Stochastic Travel Times Research Articles

Pickup and delivery problem with hard time windows considering stochastic and time-dependent travel times

Due to the uncertain nature of the traffic system, it is not trivial for delivery companies to reliably satisfy customers’ time windows. To guarantee the reliability of the pickup and delivery service under stochastic and time-dependent travel times, we consider a pickup and delivery problem with hard time windows considering stochastic and time-dependent travel times. We propose a chance-constrained model where the operational cost and the service’s reliability are considered. To quantify the service reliability, every node is associated with a desired node service level, and there exists a global service level, both measured by success probabilities. We present an estimation method for arrival times and success probabilities under stochastic travel and service times. We propose an exact solution approach based on a branch-price-and-cut framework, where a labeling algorithm generates columns. Computational experiments are conducted to assess the effectiveness of the solution framework, and Monte Carlo simulations are used to show that the proposed method can generate routes that satisfy both node and global service levels.

Internet of Vehicles and Real-Time Optimization Algorithms: Concepts for Vehicle Networking in Smart Cities

Achieving sustainable freight transport and citizens’ mobility operations in modern cities are becoming critical issues for many governments. By analyzing big data streams generated through IoT devices, city planners now have the possibility to optimize traffic and mobility patterns. IoT combined with innovative transport concepts as well as emerging mobility modes (e.g., ridesharing and carsharing) constitute a new paradigm in sustainable and optimized traffic operations in smart cities. Still, these are highly dynamic scenarios, which are also subject to a high uncertainty degree. Hence, factors such as real-time optimization and re-optimization of routes, stochastic travel times, and evolving customers’ requirements and traffic status also have to be considered. This paper discusses the main challenges associated with Internet of Vehicles (IoV) and vehicle networking scenarios, identifies the underlying optimization problems that need to be solved in real time, and proposes an approach to combine the use of IoV with parallelization approaches. To this aim, agile optimization and distributed machine learning are envisaged as the best candidate algorithms to develop efficient transport and mobility systems.

A memetic algorithm for a relocation-routing problem in green production of gas considering uncertainties

• A fuzzy chance constraint programming model for relocation-routing problem is formulated. • The uncertainty of amount of generated sewage and travel time are considered in the model. • Memetic algorithm and Monte Carlo simulation are integrated to solve the models. • Several series of experiments are conducted to evaluate the proposed model and algorithm. This study introduces a relocation-routing problem with a fuzzy amount of sewage and stochastic travel time in natural gas production. In this study, a set of sewage treatment plants (STPs) and a certain number of gas-gathering stations (GGSs) are distributed on the field. With the increasing amount of production, however, the current STPs cannot satisfy the production level. Policymakers propose several location candidates to build new STPs and aim to minimize the total cost of running the newly built STPs and the original STPs. The practical attributes of the sewage return logistics, capacity of vehicles and STPs, uncertain amount of sewage, stochastic travel times, and other constraints are taken into account. The new problem proposed in this study is defined as Relocation-Routing Problem with Fuzzy Sewage and Stochastic Travel Time (RLRPFSSTT), which has never been investigated before. To minimize the total cost, including the construction cost of newly opened STPs and transportation cost between STPs and GGSs, this paper designs a memetic algorithm to optimize location and routing problems simultaneously. Benchmark-based experimental data is designed, and the computational results demonstrate the effectiveness of the proposed memetic algorithm. Sensitivity analysis and comparisons are also carried out to validate the advantage of considering uncertainties. The proposed model and algorithm are meant to further supplement and extend the location and routing models, as well as have great significance for the decision-makers of industrial logistics in oil fields and coal mines.

Scheduling and Routing of Mobile Charging Stations With Stochastic Travel Times to Service Heterogeneous Spatiotemporal Electric Vehicle Charging Requests With Time Windows

This article presents an alternative service of mobile charging stations for the large-scale charging of electric vehicles, which consider the spatiotemporal heterogeneity of charging requests. As charging infrastructure is the key determinant for the large-scale adoption of electric vehicles, state-of-the-art scheduling and control strategies need to be explored. The charging of electric vehicles in a conventional charging station even with the fast dc–dc chargers takes around 30 min, which results in congestion and large waiting queues at public charging stations. To account for this issue, a novel strategy of routing and scheduling mobile charging stations to charge electric vehicles without the constraints of time and space is discussed in detail. Furthermore, the traveling times of mobile charging stations in reality are stochastic in nature. We formulate the optimization problem to minimize the cost of charging and show that the problem formulated is a combination of a bin packing problem and a multicity traveling salesman problem; hence, it is NP-hard and cannot be solved in reasonable CPU time, unless P = NP. We, thus, present modified saving’s heuristic and modified genetic algorithm metaheuristic to solve the optimization problem. Furthermore, numerical simulations show that the proposed scheduling and routing algorithm requires less number of mobile charging stations and can appreciably reduce the cost of charging.

