Modeling and Solution of Vehicle Routing Problem with Grey Time Windows and Multiobjective Constraints

Vehicle routing problem with fuzzy time windows

In this paper vehicle routing problem with heterogeneous vehicle regarding the delivery time windows is examined . In the present case , each customer has a hard time window and a soft time window . Delivery outside the hardware time window is not possible. Delivery outside the soft time window earliness or delay costs imposed on the model . The mathematical model of the problem , innovative genetic algorithm for a given problem is developed . The results obtained from the sample solution by genetic algorithms , the exact solution of the model in the software Lingo is obtained and s uggests that genetic provided acceptable performance and low error gives an answer in a reasonable time .

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.

In this study, Vehicle Routing Problem with Time Windows (VRPTW) with known customer demands, a single depot and identical vehicles, is considered. Minimizing the total distance and the total waiting time of the vehicles are determined as objective functions for VRPTW which is capable to serve the customers in a prespecified time interval. A hybridized version of genetic algorithm which is a metaheuristic solution technique with constructive heuristic methods is proposed to produce effective solutions for VRPTW. By using sweep algorithm in initial population generation phase of genetic algorithm, it is planned to begin the search with high quality solution sets and in this way, get more feasible solutions faster. A benchmark problem in the literature is solved and obtained results are compared with the results of genetic algorithm with the nearest neighbor algorithm based algorithm. It is observed that the proposed genetic algorithm beginning with sweep based initial population generation algorithm reaches more effective solutions.

The Vehicle Routing Problem (VRP) introduced by Dantzing and Ranser (1959) is a prominent combinatorial optimization problem. Over the last several decades, many variants of the multi-constrained vehicle routing problem have been studied and a class of problems known as rich vehicle routing problem (RVRPs), has been formed. This work is about solving a variant of RVRP with dynamically changing orders and time windows constraints. In the real world application, during the working day, new orders often occur dynamically and need to be integrated into the routes planing. A Genetic Algorithm (GA) with a simple heuristic is proposed to solve the dynamic vehicle routing problem with time windows. The performance is tested on Solomon's benchmark with different percentage of the orders revealed to the algorithm during operation time.

SYNOPTIC ABSTRACTBranch exchange techniques, such as the well-known 2-opt and 3-opt procedures, are among the most powerful heuristics available for the solution of the classic vehicle routing problem. The imposition of time window constraints on customer delivery time within the vehicle routing problem, however, introduces several complexities that can reduce the power of these techniques. In this paper, two test data sets for the vehicle routing and scheduling problem with time window constraints are studied. Initial solutions are obtained using a variety of heuristics. These solutions are then improved using branch exchange procedures modified to incorporate the time window constraints.

The ongoing rise in e-commerce comes along with an increasing number of first-time delivery failures due to the absence of the customer at the delivery location. Failed deliveries result in rework which in turn has a large impact on the carriers’ delivery cost. In the classical vehicle routing problem (VRP) with time windows, each customer request has only one location and one time window describing where and when shipments need to be delivered. In contrast, we introduce and analyze the vehicle routing problem with delivery options (VRPDO), in which some requests can be shipped to alternative locations with possibly different time windows. Furthermore, customers may prefer some delivery options. The carrier must then select, for each request, one delivery option such that the carriers’ overall cost is minimized and a given service level regarding customer preferences is achieved. Moreover, when delivery options share a common location, e.g., a locker, capacities must be respected when assigning shipments. To solve the VRPDO exactly, we present a new branch-price-and-cut algorithm. The associated pricing subproblem is a shortest-path problem with resource constraints that we solve with a bidirectional labeling algorithm on an auxiliary network. We focus on the comparison of two alternative modeling approaches for the auxiliary network and present optimal solutions for instances with up to 100 delivery options. Moreover, we provide 17 new optimal solutions for the benchmark set for the VRP with roaming delivery locations.

