Vehicle Routing Problem With Time Windows Research Articles

Solving vehicle routing problem with time windows using metaheuristic approaches

PurposeDrugs are strategic products with essential functions in human health. An optimum design of the pharmaceutical supply chain is critical to avoid economic damage and adverse effects on human health. The vehicle-routing problem, focused on finding the lowest-cost routes with available vehicles and constraints, such as time constraints and road length, is an important aspect of this. In this paper, the vehicle routing problem (VRP) for a pharmaceutical company in Turkey is discussed.Design/methodology/approachA mixed-integer programming (MIP) model based on the vehicle routing problem with time windows (VRPTW) is presented, aiming to minimize the total route cost with certain constraints. As the model provides an optimum solution for small problem sizes with the GUROBI® solver, for large problem sizes, metaheuristic methods that simulate annealing and adaptive large neighborhood search algorithms are proposed. A real dataset was used to analyze the effectiveness of the metaheuristic algorithms. The proposed simulated annealing (SA) and adaptive large neighborhood search (ALNS) were evaluated and compared against GUROBI® and each other through a set of real problem instances.FindingsThe model is solved optimally for a small-sized dataset with exact algorithms; for solving a larger dataset, however, metaheuristic algorithms require significantly lesser time. For the problem addressed in this study, while the metaheuristic algorithms obtained the optimum solution in less than one minute, the solution in the GUROBI® solver was limited to one hour and three hours, and no solution could be obtained in this time interval.Originality/valueThe VRPTW problem presented in this paper is a real-life problem. The vehicle fleet owned by the factory cannot be transported between certain suppliers, which complicates the solution of the problem.

CLUSTERING ALGORITHM FOR A VEHICLE ROUTING PROBLEM WITH TIME WINDOWS

The demand for daily food purchases has increased dramatically, especially during the Covid-19 pandemic. This requires suppliers to face a huge and complex problem of delivering products that meet the needs of their customers on a daily basis. It also puts great pressure on managers on how to make day-to-day decisions quickly and efficiently to both satisfy customer requirements and satisfy capacity constraints. This study proposes a combination of the cluster-first –route-second method and k-means clustering algorithm to deal with a large Vehicle Routing Problem with Time Windows (VRPTW) in the logistics and transportation field. The purpose of this research is to assist decision-makers to make quick and efficient decisions, based on optimal costs, the number of vehicles, delivery time, and truck capacity efficiency. A distribution system of perishable goods in Vietnam is used as a case study to illustrate the effectiveness of our mathematical model. In particular, perishable goods include fresh products of fish, chicken, beef, and pork. These products are packed in different sizes and transferred by vehicles with 1000 kg capacity. Besides, they are delivered from a depot to the main 39 customers of the company with arrival times following customers’ time window. All of the data are collected from a logistics company in Ho Chi Minh city (Vietnam). The result shows that the application of the clustering algorithm reduces the time for finding the optimal solutions. Especially, it only takes an average of 0.36 s to provide an optimal solution to a large Vehicle Routing Problem (VRP) with 39 nodes. In addition, the number of trucks, their operating costs, and their utilization are also shown fully. The logistics company needs 11 trucks to deliver their products to 39 customers. The utilization of each truck is more than 70%. This operation takes the total costs of 6586215.32 VND (Vietnamese Dong), of which, the transportation cost is 1086215.32 VND. This research mainly contributes an effective method for enterprises to quickly find the optimal solution to the problem of product supply.

Multiple GEO satellites on-orbit repairing mission planning using large neighborhood search-adaptive genetic algorithm

This paper proposes a novel large neighborhood search-adaptive genetic algorithm (LNS-AGA) for many-to-many on-orbit repairing mission planning of geosynchronous orbit (GEO) satellites with mission deadline constraint. In the many-to-many on-orbit repairing scenario, several servicing spacecrafts and target satellites are located in GEO orbits which have different inclination, right ascension of ascending node (RAAN) and true anomaly. Each servicing spacecraft need to rendezvous with target satellites to perform repairing missions under limited fuel. The mission objective is to find the optimal servicing sequence and orbit rendezvous time of each servicing spacecraft to minimize total Δv cost of all servicing spacecrafts with all target satellites repaired. Firstly, a time-dependent orbital rendezvous strategy is proposed, which can handle the mission deadline constraint. Besides, it is also cost-effective compared with the existing strategy. Based on this strategy, the many-to-many on-orbit repairing mission planning model can be simplified to an integer programming problem, which is established based on the vehicle routing problem with time windows (VRPTW) model. In order to efficiently find a feasible optimal solution under complicated constraints, a hybrid adaptive genetic algorithm combining the large neighborhood search procedure is designed. The operations of “destroy” and “repair” are used on the elite individuals in each generation of the genetic algorithm to enhance local search capabilities. Finally, simulation results under several different scenarios show the effectiveness and superiority of the presented algorithm and orbital rendezvous strategy.