Attended home delivery under uncertain travel and response time: a case of Indian public distribution system

PurposeBeing the final end of the logistic distribution, attended home delivery (AHD) plays an important role in the distribution network. AHD typically refers to the service provided by the distribution service provider to the recipient's doorstep. Researchers have always identified AHD as a bottleneck for last-mile delivery. This paper addresses a real-life stochastic multi-objective AHD problem in the context of the Indian public distribution system (PDS).Design/methodology/approachTwo multi-objective models are proposed. Initially, the problem is formulated in a deterministic environment, and later on, it is extended to a multi-objective AHD model with stochastic travel and response time. This stochastic AHD model is used to extensively analyze the impact of stochastic travel time and customer response time on the total expected cost and time-window violation. Due to the NP-hard nature of the problem, an ant colony optimization (ACO) algorithm, tuned via response surface methodology (RSM), is proposed to solve the problem.FindingsExperimental results show that a change in travel time and response time does not significantly alter the service level of an AHD problem. However, it is strongly correlated with the planning horizon and an increase in the planning horizon reduces the time-window violation drastically. It is also observed that a relatively longer planning horizon has a lower expected cost per delivery associated.Research limitations/implicationsThe paper does not consider the uncertainty of supply from the warehouse. Also, stochastic delivery failure probabilities and randomness in customer behavior have not been taken into consideration in this study.Practical implicationsIn this paper, the role of uncertainty in an AHD problem is extensively studied through a case of the Indian PDS. The paper analyzes the role of uncertain travel time and response time over different planning horizons in an AHD system. Further, the impact of the delivery planning horizon, travel time and response time on the overall cost and service level of an AHD system is also investigated.Social implicationsThis paper investigates a unique and practical AHD problem in the context of Indian PDS. In the present context of AHD, this study is highly relevant for real-world applications and can help build a more efficient delivery system. The findings of this study will be of particular interest to the policy-makers to build a more robust PDS in India.Originality/valueThe most challenging part of an AHD problem is the requirement of the presence of customers during the time of delivery, due to which the probability of failed delivery drastically increases if the delivery deviates from the customer's preferred time slot. The paper modelled an AHD system to incorporate uncertainties to attain higher overall performance and explore the role of uncertainty in travel and response time with respect to the planning horizon in an AHD, which has not been considered by any other literature.

Optimization of service frequency and vehicle size for automated bus systems with crowding externalities and travel time stochasticity

Public transport is considered as one of the most suitable candidates to benefit from autonomous driving technologies. In this research, we develop a mathematical modeling framework to optimize service frequency and vehicle size for automated bus systems, while accounting for both user and operator costs. We explicitly consider travel time stochasticity, time-dependent passenger flows, vehicle capacity limitations (extra waiting time due to denied boarding), and in-vehicle discomfort externalities for both sitting and standing passengers at a microscopic level. We attempt to provide a thorough assessment of the service and cost implications of the deployment of automated buses. Hence, a broad range of experiments are simulated by combining different deployment cases: (i) vehicle technology (human-driven or automated vehicles), (ii) travel time assumptions (deterministic or stochastic travel times), and (iii) crowding externalities (considering or ignoring in-vehicle crowding costs). The model applicability is assessed on two real-world bus corridors in Regensburg (Germany) and Santiago (Chile). Results show that, with crowding externalities, optimal vehicle size is increased at a similar rate for both human-driven and automated bus services, whereas optimal service frequency is increased at a higher rate for automated buses. Thus, under optimal levels of supply, automated vehicles are operated with lower occupancy levels than human-driven vehicles, increasing the quality of service. Besides, the deployment of automated bus systems can significantly alleviate or eliminate denied boardings. The effects of automation on travel time volatility and dwell time regularity are studied. The consideration of stochastic travel times increases optimal frequencies at a higher rate for automated services relative to human-driven vehicles. Interestingly, we find that even though the operator benefits from automation are more pronounced in high-income countries (due to a greater potential for human driving cost savings), the final outcome is counterbalanced by the actual public transport demand level, because large user cost savings from automation are reachable in crowded routes even in situations in which labor costs are lower (as in developing countries).

