Time-dependent Vehicle Routing Problem Research Articles

Integer programming formulations for the time-dependent elementary shortest path problem with resource constraints

The impact of congestion in transportation has become one of the main concerns regarding urban planing in large cities. Time-Dependent Vehicle Routing Problems (TDVRPs) is the name given to a broad family of VRPs that explicitly incorporate the congestion by considering variable travel times. In this paper we study the Time-Dependent Elementary Shortest Path Problem with Resource Constraints (TDESPPRC), that appears as the pricing sub-problem in column generation-based approaches for TDVRPs. We consider two integer programming formulations which exploit the characteristics of the time-dependent travel time function and are evaluated on benchmark instances. On preliminary computational experiments, the approach is able to effectively solve instances with up to 25 vertices in reasonable times, showing its potential to be used within a Branch and Price algorithm.

Multi-type ant system algorithm for the time dependent vehicle routing problem with time windows

The time dependent vehicle routing problem with time windows (TDVRPTW) is considered. A multi-type ant system (MTAS) algorithm hybridized with the ant colony system (ACS) and the max-min ant system (MMAS) algorithms is proposed. This combination absorbs the merits of the two algorithms in solutions construction and optimization separately. In order to improve the efficiency of the insertion procedure, a nearest neighbor selection (NNS) mechanism, an insertion local search procedure and a local optimization procedure are specified in detail. And in order to find a balance between good scouting performance and fast convergence rate, an adaptive pheromone updating strategy is proposed in the MTAS. Computational results confirm the MTAS algorithm's good performance with all these strategies on classic vehicle routing problem with time windows (VRPTW) benchmark instances and the TDVRPTW instances, and some better results especially for the number of vehicles and travel times of the best solutions are obtained in comparison with the previous research.

ABM-GIS simulation for urban freight distribution of perishable food

Freight transport is essential to modern urban civilization. No urban area could exist without a powerful freight transport system. However, the distribution of perishable foods in urban areas is seen as a source of problems, due to traffic congestion, time pressures, and environmental impact. In this paper, an Agent-Based Model integrated with Geographic Information Systems (ABM-GIS) is designed for a time-dependent vehicle routing problem with time windows. This simulation model consists of determining the quickest routes to transport fresh products, estimating Vehicle kilometer traveled VKT and vehicle hour traveled VHT where speeds and travel times depend on the time of the day. Based on a case study, analyses of changes on traffic condition were conducted to get an insight into the impact of these changes on cost, service quality represented by the respect of time windows, and carbon emissions. The results reveal that traffic jams and restrictive time windows lead to additional cost, cause delays, and increase co2 emission. As for a short-term planning, time-dependent scheduling algorithm was proposed and assessed while extending time windows. Results have proved the potential saving in cost, travel time, and carbon emission.

A time-dependent vehicle routing problem for disaster response phase in multi-graph-based network

A time-dependent vehicle routing problem for disaster response phase in multi-graph-based network

A bi-objective mathematical model for two-dimensional loading time-dependent vehicle routing problem

This paper introduces two-dimensional loading time-dependent vehicle routing problem and proposes a bi-objective mathematical model. This problem assesses the process of distributing the rectangular-shaped demanded items over an urban environment; it does not, however, allow items to be loaded on top of each other. In addition to the above assumptions, the presented model also satisfies the first-in-first-out property in the time-dependent vehicle routing problem. Given the NP-hard nature of the problem, a method called elitist non-dominated sorting local search is developed to obtain its solutions. To evaluate the performance of the proposed algorithm, the solutions of this algorithm for small-scale problem instances are compared with the results of an exact method. For the medium-scale problem instances, results of NSGA-II and SPEA2 are used as the basis of comparison. The computational results demonstrate the good performance of the proposed method.

