A Bibliometric Visualized Analysis and Classification of Vehicle Routing Problem Research

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.

With the current economic improvement, the logistics industries have been developed quickly. The logistics distribution of inter-city has been widely used in people's life. To shorten the delivery time and improve the economic benefits, how to choose the right path for the delivery personnel has become the most urgent problem. To solve this problem, the model of Vehicle Routing Problem (VRP) was proposed. Many researchers have applied various algorithms to solve VRP problems. However, because of the NP-hard characteristics of VRP problems, there is still have some room to improve the algorithms under the criteria of quality and time solutions. At the same time, there are many branches of VRP subproblems, among which the most common one is the VRP problem with capacity constraint (CVRP). As the CVRP problem belongs to the Combinatorial Optimization Problems (COPs), we select the ant colony algorithm to improve the CVRP. In this paper, based on the Max-Min Ant System (MMAS) algorithm, the utilization of mining information is strengthened by the elite ant path. The adaptive parameters are added to adjust the exploration and exploitation ability of the algorithm. Moreover, some appropriate constraints are added to the pheromone of the ant system to ensure the effectiveness of the algorithm. Based on the above strategy, the Adaptive Parameter for Max-Min Elite Ant System (APMMEAS) algorithm is proposed in this paper. The experimental results from the CVRP benchmark showed that the proposed APMMEAS algorithm is more competitive in quality and time solutions than in other ant colony series algorithms.

A new solution to vehicle routing problem (VRP) is proposed in order to overcome the disadvantages that the exact algorithms and heuristics algorithms are difficult to solve vehicle routing problem with multiple constraints. A simulation model of vehicle routing problem is built by combining the object-oriented technology and discrete event simulation technology. In this model, the events of distribution process and resources are described by the object-oriented approach. A variety of constraints which VRP problem involves can be processed in the simulation. As a result, the model has truly simulated complicated vehicle distribution process and simulation results can provide a basis for various optimization algorithms. The experimental results have validated the feasibility and effectiveness of this new method. As the simulation results can document the whole distribution process in detail, this method will have some significance to the practical application of vehicle routing problem.

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.

The field of grain logistics transport vehicle route has seen the development of a variety of mathematical techniques, and the practical application of these techniques has depended on the use of spatial information, such as regional allocation information of road network. Vehicle Routing Problem (VRP) is regarded as the key of grain logistics distribution. In this paper, firstly, focus on the grain logistics VRP with time windows, then VRP model is successful constructed. In order to reduce the cost of grain logistics distribution, to combine the VRP model to geographic information system (GIS) by analyzing the VRP model. GIS takes into account for grain logistics, and the Particle Swarm Optimization (PSO) is used for the identification of optimal routes. And the optimal route for grain distribution is urgent since it has been calculated that, of the total cost for transportation. It improves the efficiency of grain logistics distribution and gets a better effect.

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.

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.

The Vehicle Routing Problem (VRP) is a key to the efficient transportation management and supply-chain coordination. VRP research has often been too focused on idealized models with non-realistic assumptions for practical applications. Nowadays the evolution of methodologies allows that the classical problems could be used to solve VRP problems of real life. The evolution of methodologies allows the creation of variants of the VRP which were considered too difficult to handle by their variety of possible restrictions. A VRP problem that includes the addition of restrictions, which represent the variants in the problem, is called Rich VRP. This work presents an algorithm to optimize the transportation management. The authors are including a case of study which solves a real routing problem applied to the distribution of bottled products. The proposed algorithm shows a saving in quantity of vehicles and reduces the operation costs of the company.

The model and algorithm for Vehicle Routing and Scheduling Problem (VRSP) in picking up and delivering customers to airport service were presented in this paper. VRSP is an extension of the class Vehicle Routing Problem (VRP) with more resource constraints. Mathematical models are described for the VRSP with minimizing the cost based on low carbon emissions. The Bi-directional Optimization Heuristic Algorithm (BOHA) is developed for this model. The results verified the effectiveness of the model and Algorithm. The proposed model and algorithm can provide quantitative support and help the air ticket company decision-maker develop economical, punctual shuttle service with high satisfaction.