A Multi-Depot Home Care Routing Problem with Time Windows and Fuzzy Demands Solving by Particle Swarm Optimization and Genetic Algorithm

Routing of vehicles and scheduling of deliveries play a crucial role in logistics operations as they affect both the distribution cost and customer satisfaction. That is why researchers have intensively studied this problem in conjunction with the multiple variables and constraints involved in the logistics operations. In this paper, the cases of time windows and simultaneous pickups and deliveries, where goods are simultaneously delivered and collected from customers within a predetermined time slot, are studied. The objective of our research is to create efficient routes that minimize both the number of vehicles and the total distance travelled, as both of them affect the total distribution cost. Considering various plans of routes that are differentiated by the number of routes and the sequence of visitations, can be beneficial for decision-makers, since they have the opportunity to select the plan that better fits their needs. Therefore, in this paper we develop a multiobjective evolutionary algorithm (MOEA) that integrates an improved construction algorithm and a new crossover operator for efficient distribution services. Through the proposed MOEA a set of solutions (route plans), known as Pareto-optimal, is obtained, while single biased solutions are avoided. The proposed algorithm is tested in two well-known datasets in order to evaluate the algorithm’s efficiency. The results indicate that the algorithm’s solutions have small deviation from the best-published and some non-dominated solutions are also obtained.

This paper describes an exact solution approach for the Vehicle Routing and scheduling Problem with Soft Time Windows (VRPSTW), and presents its application on a realistic logistics instance based on the VICS (Vehicle Information and Communication System) data, an ITS application in Japan. Exact solutions of VRPSTW have been compared with those of the Vehicle Routing and scheduling with Hard Time Windows (VRPHTW). Detailed analysis of environmental issues and idling time along with the traditional comparison of cost and number of vehicles, shows that the exact VRPSTW solutions are not only cost efficient but helpful in reducing congestion, which implies these are more environmentally sustainable.

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.

The presence of multiple, often conflicting, objectives is a naturally occurring scenario in real-world decision making. Such problems are characterized by the existence of a set of efficient solutions instead of a single optimum. Evolutionary algorithms (EAs), which employ a population based search mechanism over a bounded decision/solution space, have emerged as popular tools for concurrently obtaining a good approximation to the entire efficient set, instead of finding a single solution at a time. While EAs hardly impose any restrictions on the form of the objective functions to be optimized, their design is generally based on the requirement that the feasible solution space of the problem be fixed. However, a situation contrary to the aforementioned is seen to occur during a bi-level formulation of the vehicle routing problem. Moreover, the problem is general enough to conceivably arise in many real-world situations. In light of this fact, the present paper alleviates the stated requirement by incorporating a bi-level perspective into a multi-objective EA. Thereafter, a preliminary study is carried out on the multi-objective variant of the NP-hard vehicle routing problem with time window constraints (VRPTW), in order to demonstrate the efficacy of the proposed approach.KeywordsBi-level ProgrammingMulti-Objective OptimizationEvolutionary AlgorithmVehicle Routing Problem with Time Windows

In this paper, we consider a variant of vehicle routing problem with multiple trip and time windows. In this alternative problem, we think about the scheduling of trucks to a number of customers in the presence of fixed fleet and time windows constraints. This type of problem can be described as determining a number of vehicle trips minimising total travelled distance complying with the time windows and the multiple use of vehicles. We call this problem a multiple trips fixed fleet vehicle routing problems with time windows (MTFFVRPTW). To solve this variant, a new hybrid evolutionary algorithm for transport optimisation problems, called estimation of distribution algorithm with local search is used. The proposed algorithm integrates a double structure of distribution technique, which is used to introduce the variables dependency. To evaluate our approach we provide a number of experimentation to a modified Solomon's instances for the case of multiple trips. The results show that the hybrid proposed algorithm offer a good quality solution in the term of objective functions, also in the running time.

The study aims to optimize the vehicle routing problem, considering infeasible routing, to minimize losses for the company. Firstly, a vehicle routing model with hard time windows and infeasible route constraints is established, considering both the minimization of total vehicle travel distance and the maximization of customer satisfaction. Subsequently, a Floyd-based improved genetic algorithm that incorporates local search is designed. Finally, the computational experiment demonstrates that compared with the classic genetic algorithm, the improved genetic algorithm reduced the average travel distance by 20.6% when focusing on travel distance and 18.4% when prioritizing customer satisfaction. In both scenarios, there was also a reduction of one in the average number of vehicles used. The proposed method effectively addresses the model introduced in this study, resulting in a reduction in total distance and an enhancement of customer satisfaction.

Vehicle routing problems with simultaneous pickup and delivery with time windows are studied in this paper. In a closed-loop logistics network, vehicles visiting customers for pickup and delivery may be only allowed for certain time intervals. A mixed integer programming model of the problem is presented. It has been known that solving vehicle routing problems with time windows is NP-hard. A heuristic solution procedure is developed to solve the problem. The proposed heuristic is tested on a number of numerical examples based on modified benchmark problems in the literature.