A combined order selection and time-dependent vehicle routing problem with time widows for perishable product delivery

Abstract This paper addresses a real-life delivery problem often encountered by urban perishable product deliverers, in which the providers suffer losses from failed delivery, such as product deterioration or violating customers’ time windows, especially when delivery orders accepted are beyond the providers’ delivery capacity. To the best of our knowledge, traditional delivery models are not applicable in such cases and few papers are related. Hence, we develop a new model that combines order selection and time-dependent vehicle routing problem with time windows in the same framework of perishable product delivery, to decide the delivery order, the service sequence and the timing to start a delivery task with the objective of profit maximization. Furthermore, a hybrid ant colony algorithm comprising local search operators is proposed. The effectiveness of our model and algorithm is demonstrated with several computational experiments, and some management insights are provided to guild practical operations.

A Novel Model for the Time Dependent Competitive Vehicle Routing Problem: Modified Random Topology Particle Swarm Optimization

This paper presents a novel model for a time dependent vehicle routing problem when there is a competition between distribution companies for obtaining more sales. In a real-world situation many factors cause the time dependency of travel times, for example traffic condition on peak hours plays an essential role in outcomes of the planned schedule in urban areas. This problem is named as “Time dependent competitive vehicle routing problem” (TDVRPC) which a model is presented to satisfy the “non-passing” property. The main objectives are to minimize the travel cost and maximize the sale in order to serve customers before other rival distributors. To solve the problem, a Modified Random Topology Particle Swarm Optimization algorithm (RT-PSO) is proposed and the results are compared with branch and bound algorithm in small size problems. In large scales, comparison is done with original PSO. The results show the capability of the proposed RT-PSO method for handling this problem.

A Simulation Based Restricted Dynamic Programming approach for the Green Time Dependent Vehicle Routing Problem

This paper addresses a Green Time Dependent Capacitated Vehicle Routing Problem that accounts for transportation emissions. The problem has been formulated and solved using Dynamic Programming approach. The applicability of Dynamic Programming in large sized problems is, however, limited due to exponential memory and computation time requirements. Therefore, we propose a generic heuristic approach, Simulation Based Restricted Dynamic Programming, based on weighted random sampling, the classical Restricted Dynamic Programming heuristic and simulation for the model to solve large sized instances. These decision support tools can be used to aid logistics decision-making processes in urban distribution planning. The added values of the proposed model and the heuristic have been shown based on a real life urban distribution planning problem between a pharmaceutical warehouse and a set of pharmacies, and ten relatively larger instances. The results of the numerical experiments show that the Simulation Based Restricted Dynamic Programming heuristic can provide promising results within relatively short computation times compared to the classical Restricted Dynamic Programming for the Green Time Dependent Capacitated Vehicle Routing Problem. The Simulation Based Restricted Dynamic Programming algorithm yields 2.3% lower costs within 93.1% shorter computation times on average, compared to the classical Restricted Dynamic Programming. Moreover, the analyses on the effect of traffic congestion in our base case reveal that 2.3% benefit on total emissions and 0.9% benefit on total routing cost could be obtained if vehicles start delivery after heavy congested period is passed.

A way to optimally solve a green time-dependent vehicle routing problem with time windows

This study presents a novel approach to solve 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 planning. 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 graph transformation approach is proposed to reduce the complexity of the problem. By means of several steps, the problem is transformed into a vehicle routing problem without time windows. In this way, we can reduce the complexity of the problem. Our method can be used in practice to decrease fuel consumption and greenhouse gas emissions, while total cost is also controlled to some extent. Finally, future research directions and conclusion remarks are provided.

Multi-objective cooperative QEA for low-carbon time dependent vehicle routing problem with simultaneous delivery and pickup

Emissions reduction has been a hot issue. This paper concerns a Low-Carbon Time Dependent Vehicle Routing Problem with Simultaneous Delivery and Pickup (LTDVRPSDP) in which the time dependent travel speed is variable depending on the time of travel. And a mixed integer linear program model is developed for this optimisation problem which aims at two objectives of minimising travel times and carbon emissions at the same time. To calculate the carbon emissions the relation of carbon emissions and travel speeds is found. A Multi-objective Cooperative Quantum Evolutionary Algorithm (MCQEA) is proposed for this NP-hard problem. In the MCQEA, co-evolutionary strategy of optimal solution preservation and two subpopulation cooperation co-evolution is adopted. Results of simulation and comparison show that the established model is valid and the MCQEA is effective for this problem.

