Time-dependent Vehicle Routing Problem Research Articles

Time-dependent vehicle routing problem with path flexibility

Conventionally, vehicle routing problems are defined on a network in which the customer locations and arcs are given. Typically, these arcs somehow represent the distances or expected travel time derived from the underlying road network. When executed, the quality of the solutions obtained from the vehicle routing problem depends largely on the quality of the road network representation. This paper explicitly considers path selection in the road network as an integrated decision in the time-dependent vehicle routing problem, denoted as path flexibility (PF). This means that any arc between two customer nodes has multiple corresponding paths in the road network (geographical graph). Hence, the decisions to make are involving not only the routing decision but also the path selection decision depending upon the departure time at the customers and the congestion levels in the relevant road network. The corresponding routing problem is a time-dependent vehicle routing problem with path flexibility (TDVRP–PF). We formulate the TDVRP–PF models under deterministic and stochastic traffic conditions. We derive important insights, relationships, and solution structures. Based on a representative testbed of instances (inspired on the road network of Beijing), significant savings are obtained in terms of cost and fuel consumption, by explicitly considering path flexibility. Having both path flexibility and time-dependent travel time seems to be a good representation of a wide range of stochasticity and dynamics in the travel time, and path flexibility serves as a natural recourse under stochastic conditions. Exploiting this observation, we employ a Route-Path approximation method generating near-optimal solutions for the TDVRP–PF under stochastic traffic conditions.

Probabilistic time-dependent vehicle routing problem

The probabilistic time-dependent vehicle routing problem is presented in this paper. It is a novel variant of the vehicle routing problem. The variant is a problem of finding optimal routes for a fleet of vehicles visiting customers in order to proceed delivery or pick-up. All customers must be visited in designated times with given probabilities and services must begin within the given time windows. Each vehicle has a given capacity, which must not be exceeded. The travel time between each two locations is dependent on a vehicle departure time. The paper also contains examples and solution results of testing data sets using the adaptive large neighbourhood search algorithm.

TDVRP and BIM Integrated Approach for In-Building Emergency Rescue Routing

AbstractRouting decisions for rescue and evacuation are critical for emergency-response missions. For infrastructures with large and complex geometric spaces, routing decisions could be facilitated with automated approaches for higher efficiency and accuracy. This research aims to respond to emergencies in buildings. In this work, network analysis is combined with building information modeling (BIM) models. Building geometry is retrieved from the BIM model for the construction of a graph, which is an essential element in network modeling. Rescue routes based on a graph can be determined depending on actual building layouts and conditions. In this paper, medial axis transform (MAT) is utilized for the graph construction from BIM models. A time-dependent vehicle routing problem (TDVRP) model is formed for the planning of rescue routes. Risk based on building materials and congestion based on pedestrian flow are to be adapted for network edge costs to enable a lowest utility route finding in the future, and ...

A novel comprehensive macroscopic model for time-dependent vehicle routing problem with multi-alternative graph to reduce fuel consumption: A case study

Vehicle routing problem (VRP) has attracted the attention of many researchers in recent years, but in spite of its application, researchers have shown little interest in the time-dependent vehicle routing problem. In recent years, much attention has been paid to the reduction of environmental emissions and reduction of fuel consumption. In this paper, the factors effective in the fuel consumption in time-dependent vehicle routing have been comprehensively studied and by considering factors such as load, vehicle speed, road gradient, and urban traffic, a novel comprehensive macroscopic model is presented to calculate fuel consumption in time-dependent vehicle routing problem. Additionally, the multi-alternative graph which enjoys great importance in time-dependent routing problem is also considered in the model presented. With regard to the issue that proposed problem belongs to the class of NP-hard problems, to find suitable routes with the least fuel consumption, an improved algorithm based on Gaussian Firefly algorithm is proposed. The results obtained from the proposed algorithm in comparison to Gaussian and basic Firefly algorithms show the appropriate performance of the suggested algorithm. Ultimately, one of the distribution companies in one of the cities of Iran (Esfahan) is studied as a case study.

Improvement Metaheuristic for the Time Dependent Vehicle Routing Problem Based on Simulated Annealing

The time dependent vehicle routing problem (TDVRP) is defined as a vehicle fleet of fixed capacities serves customers of fixed demands from a central depot with consideration of road networks conditions. The travel time between two customers or between customer and the depot depends on the distance of the two points and time of a day. A mathematical model is formulated for the TDVRP problem and a simulated annealing (SA) based improvement method is proposed for solving it. The main objective is to minimize the number of vehicles and the second objective is to minimize the total travel distance of the vehicles. The proposed approach was tested on the 56 test problems with 100 customers from Figliozzi’s benchmark, and results show that the improvement metaheuristic could get better solutions than Figliozzi’s algorithm in the different time dependent speeds function within an accepted computational time.