Machine learning algorithms for the problem of optimizing the distribution of parcels in time-dependent networks: the case study

In the paper we present machine learning algorithms for the problem of optimizing the distribution of parcels in sto-chastic time-dependent networks, which have been built as a part of some Distribution Optimization System. The prob-lem solved was a modified VRPTW (Vehicle Routing Problem with Time Windows) with many warehouses, a heteroge-neous fleet, travel times depending on the time of departure (stochastic time-dependent network) and an extensive cost function as an optimization criterion. To solve the problem a modified simulated annealing (SATM) algorithm has been proposed. The paper presents the results of the algorithm learning process: the calibration of input parameters and the study of the impact of parameters on the quality of the solution (calculation time, transport cost function value) de-pending on the type of input data. The idea is to divide the input data into classes according to a proposed classifica-tion rule and to propose several strategies for selecting the optimal set of calibration parameters. These strategies consist in solving some multi-criteria optimization tasks in which four criterion functions are used: the length of the designated routes, the computation time, the number of epochs used in the algorithm, the number of designated routes. The subproblem was building a network model of travel times that is used in constructed SATM algorithm to determine the travel time between recipients, depending on the time of departure from the start location. An attempt has been made to verify the research hypothesis that the time between two points can be estimated with sufficient accuracy depending on their geographical location and the time of departure (without reference to the micro-scale, i.e. the detailed structure of the road network). The research was conducted on two types of data for Warsaw: from transport companies and one of the Internet traffic data providers. Learning the network model of travel times has produced very promising results, which will be described in the paper.

Constraint-aware Policy Optimization to Solve the Vehicle Routing Problem with Time Windows

The vehicle routing problem with time windows (VRPTW) as one of the most known combinatorial operations (CO) problem is considered to be a tough issue in practice and the main challenge of that is to find the approximate solutions within a reasonable time. In recent years, reinforcement learning (RL) based methods have gained increasing attention in many CO problems, such as the vehicle routing problems (VRP), due to their enormous potential to efficiently generate high-quality solutions. However, neglecting the information between the constraints and the solutions makes previous approaches performance unideal in some strongly constrained problems, like VRPTW. We present the constraint-aware policy optimization (CPO) for VRPTWthat can let the agent learn the constraints as a representation of the whole environment to improve the generalization of RL methods. Extensive experiments on both the Solomon benchmark and the generated datasets demonstrate that our approach significantly outperforms other competition methods.

Robust Electric Vehicle Routing Problem with Time Windows under Demand Uncertainty and Weight-Related Energy Consumption

Vehicle routing problem with time windows (VRPTW) is a core combinatorial optimization problem in distribution tasks. The electric vehicle routing problem with time windows under demand uncertainty and weight-related energy consumption is an extension of the VRPTW. Although some researchers have studied either the electric VRPTW with nonlinear energy consumption model or the impact of the uncertain customer demand on the conventional vehicles, the literature on the integration of uncertain demand and energy consumption of electric vehicles is still scarce. However, practically, it is usually not feasible to ignore the uncertainty of customer demand and the weight-related energy consumption of electronic vehicles (EVs) in actual operation. Hence, we propose the robust optimization model based on a route-related uncertain set to tackle this problem. Moreover, adaptive large neighbourhood search heuristic has been developed to solve the problem due to the NP-hard nature of the problem. The effectiveness of the method is verified by experiments, and the influence of uncertain demand and uncertain parameters on the solution is further explored.