Multi-objective cooperative QEA for low-carbon time dependent vehicle routing problem with simultaneous delivery and pickup

Emissions reduction has been a hot issue. This paper concerns a Low-Carbon Time Dependent Vehicle Routing Problem with Simultaneous Delivery and Pickup (LTDVRPSDP) in which the time dependent travel speed is variable depending on the time of travel. And a mixed integer linear program model is developed for this optimisation problem which aims at two objectives of minimising travel times and carbon emissions at the same time. To calculate the carbon emissions the relation of carbon emissions and travel speeds is found. A Multi-objective Cooperative Quantum Evolutionary Algorithm (MCQEA) is proposed for this NP-hard problem. In the MCQEA, co-evolutionary strategy of optimal solution preservation and two subpopulation cooperation co-evolution is adopted. Results of simulation and comparison show that the established model is valid and the MCQEA is effective for this problem.

A unified framework for routing problems with a fixed fleet size

Vehicle routing problems constitute the core of many operations research efforts. Early studies introduced tailor-made solutions for each variant of a vehicle routing problem, but unified frameworks have emerged more recently. These approaches typically generalise across many vehicle routing problems and implement a method for tackling the generalised problem. In line with this, this research proposes a generic method for solving several fixed fleet vehicle routing problems - capacitated vehicle routing, open vehicle routing, vehicle routing with soft and hard time windows, open vehicle routing with soft and hard time windows, and time-dependent vehicle routing with soft and hard time windows - by transforming them into a time-dependent vehicle routing problem with soft time windows, solved by a variable neighbourhood search using a unique parameter setting, regardless of the original problem. Computational tests using standard benchmark instances from prior literature show that genericity does not come at the expense of solution quality. Moreover, the algorithm yields competitive results and some new best known solutions are obtained for the vehicle routing problem with soft time windows, the open vehicle routing problem with hard time windows, and time-dependent vehicle routing problem with hard time windows.

A unified framework for routing problems with a fixed fleet size

Vehicle routing problems constitute the core of many operations research efforts. Early studies introduced tailor-made solutions for each variant of a vehicle routing problem, but unified frameworks have emerged more recently. These approaches typically generalise across many vehicle routing problems and implement a method for tackling the generalised problem. In line with this, this research proposes a generic method for solving several fixed fleet vehicle routing problems - capacitated vehicle routing, open vehicle routing, vehicle routing with soft and hard time windows, open vehicle routing with soft and hard time windows, and time-dependent vehicle routing with soft and hard time windows - by transforming them into a time-dependent vehicle routing problem with soft time windows, solved by a variable neighbourhood search using a unique parameter setting, regardless of the original problem. Computational tests using standard benchmark instances from prior literature show that genericity does not come at the expense of solution quality. Moreover, the algorithm yields competitive results and some new best known solutions are obtained for the vehicle routing problem with soft time windows, the open vehicle routing problem with hard time windows, and time-dependent vehicle routing problem with hard time windows.

A hybrid metaheuristic for the time-dependent vehicle routing problem with hard time windows

This article paper presents a hybrid metaheuristic algorithm to solve the time-dependent vehicle routing problem with hard time windows. Time-dependent travel times are influenced by different congestion levels experienced throughout the day. Vehicle scheduling without consideration of congestion might lead to underestimation of travel times and consequently missed deliveries. The algorithm presented in this paper makes use of Large Neighbourhood Search approaches and Variable Neighbourhood Search techniques to guide the search. A first stage is specifically designed to reduce the number of vehicles required in a search space by the reduction of penalties generated by time-window violations with Large Neighbourhood Search procedures. A second stage minimises the travel distance and travel time in an ‘always feasible’ search space. Comparison of results with available test instances shows that the proposed algorithm is capable of obtaining a reduction in the number of vehicles (4.15%), travel distance (10.88%) and travel time (12.00%) compared to previous implementations in reasonable time