Measurement, evaluation and minimization of CO2, NOx, and CO emissions in the open time dependent vehicle routing problem

In this paper, a new comprehensive model has been presented for the measurement, evaluation and minimization of CO2, NOx and CO as three important emissions (emitted from vehicles) in the open time dependent vehicle routing problem (OTDVRP). In the OTDVRP, traffic properties of congested regions like city centers are considered. Travel time between two points depends on the time of departure, and the vehicles do not come back to the depot. In some distribution companies, vehicles are rental; therefore, they do not come back to the depot from the last customer. To solve the proposed problem, an improved Particle Swarm Optimization algorithm is developed. The results show good performance in computation experiments compared to original PSO algorithm. The results of the experiments show that considering minimization, the pollutants can reduce emissions by 16% on the average compared to the classical open TDVRP. Factors causing the variation in emissions are also identified and discussed in this study.

Modified particle swarm optimization in a time-dependent vehicle routing problem: minimizing fuel consumption

In this paper, a new mathematical model for a time-dependent vehicle routing problem (TDVRP) is introduced as one of the sub-problems in the green VRP field. The model results in reducing carbon emissions by minimizing travel times, while congested routes are avoided and customers are served at the time of the day with an optimized speed. Hence, this paper presents a new bi-objective mathematical model in such a way that the total travel times and total fuel consumption are minimized in a time-dependent situation by considering the air drag, roads’ physical condition, the physical features of each vehicle, and the weight and load of the vehicles. To solve such a hard problem, a new method based on the modified particle swarm optimization (PSO) algorithm is proposed and the results are compared with the standard PSO on well-known benchmark problems with constant travel speeds and time-dependent travel speeds. The results show the capability of the proposed optimization algorithm for handling this problem.

Multi-depot time dependent vehicle routing problem with heterogeneous fleet and time windows

Extensive research has been devoted to the vehicle routing problem (VRP). Most of these researches assume a homogenous fleet with constant travel times and single depot. In this paper, we consider the time dependent multi-depot vehicle routing problem. The objective is to minimise the total heterogeneous fleet cost assuming that the travel time between two locations depends on the departure time of vehicles. Also, hard time window constraints for the customers and transit restrictions should be satisfied. The problem is formulated as a mixed integer programming model. Due to NP-hardness of the problem a parameters-tuned simulated annealing (SA) is proposed to obtain a satisfying solution. The efficiency of the proposed SA is evaluated on 180 test problems. The obtained computational results indicate that the proposed procedure is efficient.

Stochastic time-dependent vehicle routing problem: Mathematical models and ant colony algorithm

This article addresses the stochastic time-dependent vehicle routing problem. Two mathematical models named robust optimal schedule time model and minimum expected schedule time model are proposed for stochastic time-dependent vehicle routing problem, which can guarantee delivery within the time windows of customers. The robust optimal schedule time model only requires the variation range of link travel time, which can be conveniently derived from historical traffic data. In addition, the robust optimal schedule time model based on robust optimization method can be converted into a time-dependent vehicle routing problem. Moreover, an ant colony optimization algorithm is designed to solve stochastic time-dependent vehicle routing problem. As the improvements in initial solution and transition probability, ant colony optimization algorithm has a good performance in convergence. Through computational instances and Monte Carlo simulation tests, robust optimal schedule time model is proved to be better than minimum expected schedule time model in computational efficiency and coping with the travel time fluctuations. Therefore, robust optimal schedule time model is applicable in real road network.

A green perspective on capacitated time-dependent vehicle routing problem with time windows

This study presents a novel approach to the vehicle routing problem by focusing on greenhouse gas emissions and fuel consumption aiming to mitigate adverse environmental effects of transportation. A time-dependent model with time windows is developed to incorporate speed and schedule in transportation. The model considers speed limits for different times of the day in a realistic delivery context. Due to the complexity of solving the model, a simulated annealing algorithm is proposed to find solutions with high quality in a timely manner. Our method can be used in practice to lower fuel consumption and greenhouse gas emissions while total route cost is also controlled to some extent. The capability of method is depicted by numerical examples productively solved within 3.5% to the exact optimal for small and mid-sized problems. Moreover, comparatively appropriate solutions are obtained for large problems in averagely one tenth of the exact method restricted computation time.