The flying sidekick traveling salesman problem with stochastic travel time: A reinforcement learning approach

As a novel urban delivery approach, the coordinated operation of a truck–drone pair has gained increasing popularity, where the truck takes a traveling salesman route and the drone launches from the truck to deliver packages to nearby customers. Previous studies have referred to this problem as the flying sidekick traveling salesman problem (FSTSP) and have proposed numerous algorithms to solve it. However, few studies have considered the stochasticity of the travel time on the road network, mainly caused by traffic congestion, harsh weather conditions, etc, which heavily impacts the speed of the truck, thus affecting the drone’s operations and overall delivery routine. In this study, we extend the FSTSP with stochastic travel times and formulate the problem into a Markov decision process (MDP). The model is solved using reinforcement learning (RL) algorithms including the deep Q-network (DQN) and the Advantage Actor-Critic (A2C) algorithm to overcome the curse of dimensionality. Using an artificially generated dataset that was widely accepted as benchmarks in the literature, we show that the reinforcement learning algorithms also perform well as approximate optimization algorithms, outperforming a mixed integer programming (MIP) model and a local search heuristic algorithm on the original FSTSP without the stochastic travel time. On the FSTSP with stochastic travel time, the reinforcement learning algorithms obtain flexible policies that make dynamic decisions based on different traffic conditions on the roads, saving up to 28.65% on delivery time compared with the MIP model and a dynamic local search (DLS) algorithm. We also conduct a case study using real-time traffic data collected in a middle-sized city in the U.S. using Google Map API. Compared with a benchmark calculated by the DLS, the DRL approach saves 32.68% total delivery time in the case study, showing great potential for future practical adoption.

A Granular Local Search Matheuristic for a Heterogeneous Fleet Vehicle Routing Problem with Stochastic Travel Times

A Granular Local Search Matheuristic for a Heterogeneous Fleet Vehicle Routing Problem with Stochastic Travel Times

Global synchromodal shipment matching problem with dynamic and stochastic travel times: a reinforcement learning approach

Global synchromodal transportation involves the movement of container shipments between inland terminals located in different continents using ships, barges, trains, trucks, or any combination among them through integrated planning at a network level. One of the challenges faced by global operators is the matching of accepted shipments with services in an integrated global synchromodal transport network with dynamic and stochastic travel times. The travel times of services are unknown and revealed dynamically during the execution of transport plans, but the stochastic information of travel times are assumed available. Matching decisions can be updated before shipments arrive at their destination terminals. The objective of the problem is to maximize the total profits that are expressed in terms of a combination of revenues, travel costs, transfer costs, storage costs, delay costs, and carbon tax over a given planning horizon. We propose a sequential decision process model to describe the problem. In order to address the curse of dimensionality, we develop a reinforcement learning approach to learn the value of matching a shipment with a service through simulations. Specifically, we adopt the Q-learning algorithm to update value function estimations and use the $$\epsilon $$ -greedy strategy to balance exploitation and exploration. Online decisions are created based on the estimated value functions. The performance of the reinforcement learning approach is evaluated in comparison to a myopic approach that does not consider uncertainties and a stochastic approach that sets chance constraints on feasible transshipment under a rolling horizon framework.

Robot-Based Last-Mile Deliveries With Pedestrian Zones

Since delivery robots share sidewalks with pedestrians, it may be beneficial to choose paths for them that avoid zones with high pedestrian density. In this paper, we investigate a robot-based last-mile delivery problem considering path flexibility given the presence of zones with varying pedestrian level of service (LOS). Pedestrian LOS is a measure of pedestrian flow density. We model this new problem with stochastic travel times and soft customer time windows. The model includes an objective that reflects customer service quality based on early and late arrivals. The heuristic solution approach uses the minimum travel time paths from different LOS zones (path flexibility). We demonstrate that the presence of pedestrian zones leads to alternative path choices in 30% of all cases. In addition, we find that extended time windows may help increase service quality in zones with high pedestrian density by up to 40%.

