adds dimensions and difficulties not present in typical ground-based applications. Previous UAV routing work has focused on primarily on static, pre-planned situations; however, scheduling military operations, which are often ad-hoc, drives the need for a dynamic route solver that can respond to rapidly evolving problem constraints. With these considerations in mind, we examine the use of a Java-encoded metaheuristic to solve these dynamic routing problems, explore its operation with several general problem classes, and look at the advantages it provides in sample UAV routing problems. The end routine provides routing information for a UAV virtual battlespace simulation and allows dynamic routing of operational missions.

We propose and analyze a generic mathematical model for dynamic, stochastic vehicle routing problems, the dynamic traveling repairman problem (DTRP). The model is motivated by applications in which the objective is to minimize the wait for service in a stochastic and dynamically changing environment. This is a departure from classical vehicle routing problems where one seeks to minimize total travel time in a static, deterministic environment. Potential areas of application include repair, inventory, emergency service and scheduling problems. The DTRP is defined as follows: Demands for service arrive in time according to a Poisson process, are independent and uniformly distributed in a Euclidean service region, and require an independent and identically distributed amount of on-site service by a vehicle. The problem is to find a policy for routing the service vehicle that minimizes the average time demands spent in the system. We propose and analyze several policies for the DTRP. We find a provably optimal policy in light traffic and several policies with system times within a constant factor of the optimal policy in heavy traffic. We also show that the waiting time grows much faster than in traditional queues as the traffic intensity increases, yet the stability condition does not depend on the system geometry.

Dynamic rerouting of a fleet of vehicles in agricultural operations through a Dynamic Multiple Depot Vehicle Routing Problem representation

Routing delivery vehicles to serve customers in dynamic and uncertain environments like dense city centers is a challenging task that requires robustness and flexibility. Most existing approaches to routing problems produce solutions offline in the form of plans, which only apply to the situation they have been optimized for. Instead, we propose to learn a policy that provides decision rules to build the routes from online measurements of the environment state, including the customers configuration itself. Doing so, we can generalize from past experiences and quickly provide decision rules for new instances of the problem without re-optimizing any parameters of our policy. The difficulty with this approach comes from the complexity to represent this state. In this paper, we introduce a sequential multi-agent decision-making model to formalize the description and the temporal evolution of a Dynamic and Stochastic Vehicle Routing Problem. We propose a variation of Deep Neural Network using Attention Mechanisms to learn generalizable representation of the state and output online decision rules adapted to dynamic and stochastic information. Using artificially-generated data, we show promising results in these dynamic and stochastic environments, while staying competitive in deterministic ones compared to offline classical heuristics.

Demand coverage diversity based ant colony optimization for dynamic vehicle routing problems

A vehicle routing problem involves finding a set of optimal route for a fleet of capacitated vehicles which are available at a location to service the demands of a set of customers. In its simplest form, a customer is required to be visited once and the capacity of a vehicle must not be exceeded. In this paper, a review of four common and applicable variants of the vehicle routing problem, namely, capacitated vehicle routing problem, vehicle routing problem with time windows, periodic vehicle routing problem and the dynamic vehicle routing problem, are considered based on formulation techniques, methods of solution and areas of application. A summary table is presented for each variant to emphasis some key features that represent direction of current research.

A comparative study between dynamic adapted PSO and VNS for the vehicle routing problem with dynamic requests

Over the years, several variations of the dynamic vehicle routing problem (DVRP) have been considered due to its similarities with many real-world applications. Several methods have been applied to address DVRPs, in which ant colony optimization (ACO) has shown promising results due to its adaptation capabilities. In this chapter, we generate another variation of the DVRP with traffic factor and propose a memetic algorithm based on the ACO framework to address it. Multiple local search operators are used to improve the exploitation capacity and a diversity scheme based on random immigrants is used to improve the exploration capacity of the algorithm. The proposed memetic ACO algorithm is applied on different test cases of the DVRP with traffic factors and is compared with other peer ACO algorithms. The experimental results show that the proposed memetic ACO algorithm shows promising results.