Vehicle routing problem solution considering minimising fuel consumption

Recently, logistics is not only playing more and more important role in social and economic development, but also caused serious energy consumption and environment pollution problems. Reasonable vehicle route planning is viewed as an important solution to reduce logistics enterprises’ operation costs as well as alleviate the energy and environmental problems. This study aims to propose a solution to time-dependent vehicle routing problem with time windows (TDVRPTW) considering minimising fuel consumption. First, a mathematical TDVRPTW model with the minimum fuel consumption as an objective function is established, in which the three-dimensional bin-packing problem is considered as a sub-problem and the alternative stop point concept is newly proposed to reduce the possible detouring distance and fuel consumption of logistic vehicle. Then, an ant colony algorithm is applied to solve the problem, and the departure time optimisation is introduced to further improve the obtained results. Finally, the proposed approach is evaluated with the real road network and traffic data of Beijing. The results show that the method introduced in this study outperforms the existing approaches in reducing fuel consumption as well as route length.

Urban Freight Management with Stochastic Time-Dependent Travel Times and Application to Large-Scale Transportation Networks

This paper addressed the vehicle routing problem (VRP) in large-scale urban transportation networks with stochastic time-dependent (STD) travel times. The subproblem which is how to find the optimal path connecting any pair of customer nodes in a STD network was solved through a robust approach without requiring the probability distributions of link travel times. Based on that, the proposed STD-VRP model can be converted into solving a normal time-dependent VRP (TD-VRP), and algorithms for such TD-VRPs can also be introduced to obtain the solution. Numerical experiments were conducted to address STD-VRPTW of practical sizes on a real world urban network, demonstrated here on the road network of Shenzhen, China. The stochastic time-dependent link travel times of the network were calibrated by historical floating car data. A route construction algorithm was applied to solve the STD problem in 4 delivery scenarios efficiently. The computational results showed that the proposed STD-VRPTW model can improve the level of customer service by satisfying the time-window constraint under any circumstances. The improvement can be very significant especially for large-scale network delivery tasks with no more increase in cost and environmental impacts.

A Time-Dependent Vehicle Routing Problem with Time Windows for E-Commerce Supplier Site Pickups Using Genetic Algorithm

The VRP is classified as an NP-hard problem. Hence exact optimization methods may be difficult to solve these problems in acceptable CPU times, when the problem involves real-world data sets that are very large. To get solutions in determining routes which are realistic and very close to the actual solution, we use heuristics and metaheuristics which are of the combinatorial optimization type. A literature review of VRPTW, TDVRP, and a metaheuristic such as the genetic algorithm was conducted. In this paper, the implementation of the VRPTW and its extension, the time-dependent VRPTW (TDVRPTW) has been carried out using the model as well as metaheuristics such as the genetic algorithm (GA). The algorithms were implemented, using Matlab and HeuristicLab optimization software. A plugin was developed using Visual C# and DOT NET framework 4.5. Results were tested using Solomon’s 56 benchmark instances classified into groups such as C1, C2, R1, R2, RC1, RC2, with 100 customer nodes, 25 vehicles and each vehicle capacity of 200. The results were comparable to the earlier algorithms developed and in some cases the current algorithm yielded better results in terms of total distance travelled and the average number of vehicles used.

A Time-Dependent Vehicle Routing Problem with Time Windows for E-Commerce Supplier Site Pickups Using Genetic Algorithm

A Time-Dependent Vehicle Routing Problem with Time Windows for E-Commerce Supplier Site Pickups Using Genetic Algorithm

A Comparative Study of Proposed Genetic Algorithm-Based Solution with Other Algorithms for Time-Dependent Vehicle Routing Problem with Time Windows for E-Commerce Supply Chain

The vehicle routing problem (VRP) is classified as an NP-hard problem. Hence exact optimization methods may be difficult to solve these problems in acceptable CPU times, when the problem involves real-world data sets that are very large. To get solutions in determining routes which are realistic and very close to the optimal solution, one has to use heuristics and meta-heuristics. In this paper, an attempt has been made to develop a GA based meta-heuristic to solve the time dependent vehicle route problem with time windows (TDVRPTW). This algorithm is compared with five other existing algorithms in terms of minimizing the number of vehicles used as well as the total distance travelled. The algorithms are implemented using Matlab and HeuristicLab optimization software. A plugin was developed using Visual C# and NET Framework 4.5. Results were tested using Solomon’s 56 benchmark instances (of which 24 instances are used with 4 in each of the 6 problem classes) classified into groups such as C1, C2, R1, R2, RC1, and RC2. For each of the performance measures, through a complete factorial experiment with two factors, it is proved that the proposed algorithm is the best among all the six algorithms compared in this paper.