ENHANCED HEURISTIC ALGORITHMS WITH A VEHICLE TRAVEL SPEED MODEL FOR TIME-DEPENDENT VEHICLE ROUTING: A WASTE COLLECTION PROBLEM

This paper proposes a vehicle travel speed model to enhance two heuristic algoritihms from previous studies, namely current initial solution (CIS) and different initial customer (DIC). Both algorithms are used to solve a real-life waste collection vehicle routing benchmark problem with dynamic travel speeds. This problem is referred to as Time-Dependent Vehicle Routing Problem (TD-VRP) in previous literature. The benchmark problem consisted of ten sub problems, involving up to 2092 customers. Previous studies solved the benchmark problem using DIC and CIS algorithms with the assumption that the vehicles are travelling with a static speed when collecting the waste. However, in this paper the static speed that was considered in both algorithms were improved by introducing dynamic travel speeds to construct vehicle routes for the waste collection drivers. Compared to previous studies the enhanced CIS and DIC with dynamic travel speeds affected the waste collection problem in terms of the number of vehicles used, the total distance travelled and the total travel time. However, different settings of speed may give different impacts to the solution. The study reveals that with a setting of dynamic speed between 40 mph and 55 mph, DIC is able to reduce two vehicles (from 98 to 96 number of vehicles used), 7.85% of total distance travelled, and 19.10% of total travel time.

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.

Development of an Efficient Genetic Algorithm for the Time Dependent Vehicle Routing Problem with Time Windows

This research considers the time-dependent vehicle routing problem (TDVRP). The time-dependent VRP does not assume constant speeds of the vehicles. The speeds of the vehicles vary during the various times of the day, based on the traffic conditions. During the periods of peak traffic hours, the vehicles travel at low speeds and during non-peak hours, the vehicles travel at higher speeds. A survey by TCI and IIM-C (2014) found that stoppage delay as percentage of journey time varied between five percent and 25 percent, and was very much dependent on the characteristics of routes. Costs of delay were also estimated and found not to affect margins by significant amounts. This study aims to overcome such problems arising out of traffic congestions that lead to unnecessary delays and hence, loss in customers and thereby valuable revenues to a company. This study suggests alternative routes to minimize travel times and travel distance, assuming a congestion in traffic situation. In this study, an efficient GA-based algorithm has been developed for the TDVRP, to minimize the total distance travelled, minimize the total number of vehicles utilized and also suggest alternative routes for congestion avoidance. This study will help to overcome and minimize the negative effects due to heavy traffic congestions and delays in customer service. The proposed algorithm has been shown to be superior to another existing algorithm in terms of the total distance travelled and also the number of vehicles utilized. Also the performance of the proposed algorithm is as good as the mathematical model for small size problems.

Modelos matemáticos baseados no Time Dependent Vehicle Routing Problem para planejamento da logística urbana sob a ótica ambiental

Empresas que operam com logística urbana direcionam seus esforços para soluções que buscam reduções de custo, desconsiderando questões ambientais. Isso ocorre em função da crença que soluções ambientalmente corretas são mais caras. No entanto, com as crescentes preocupações ambientais, as empresas têm levado em conta os fatores ambientais buscando a responsabilidade social. Assim, este artigo apresenta dois modelos matemáticos, ambos baseados no Time Dependent Vehicle Routing Problem (TDVRP), sendo um com objetivo de avaliar a redução do tempo das rotas e o outro com objetivo avaliar a redução da emissão de poluentes. Para testar o modelo, foi realizada uma aplicação real de uma empresa de distribuição de alimentos na região metropolitana de Vitória, ES. Usou-se o CPLEX 12.6 para rodar os modelos propostos com cenários baseados em dados reais da empresa. Os resultados mostraram que a solução com viés ambiental pode ser financeiramente vantajosa para a empresa.

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.