Dynamic Route Optimization in Last-Mile Delivery Using Predictive Analytics: A Case Study of E-commerce in the U.S.

‘Route balance’ is the difference between the longest and the shortest among all the route lengths. The route balance is frequently considered in a vehicle routing problem (VRP) for balancing the distance travelled among delivery vehicles. This is a common practice since in VRPs there are no time elements. However, in recent years, some research works have considered route balance in a vehicle routing problem with time windows (VRPTW). As there are more time elements in VRPTW, this paper refutes that route balance is sufficient for VRPTW by simultaneously optimising makespan and workload imbalance using ‘total time balance’ instead of route balance. On the other hand, ‘total time balance’ is the difference between the longest total time taken and the shortest total time taken among delivery vehicles. As such, makespan is the longest total time taken among vehicles. Total time taken for a vehicle is the sum of vehicle run time, waiting time and service time. In order to demonstrate the importance of using total time balance instead of route balance on VRPTW, three different multi-objective VRPTW models, namely, (1) only with general VRPTW objectives (i.e. ‘total distance travelled’ by all vehicles and ‘total number of vehicles’ used), (2) general VRPTW objectives with route balance and (3) general VRPTW objectives with total time balance are developed and solved by fitness aggregated genetic algorithm (FAGA) for 36 Solomon’s benchmark instances. By comparison of the makespan produced by the FAGA between the three cases, the importance of using total time balance instead of route balance on multi-objective VRPTW is demonstrated. Also, the makespan produced by the FAGA for the third case, i.e. general VRPTW objectives with total time balance is compared with the makespan produced by fitness aggregated differential evolution (FADE). By comparing makespan with statistical testing between FAGA and FADE, the outperformance of FAGA over FADE is verified. To check the practicality of the total time balance on multi-objective VRPTW, an instance with real time windows is also solved for the three cases by the FAGA and its makespan are compared and reported.

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.

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 an important problem occurring in many distribution systems, which is also defined as a family of different versions such as the Capacitated Vehicle Routing Problem (CVRP) and the Vehicle Routing Problem with Time Windows (VRPTW). The Ant Colony Optimization (ACO) is a metaheuristic for combinatorial optimization problems. Given the ACO inadequacy, the vehicle routing optimization model is improved and the transfer of the algorithm in corresponding rules and the trajectory updated regulations is reset in this paper, which is called the Improved Ant Colony Optimization (I-ACO). Compared to the calculated results with genetic algorithm (GA) and particle swarm optimization (PSO), the correctness of the model and algorithm is verified. Experimental results show that the I-ACO can quickly and effectively obtain the optimal solution of VRFTW.

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.

In the field of operations research, the vehicle routing problem with time windows (VRPTW) has been widely studied because it is extensively used in practical applications. Real-life situations discussed in the relevant research include time windows and vehicle capabilities. Among the constraints in a VRPTW, the practical consideration of the fairness of drivers’ performance bonuses has seldom been discussed in the literature. However, the shortest routes and balanced performance bonuses for all sales drivers are usually in conflict. To balance the bonuses awarded to all drivers, an auction bidding approach was developed to address this practical consideration. The fairness of performance bonuses was considered in the proposed mathematical model. The nearest urgent candidate heuristic used in the auction bidding approach determined the auction price of the sales drivers. The proposed algorithm both achieved a performance bonus balance and planned the shortest route for each driver. To evaluate the performance of the auction bidding approach, several test instances were generated based on VRPTW benchmark data instances. This study also involved sensitivity and scenario analyses to assess the effect of the algorithm’s parameters on the solutions. The results show that the proposed approach efficiently obtained the optimal routes and satisfied the practical concerns in the VRPTW.

Vehicle Routing Problem with Time Windows (VRPTW) is a constrained NP-hard problem that designs the least cost routes from one depot to a set of geographically scattered points. Most of traditional techniques are difficult to solve this kind of problem. In this paper, we explored the validity of another swarm-intelligence-based model-Bacterial Foraging Optimization (BFO) for VRPTW solving. Original BFO, BFO with linear decreasing chemotaxis step (BFO-LDC) and BFO with non-linear decreasing chemotaxis step (BFO-NDC) are used to obtain the best solutions of a given VRPTW problem, respectively. The experimental results demonstrated that the proposed BFO algorithms have the potential to solve Vehicle Routing Problem with Time Windows (VRPTW) with rapid convergence rate and the good result accuracy.

In this paper, the vehicle routing problem with time windows (VRPTW) was considered, and a mixed integer programming mathematic model of VRPTW was proposed in detail. Meantime, an improved ant colony algorithm (IACA) was proposed to overcome the shortcomings of premature convergence and slow convergence of conventional ant colony algorithm (ACA). The experiment results showed that the IACA can solve VRPTW effectively.

The Vehicle Routing Problem with Time Windows (VRPTW) consists of a homogenous set of vehicles and a set of customer located in a city. In VRPTW all the vehicles starts from the depot visit the customer and end at the depot. Each customer is visited exactly by one vehicle within the specified time window. The objective is to minimize the number of vehicles and total distance travelled simultaneously. This represents the multiobjective Vehicle Routing Problem with Time Windows. The proposed work consists of Hybrid Genetic Search with Diversity Control using the Genetic Algorithm for solving the VRPTW. The Pareto approach is used for finding the set of optimal solutions for achieving the multiobjective. The crossover operator is used for exchanging the best routes, which have shortest distance. Two mutation operators such as relocation mutation operator and split mutation operator were used in this application. In this, it accounts penalty for an infeasible solutions with respect to time-window and duration constrains. The computations are performed using the instances which are obtained from the VRPLIB.