Over the past two decades, equity aspects have been considered in a growing number of models and methods for vehicle routing problems (VRPs). Equity concerns most often relate to fairly allocating workloads and to balancing the utilization of resources, and many practical applications have been reported in the literature. However, there has been only limited discussion about how workload equity should be modeled in the context of VRPs, and various measures for optimizing such objectives have been proposed and implemented without a critical evaluation of their respective merits and consequences. This article addresses this gap by providing an analysis of classical and alternative equity functions for biobjective VRP models. In our survey, we review and categorize the existing literature on equitable VRPs. In the analysis, we identify a set of axiomatic properties that an ideal equity measure should satisfy, collect six common measures of equity, and point out important connections between their properties and the properties of the resulting Pareto-optimal solutions. To gauge the extent of these implications, we also conduct a numerical study on small biobjective VRP instances solvable to optimality. Our study reveals two undesirable consequences when optimizing equity with nonmonotonic functions: Pareto-optimal solutions can consist of non-TSP-optimal tours, and even if all tours are TSP optimal, Pareto-optimal solutions can be workload inconsistent, i.e., composed of tours whose workloads are all equal to or longer than those of other Pareto-optimal solutions. We show that the extent of these phenomena should not be underestimated. The results of our biobjective analysis remain valid also for weighted sum, constraint-based, or single-objective models. Based on this analysis, we conclude that monotonic equity functions are more appropriate for certain types of VRP models, and suggest promising avenues for further research on equity in logistics. The data are available at https://doi.org/10.1287/trsc.2017.0744 .

Solving the vehicle routing problem (VRP) is one of the best-known optimization issues in the TLS (transport, logistic, spedition) branch market. Various variants of the VRP problem have been presented and discussed in the literature for many years. In most cases, batch versions of the problem are considered, wherein the complete data, including customers’ geographical distribution, is well known. In real-life situations, the data change dynamically, which influences the decisions made by optimization systems. The article focuses on the aspect of geopositioning updates and their impact on the effectiveness of optimization algorithms. Such updates affect the distance matrix, one of the critical datasets used to optimize the VRP problem. A demonstration version of the optimization system was developed, wherein updates are carried out in integration with both open source routing machine and GPS tracking services. In the case of a dynamically changing list of destinations, continuous and effective updates are required. Firstly, temporary values of the distance matrix based on the correction of the quasi-Euclidean distance were generated. Next, the impact of update progress on the proposed optimization algorithms was investigated. The simulation results were compared with the results obtained “manually” by experienced planners. It was found that the upload level of the distance matrix influences the optimization effectiveness in a non-deterministic way. It was concluded that updating data should start from the smallest values in the distance matrix.

In actual distribution process, the traffic flow varies with time, and each consumer has multiple fuzzy windows. To minimize the total distribution cost and mean consumer dissatisfaction, this paper sets up a vehicle routing problem (VRP) model with multiple fuzzy time windows, based on time-varying traffic flow. In addition, the Ito algorithm was improved based on time-varying traffic flow. The model and algorithm were verified through example simulation, in comparison with ant colony optimization (ACO). During the simulation, the improved Ito algorithm effectively reduced the distribution cost and consumer dissatisfaction, and outperformed the ACO in solving efficiency and solution quality. The results fully demonstrate the feasibility and effectiveness of the proposed algorithm. The research findings provide a desirable solution to VRPs with multiple fuzzy windows and time-varying traffic flow in the real world.

Automotive industry is very competitive and efficiency is needed in key processes such as logistics in all companies at the supply chain. Using optimization models to increment the efficiency of inbound logistics, such as the in-plant transportation systems, can bring competitive advantages to these companies. This work presents a Vehicle Routing Problem (VRP) model to support and optimize the in-plant transportation system routing, Milk-Run, at the worldwide manufacturing plant of manual assembly in an automotive company, where the routing was planed manually, and too much time and resources were used on this task. At the present, 4 or 5 routes were necessary to supply and collect both raw material and finished items in the plant with 21 workstations. A VRP model was developed into a decision support tool using Integer Programming. The IBM ILOG CPLEX 12.0.8 was used to run the developed model using the production plan of two months of 2018. The results point out an optimal number of 2 milk-runs, a reduction of circa 50%, allowing the freed resources to be used in other production areas of the plant.

Contributors

Transportation is part of the logistics activities that are very important and cost the most. The problem faced in relation to distribution is determining vehicle routing problems. Transportation contributes to the increase in pollution and greenhouse gas emissions that result in global warming. Therefore, a vehicle routing problem model is needed in the electric fleet. VRP plays an important role in goods distribution activities that aim to optimize distribution activities by minimizing costs and time. The vehicle routing problem in electric fleets also takes into account battery capacity, charging time and charging station location.