An estimation of distribution algorithm for combinatorial optimization problems

This paper considers solving more than one combinatorial problem considered some of the most difficult to solve in the combinatorial optimization field, such as the job shop scheduling problem (JSSP), the vehicle routing problem with time windows (VRPTW), and the quay crane scheduling problem (QCSP). A hybrid metaheuristic algorithm that integrates the Mallows model and the Moth-flame algorithm solves these problems. Through an exponential function, the Mallows model emulates the solution space distribution for the problems; meanwhile, the Moth-flame algorithm is in charge of determining how to produce the offspring by a geometric function that helps identify the new solutions. The proposed metaheuristic, called HEDAMMF (Hybrid Estimation of Distribution Algorithm with Mallows model and Moth-Flame algorithm), improves the performance of recent algorithms. Although knowing the algebra of permutations is required to understand the proposed metaheuristic, utilizing the HEDAMMF is justified because certain problems are fixed differently under different circumstances. These problems do not share the same objective function (fitness) and/or the same constraints. Therefore, it is not possible to use a single model problem. The aforementioned approach is able to outperform recent algorithms under different metrics for these three combinatorial problems. Finally, it is possible to conclude that the hybrid metaheuristics have a better performance, or equal in effectiveness than recent algorithms.

A Simulated Annealing Algorithm for the Vehicle Routing Problem With Parcel Lockers

Due to the growth in e-commerce, city logistics needs to cope with the rise of customers’ demand. Consequently, it adds to the complexity of the last-mile delivery process. Moreover, this process often contributes significantly to the distribution cost of companies. An alternative to alleviate the problem is the utilization of parcel lockers. It allows the delivery to be extended not only for home delivery but also for locker delivery, which brings several advantages in terms of cost-saving. However, considering multiple delivery options means adding new complexity to the delivery system. In the previous works, vehicle routing problem with time windows (VRPTW) has been widely dealt by only considering home delivery. This research proposes a new VRPTW variant by adding locker delivery as one of the delivery options. The developed problem is called the vehicle routing problem with parcel lockers (VRPPL). The goal of VRPPL is to minimize the total traveling cost. In this research, we formulate a new mathematical programming model and develop a simulated annealing (SA) algorithm to deal with VRPPL. A newly generated set of instances was developed from the well-known Solomon’s VRPTW instances. The performance of the proposed algorithm is also presented.

Decomposition of the vehicle routing problem with time windows on the time dimension

The Vehicle Routing Problem with Time Windows (VRPTW) asks for the optimal set of routes to be performed by a fleet of vehicles to serve a set of customers within their assigned time windows. In this work, we propose a matheuristic for the VRPTW which utilizes the sub-problem constituted by optimizing only a selected time window of the VRPTW whereas the tours outside of this time window are regarded as fixed. We call this problem the Single Time Window Vehicle Routing Problem (STWVRP). For applying the STWVRP, we must assume that several customers are assigned to the same time window, i.e., the number of time windows is much smaller than the number of customers. An exact problem description of the STWVRP is given in the form of a Mixed-Integer Linear Programming formulation. We apply this exact formulation within a matheuristic for the VRPTW. The paper concludes with extensive computational experiments.

Data-Driven Bus Route Optimization Algorithm Under Sudden Interruption of Public Transport

With the continuous expansion of urban traffic operation scale, public transport emergencies occur from time to time, causing serious traffic jams and potential safety hazards in a short time. In view of this, a new adaptive bus route optimization strategy based on the emergency demand responsive public transport is proposed. Firstly, in order to improve the fine-grained passenger carrying capacity of emergency demand responsive public transport and build a clustering model of passenger information, this paper proposes an adaptive clustering algorithm, which considers the main influencing factors such as vehicle capacity, passenger travel time window and the number of stations visited. Aiming at minimizing the cost of vehicle operation and passenger traffic, a multi-objective optimization model of emergency bus route is constructed based on Vehicle Routing Problems with Time Windows (VRPTW) to ensure the operation efficiency of emergency bus. Secondly, a Modified Adaptive Large Neighborhood Search with Nearest Vehicle Dispatch (NVD) algorithm (MALNSN) is proposed, which is an extension of the Adaptive Large Neighborhood Search algorithm (ALNS), by improving the generation rules of initial solutions with NVD and operator selection strategy with Modified Choice Function (MCF), and the effectiveness of algorithm is analyzed according to the Solomon benchmark. The average gain of the proposed MALNSN algorithm is 17.11% higher than that of the original algorithm. Finally, based on the actual road network, experiments are carried out to compare the proposed algorithm with the representative algorithms. The experimental results show that the MALNSN algorithm proposed in this paper can not only ensure the stability of the algorithm, but also formulate a reasonable route optimization strategy in a shorter time, effectively reducing the consumption of transport capacity resources, improving the operation efficiency of public transport and increasing the accessibility of public transport. The theoretical analysis was consistent with the experimental results.

A multi-center joint distribution optimization model considering carbon emissions and customer satisfaction.