In the dynamic business environment, leveraging predictive analytics for sales optimization and business development has become crucial for achieving sustained growth. As the e-commerce landscape continues to evolve, many e-businesses must harness the power of predictive analytics to anticipate sales trends and optimize business development strategies. This paper explores the application of sales predictive analytics, focusing on its role in forecasting sales, optimizing resource allocation, and enhancing customer relationship management. The application of predictive analytics in sales forecasting in online marketplace platforms is also explored, through the examination of various predictive models using real-world case studies. By exploring various methodologies and tools, the study illustrates how predictive analytics can be integrated into e-businesses' operations to drive growth, and enhance decision-making, highlighting the transformative potential of analytics in making data-driven decisions, ultimately fostering sustainable growth and competitive advantage. Through the analysis of historical sales data, consumer behaviour patterns, and market trends, predictive analytics provides actionable insights that are crucial for strategic planning and operational efficiency. The paper also addresses challenges and best practices for implementing predictive analytics into the business process of e-businesses. ‍

The Vehicle Routing Problem (VRP) is a well-known combinatorial optimization problem where a number of customers must be served with a fleet of vehicles. The classical variation of the VRP is the Capacicated Vehicle Routing Problem (CVRP) with the additional constraint that each vehicle must have uniform capacity. Many Decision Support Systems (DSS) have been implemented to solve real life problems of the VRP and its’ variants, but they do not allow multiple decision makers to explore several scenarios of a given problem simultaneously and collaborate with each other in order to find the best possible solution. In this paper, we extend our previous work [35] and incorporate in our spatial DSS four variants of the CVRP: (i) Distance Constrained Vehicle Routing Problem (DVRP), (ii) Vehicle Routing Problem with Time Windows (VRPTW), (iii) Vehicle Routing Problem with Backhauls (VRPB), and (iv) Vehicle Routing Problem With Pickup and Delivery (VRPPD). This extension allows decision makers to solve specific routing problems according to their needs. The proposed collaborative spatial DSS allows two decision makers to collaborate with each other in order to find the best possible solution through a tangible interface. The locations are added through interactive Google Maps and other parameters through user-friendly forms that can be manipulated via tangible interfaces. The proposed DSS has been implemented using Java, TUIO protocol, jsprit, and Google Maps.

Vehicle routing problem with time windows (VRPTW) is a practical and complex vehicle routing problem (VRP) which is faced by thousands of companies in logistics and transportation. Usually, VRP is solved by traditional heuristic algorithms. Recently, deep learning models under the reinforcement learning (RL) framework have been proposed to solve variants of VRP. In our study, we propose to use the hierarchical RL to find an optimal policy for generating optimal routes in VRPTW. The hierarchical RL structure includes a low level which generates feasible solutions and a high level which further searches for an optimal solution. Experimental results show that the proposed hierarchical RL model outperforms the non-hierarchical RL model and the heuristic algorithms Google OR-Tools. The proposed model also shows generalization capability in three different scenarios: varied time window constraints, from small-scale to large-scale problems, and generalization across different datasets. The flexible framework of hierarchical RL can also be applied to solve other complex VRPs with multiple objectives.

Combining genetic local search into a multi-population Imperialist Competitive Algorithm for the Capacitated Vehicle Routing Problem

This paper investigates a well-known complex combinatorial problem known as the vehicle routing problem with time windows (VRPTW). Unlike the standard vehicle routing problem, each customer in the VRPTW is served within a given time constraint. This paper solves the VRPTW using an improved artificial bee colony (IABC) algorithm. The performance of this algorithm is improved by a local optimization based on a crossover operation and a scanning strategy. Finally, the effectiveness of the IABC is evaluated on some well-known benchmarks. The results demonstrate the power of IABC algorithm in solving the VRPTW.

The Vehicle Routing Problem with Time Windows (VRPTW) is a critical combinatorial optimization problem in modern logistics, where finding optimal routes is essential for minimizing operational costs and enhancing service reliability. While Genetic Algorithms (GAs) are a powerful tool for solving VRPTW, their effectiveness is often undermined by premature convergence, a phenomenon in which the algorithm stagnates at suboptimal solutions, thus failing to achieve maximum efficiency. This study directly addresses this challenge by systematically evaluating how different reproduction schemes impact GA performance. The primary objective is to identify operator combinations that mitigate premature convergence to achieve superior solution quality, measured by total travel time, while also analyzing the trade-off with computational cost. We investigate combinations of conventional operators, such as Tournament Selection (TS) and Order Crossover (OX), against more advanced schemes, including Split Rank Selection (SRS) and Multi-Parent Order Crossover (MPOX), as well as different mutation methods, namely Scramble Mutation (SM) and Inversion Mutation (IM). Results demonstrate that advanced schemes, particularly the combination of SRS, MPOX, and IM, yield the most robust convergence and the lowest average total travel time of 48,422.8 minutes. However, this superior performance requires the longest computation time at 30.9 h. In contrast, conventional operator combinations are significantly faster, with execution times as low as 8.7 h, but they produce lower-quality solutions and exhibit unstable convergence. This study highlights the crucial role of the reproduction scheme in balancing the trade-off between solution quality and computational efficiency, confirming that a synergistic combination of advanced operators is essential for solving complex VRPTW instances effectively.