The dynamic vehicle routing problem, DVRP, consists in optimally routing a fleet occur at random. The optimization consists in finding the solution that minimizes the total length of tours and satisfying the customer delivery time window. In this paper, we present a hybrid ant system to handle the dynamism by means of modifying the pheromone matrix and candidate sets strategy. In addition, we make further improvements on vehicle routes with the local search heuristics. The results show that the hybrid ant system works effectively to find competitive solutions.

In recent decades, research concern in vehicle routing has progressively more concentrated on dynamic and stochastic approaches in solving sophisticated dynamic vehicle routing problems (DVRP) due to its importance in helping potential customers to better manage their applications and to provide e-freight and e-commerce systems similarly. Many techniques were introduced in the DVRP field to solve part of its challenges since it’s hard to achieve equilibrium between finding feasible set of tours, minimum total travel time, shortest routing path and the capability of redirect a stirring vehicle to a new demand for additional savings; due to the fact that each one can be achieved at the expense of the other and combining them does not give an ideal result which requires a solution to track the optimum route during changes. In this paper, the game theory (GT) is integrated with Ant Colony Optimization algorithms (ACO) to adjust the attractiveness of arc and the pheromone level as it considers them competing players that prefer one according to the expected payoff. In addition, GT can be adapted inside the algorithm to facilitate the optimization, as it is considered a powerful technique in decision making and to find optimal solutions to conditions of conflict and cooperation. Experimental results show that the integration of GT with ACO algorithm improves the system performance in tackling DVRPs.

The last-mile delivery problem is one of the most complex and resource-intensive aspects of modern logistics, especially within the growing e-commerce sector. As online shopping continues to expand, companies are under immense pressure to deliver goods more quickly, efficiently, and at lower costs, all while meeting the demands of increasingly time-sensitive customers. This has created a need for innovative solutions that can tackle challenges related to dynamic traffic patterns, fluctuating customer preferences, and operational constraints such as vehicle capacities and delivery windows. In response to these challenges, this paper explores the application of predictive analytics as a tool for optimizing last-mile delivery routes in real-time.The study begins by identifying the core challenges inherent in last-mile logistics, particularly in the U.S. e-commerce landscape, where the cost of last-mile delivery can represent up to 53% of total shipping costs. With traffic congestion, unpredictable customer availability, and delivery time constraints posing significant hurdles, conventional static route planning models often fall short. In this paper, predictive analytics is proposed as a solution to these challenges, utilizing real-time data to inform more efficient routing decisions. By processing vast amounts of real-time traffic data, customer preferences, and delivery constraints, predictive models can offer a more flexible and responsive approach to last-mile delivery.The research then presents a comprehensive literature review of existing route optimization methods, such as the traditional Vehicle Routing Problem (VRP) and its extensions, including VRP with Time Windows (VRPTW), Dynamic VRP (DVRP), and Capacitated VRP (CVRP). While these models have proven useful, their limitations are exposed when faced with real-time operational complexities in the e-commerce sector. Therefore, this study introduces an advanced dynamic routing model that integrates machine learning algorithms—such as decision trees and neural networks—with traditional VRP frameworks. These machine learning models, trained on historical data, are capable of predicting future traffic patterns, customer behavior, and delivery time windows.A case study is conducted using data from U.S.-based e-commerce companies to demonstrate the practical application of predictive analytics in optimizing last-mile delivery. The case study outlines how predictive models are used to dynamically adjust delivery routes based on real-time conditions, leading to significant improvements in efficiency, cost savings, and customer satisfaction. Key performance indicators such as delivery times, fuel consumption, and vehicle utilization are examined before and after the implementation of the predictive models, with the results showing a reduction in delivery time by 20% and fuel costs by 15%, alongside improved on-time delivery rates.The paper concludes by presenting the proposed dynamic route optimization model as a solution that combines the flexibility and responsiveness of predictive analytics with the robust framework of traditional VRP models. Through the integration of machine learning, real-time data processing, and dynamic routing, the model is shown to significantly improve last-mile delivery efficiency. This study's findings highlight the potential for predictive analytics to revolutionize the logistics industry, particularly in the high-demand e-commerce sector, where quick and reliable delivery is paramount. The research suggests that as e-commerce continues to grow, predictive analytics will play an increasingly critical role in ensuring that last-mile delivery is both cost-effective and responsive to the evolving needs of consumers.