Logistics enterprises are searching for a sustainable solution between the economy and the environment under the concept of green logistics development. Given that, this study integrates carbon emission as one of the costs into the vehicle routing problem with time window (VRPTW) and establishes a multi-center joint distribution optimization model taking into account distribution cost, carbon emission, and customer satisfaction. In the study of carbon emissions, this paper selected the vehicle load rate and vehicle distance as the main indicators. An improved ant colony algorithm is designed to solve the model by introducing the elite strategy, the saving strategy, vehicle service rules, and customer selection rules. Simulation results show that compared with the traditional ant colony optimization and genetic algorithm, the improved ant colony algorithm can effectively reduce the distribution cost and carbon emission and, improve customer satisfaction.

Clustering and heuristics algorithm for the vehicle routing problem with time windows

This article presents a novel algorithm based on the cluster first-route second method, which executes a solution through K-means and Optics clustering techniques and Nearest Neighbor and Local Search 2-opt heuristics, for the solution of a vehicle routing problem with time windows (VRPTW). The objective of the problem focuses on reducing distances, supported by the variables of demand, delivery points, capacities, time windows and type of fleet in synergy with the model's taxonomy, based on data referring to deliveries made by a logistics operator in Colombia. As a result, good solutions are generated in minimum time periods after fulfilling the agreed constraints, providing high performance in route generation and solutions for large customer instances. Similarly, the algorithm demonstrates efficiency and competitiveness compared to other methods detailed in the literature, after being benchmarked with the Solomon instance data set, exporting even better results.

VRP variants applicable to collecting donations and similar problems: A taxonomic review

This paper presents a taxonomic review of Vehicle Routing Problem (VRP) with Time Windows (VRPTW), Pick-up and Delivery Problem (PDP), and Periodic Vehicle Routing Problem (PVRP). We focus on the problems of collection goods and similar. The applications of these models are typical like found in the literature; however, not applications specifically about collecting donations were found. Because of concern for the environment, social equity, and business efficiency, specific research fields related to green and reverse logistics have arisen; thus, optimization of waste (second-hand goods, food, recyclable/no recyclable waste, etc.) collection routes gain interest. In the literature reviewed, we found several VRP models of goods collection applied to picks-up of returned items, End-of-Life (EOL) products, Municipal Solid Waste collection (MSW), and Waste Collection Problem (WCP). The primary purpose of this paper is to structure the taxonomy of VRPTW, PDP and PVRP problems applicable to collecting donations according to its features, solution methods, and mathematical formulation. Likewise, provide the reader with an outline orderly and differentiated from the VRP models associated with pick up items and delivery orders (VRPPD), backhauling customers (VRPB), collection waste, and similar problems to propose our problem. For clarity, Appendix A includes the acronym used in these types of problems. This paper is part of a larger research project called “CVRPTW model applied to collecting food donations,” intending to contribute to a new perspective on the routing problems little explored.

Flower Pollination Algorithm for Vehicle Routing Problem with Time Windows (VRPTW)

Vehicle Routing Problem with Time Windows (VRPTW) is a vehicle route deciding problem that is used in order to serve customer who involved more than one vehicle with a limited time, so as a minimum distance route is obtained without disobeying vehicle capacity cargo restriction and time range. Flower Pollination Algorithm (FPA) is an algorithm which inspires from nature and that is flower pollination process toward a plant. Within an FPA, there are two main steps to use, they are global flower pollination and local flower pollination. Those two steps are determined by using switch probability parameter. This program is made in Java language program to apply FPA in solving VRPTW which is implemented in three example cases, they are small-scale datum with 25 customers, medium-scale datum with 50 customers, and big-scale datum with 100 customers. According to the results, it can be concluded that the larger number of flowers and iterations can affect the number of total minimum travel distance become smaller. Furthermore, a better total minimum travel distances also will be obtained if the value of switch probability parameter is larger.

An Auction Bidding Approach to Balance Performance Bonuses in Vehicle Routing Problems with Time Windows

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.