A time-dependent vehicle routing problem in multigraph with FIFO property

The classic vehicle routing problems are usually designed with one edge (or arc) between two nodes. However, sometimes, there are situations in which one node can be accessible from another with more than one edge. In this paper, a new extension of the time-dependent vehicle routing problem was studied. In this problem, the existence of more than one edge between the nodes was allowed. This property can be important in competitive markets in order to achieve better and faster product deliveries/services. So, the problem was modeled as the time-dependent vehicle routing problem in multigraph which provided the FIFO property. In addition, a heuristic tabu search (TS) algorithm was proposed to solve the problem, in which neighborhood search was randomly selected among swap or reverse exchanges. Finally, computational results of TS algorithm and exact solution method were represented over forty instances. It was shown that TS was more effective than exact solution method in terms of the quality of results and computational time.

The time-dependent vehicle routing problem with soft time windows and stochastic travel times

This paper studies a vehicle routing problem with time-dependent and stochastic travel times. In our problem setting, customers have soft time windows. A mathematical model is used in which both efficiency for service as well as reliability for customers are taken into account. Depending on whether service times are included or not, we consider two versions of this problem. Two metaheuristics are built: a Tabu Search and an Adaptive Large Neighborhood Search. We carry out our experiments for well-known problem instances and perform comprehensive analyses on the numerical results in terms of the computational time and the solution quality. Experiments confirm that the proposed procedure is effective to obtain very good solutions to be performed in real-life environment.

A Method of Energy-Saving Optimization of Logistics Distribution Plan

Reasonable logistics distribution plan can not only reduce distribution costs, but also be conducive to energy saving and emissions reduction. This study aims to optimize logistics distribution plan with the minimum energy consumption as objective. Firstly, as for the time-dependent vehicle routing problem with time windows (TDVRPTW), considering the effect of total vehicle weight and travel speed on energy consumption factor, an optimization function is proposed to minimize the fuel consumption during delivery; secondly, based on the road network and traffic information, the ant colony algorithm is used to solve the TDVRPTW to optimize the distribution plan; finally, experiments are designed to evaluate the effectiveness of the proposed optimization method, and the results show that, compared to the existing optimization approach, the proposed method can effectively reduce the energy consumption of delivery vehicles by about 12.76%.

Integrated Ant Colony and Tabu Search approach for time dependent vehicle routing problems with simultaneous pickup and delivery

Today manufacturers have become much more concerned with the coordination of both manufacturing (of new products) and recycling (of reusable resources) operations. This requires simultaneous scheduling of both forward and reverse flows of goods over a supply chain network. This paper studies time dependent vehicle routing problems with simultaneous pickup and delivery (TD-VRPSPD). We formulate this problem as a mixed integer programming model, where the time step function is used to calculate the travel time. To efficiently solve this complex problem, we develop a hybrid algorithm that integrates both Ant Colony System (ACS) and Tabu Search (TS) algorithms. Our algorithm uses the pheromones, travel time and vehicle residual loading capacity as a factor structure according to the characteristics of TD-VRPSPD. In our computational experiments, 56 groups of benchmark instances are used to evaluate the performance of our hybrid algorithm. In addition, we compare the performance of our hybrid algorithm with those of individual ACS and TS algorithms. The computational results suggest that our hybrid algorithm outperform stand-alone ACS and the TS algorithms.

Two-stage Particle Swarm Optimization Algorithm for the Time Dependent Alternative Vehicle Routing Problem

This study considered a Time Dependent Alternative Vehicle Routing Problem (TDAVRP) in a multi-graph network (TDAVRP) and was formulated into a Mixed Integer Programming model. Due to its NP nature, an algorithm based on Particle Swarm Optimization (PSO) with local improvement was developed to speed up the solution procedure. By using different sets of Solomon’s benchmark problems and continuous travel time functions, the accuracy and efficiency of the two-stage PSO were evaluated. The computational results showed that the proposed algorithm is capable of deriving optimal or near optimal solutions in a short period of time when the size of the problems are small and is able to obtain feasible solutions within a reasonable time when solving the large problems which cannot be solved by ILOG CPLEX. In addition, Sensitivity Analysis was conducted to evaluate the performances of the parameters. The results indicated that the number of customers is a sensitive parameter and will influence the required number of vehicles, value of violations and percentage of alternative edges in the solution sets.