Simplified Swarm Optimization for the Heterogeneous Fleet Vehicle Routing Problem with Time-Varying Continuous Speed Function

Transportation planning has been established as a key topic in the literature and practices of social production, especially in urban contexts. To consider traffic environment factors, more and more researchers are taking time-varying factors into account when scheduling their logistic activities. The time-dependent vehicle routing problem (TDVRP) is an extension of the classical Vehicle Routing Problem with Time Windows (VRPTW) by determining a set of optimal routes serving a set of customers within specific time windows. However, few of them use the continuous speed function to express the time-varying. In practice, many vehicle routing problems are addressed by a fleet of heterogeneous vehicles with different capacities and travel costs including fix costs and variable costs. In this study, a Heterogeneous Fleet Vehicle Routing Problem (HFPRP) Time-Varying Continuous Speed Function has been proposed. The objective is to minimize distribution costs, which contained fixed costs of acquiring and variable fuel costs. To address this problem, our research developed a mathematical model and proposed a Simplified Swarm Optimization (SSO) heuristic for HFVRP with Time-Varying Continuous Speed Function.

A MIXED INTEGER GOAL PROGRAMMING (MIGP) MODEL FOR DONATED BLOOD TRANSPORTATION PROBLEM – A PRELIMINARY STUDY

Blood Supply Chain (BSC) concerns with flow of blood products from blood collection by donors to transfusion of blood components to patients. BSC comprises of collection, testing, processing, storage, distribution and transfusion activities, which are normally responsibility of Blood Centre and hospitals. In Malaysia, National Blood Centre (PDN) is responsible to organize blood donation, collection and processing. Current procedure practised by PDN is to have vehicles sending staffs and equipment while one vehicle is assigned to collect donated blood from donation sites and transport the blood to PDN within six hours. As consequence, vehicles shortages are encountered and resources optimization unachieved especially when many blood donation sites involved per day. This paper presents the results of a preliminary study which aims at proposing blood collection optimal routes for blood collecting vehicles that adhere to all pre-determined time windows for blood collection at blood donation sites. A Mixed Integer Goal Programming (MIGP) model based on Vehicle Routing Problem with Time Windows (VRPTW) has been formulated. The MIGP model pursues four goals, namely, to minimize total distance travelled, to minimize total travel time, to minimize total waiting time of vehicles and to minimize number of vehicles (routes). The model was solved using preemptive goal programming approach and existing heuristics for the VRPTW. Based on the results, it can be concluded that the donated blood can be collected and transported using reduced number of vehicles as proposed by the MIGP model’s optimal compared to the total number of vehicles used by current practice, Thus, the proposed VRPTW based MIGP model has promising significant impact for donated blood transportation in terms of resources optimization and costs savings. The model and approach could be easily extended to solve larger problem involving large number of donation sites with variants of time windows for the sites.

Optimization of Conventional and Green Vehicles Composition under Carbon Emission Cap

The CO2 emission of transportation is significantly reduced by the employment of green vehicles to the existing vehicle fleet of the organizations. This paper intends to optimize the composition of conventional and green vehicles for a logistics distribution problem operating under a carbon emission cap imposed by the government. The underlying problem involves product delivery by the vehicles starting from a single depot to geographically distributed customers. The delivery occurs within specified time windows. To solve the proposed problem, we design a hybrid metaheuristic solution based on ant colony optimization (ACO) and variable neighborhood search (VNS) algorithms. Extensive computational experiments have been performed on newly generated problem instances and benchmark problem instances adopted from the literature. The proposed hybrid ACO is proven to be superior to the state-of-the-art algorithms available in the literature. We obtain 21 new best-known solutions out of 56 benchmark instances of vehicle routing problem with time windows (VRPTW). The proposed mixed fleet model obtains the best composition of conventional and green vehicles with a 6.90% reduced amount of CO2 emissions compared to the case when the fleet consists of conventional vehicles only.

Hierarchical Reinforcement Learning for Vehicle Routing Problems with Time Windows

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.

Solving Last-Mile Deliveries for Dairy Products Using a Biased Randomization-Based Spreadsheet. A Case Study

During recent years, Last-mile deliveries (LMD) have become relevant due to its application in e-commerce, urban logistics, and food delivery among others. This work addresses an LMD denoted as a Vehicle Routing Problem with time windows (VRPTW) and aims to minimize total time of the distribution process (i.e., makespan). The LMD is an NP-Hard problem that refers to the delivery of goods from a consolidation center to a destination. For solving the problem, a spreadsheet-based solution that employs a multi-start algorithm based on the biased-randomized version of the nearest neighbor heuristic is introduced. Real historical data of last-mile deliveries for dairy products in Bogotá (Colombia) was considered for evaluating our proposed method. Computational experiments are carried out to show the competitiveness of our method in terms of makespan, number of vehicles, average vehicle occupancy, average load and costs. Some insights for future works are also provided.