A Simulation-based Optimization Model for the Vehicle Routing Problem with Bimodal Stochastic Travel Time Distribution

This paper proposes a simulation-based optimization model for solving a realistic delivery problem within an urban area that respects the customers’ availability. Specifically, the originality of this work is to consider the bimodal realistic traffic pattern when solving the classic capacitated vehicle routing problem with time windows. Computational results have shown that under bimodal travel time distribution the routing solution changes considerately. Thus, this work emphasizes the need to fully integrate the traffic behavior when solving this class of routing problem with stochastic travel times. Furthermore, it highlights the easiness of such integration, when the routing problem is modeled and solved using this promising simulation-based optimization approach.

A simulation-optimization approach for solving the forestry logistics problem

Solving the forestry logistic problem is involved with multiple short- and long-term operational decisions such as truck routing, inventory management, and scheduling. Although these problems are separately studied in the literature, but in many situations, a near-optimal solution of the “comprehensive” problem suffices the managerial needs and directions. In this paper, we consider the forestry logistic and use a simulation-optimization method to reach a near-optimal solution. This method enables us to incorporate different uncertainties such as stochastic travel time and occurrence of external factors. We use real-world data to evaluate our model and measure the complexity of real-world constraints.

Heterogeneous Route Choice Model Incorporating Group Segmentation Based on Travel Experience

Travelers make different choices about their routes based on the perceived travel time. This study aims to analyze the route choice behaviors by grouping them according to their perceived travel times. Reliability preference is a behavioral characteristic for travelers' on-time arrival according to stochastic travel time, and it is used to classify the travelers into four groups. From Dedicated Short Range Communication (DSRC) data in Daegu, 9,758 travelers are observed to analyze their route choice behaviors. A stochastic model with generated sets of choices is developed using the probabilistic characteristics of travel times. A route-choice model is also estimated for each group, and the travelers' route-choice behaviors are analyzed using a mixed path-size correction logit (MPSCL) model. The statistical analysis indicates that there are different route-choice behaviors among the four groups. The different behaviors concerning the routes are analyzed by comparing the magnitude of the different coefficients. This study contributes to constructing different strategies for acquiring information considering the route-choice behaviors of each group. Providing travel information that considers individual preferences in travel choice is essential in smart mobility transportation systems.

A Multiclass Cumulative Prospect Theory-Based Stochastic User Equilibrium Model with Path Constraints in Degradable Transport Networks

The limited driving range and the unavailability or insufficiency of battery charging/swapping stations cause the so-called range anxiety issue for traffic assignment involving battery electric vehicle (BEV) users. In addition, expected utility theory-based stochastic user equilibrium (EUT-SUE) model generates the perfectly rational issue when the travellers make route choice decisions. To tackle these two problems, this article improves the cumulative prospect theory-based stochastic user equilibrium (CPT-SUE) model in a degradable transport network through incorporating the constraints of multiple user classes and distance limit. In this degradable network, the travellers experience stochastic travel times due to network link capacity degradations. For this improved CPT-SUE model, the equivalent variational inequality (VI) model and associated method of successive averages (MSA) based solution are provided. The improved CPT-SUE model is tested and compared with the EUT-SUE model with distance limit, with results showing that the improved CPT-SUE model can handle jointly the range anxiety issue and the perfectly rational issue.

Optimal Routing in Stochastic Networks with Reliability Guarantees.

Optimal routing in highly congested street networks where the travel times are often stochastic is a challenging problem with significant practical interest. While most approaches to this problem use minimizing the expected travel time as the sole objective, such a solution is not always desired, especially when the variance of travel time is high. In this work, we pose the problem of finding a routing policy that minimizes the expected travel time under the hard constraint of retaining a specified probability of on-time arrival. Our approach to this problem models the stochastic travel time on each segment in the road network as a discrete random variable, thus translating the model of interest into a Markov decision process. Such a setting enables us to interpret the problem as a linear program. Our work also includes a case study on the street of Manhattan, New York where we constructed the model of travel times using real-world data, and employed our approach to generate optimal routing policies.

Target-Oriented User Equilibrium Considering Travel Time, Late Arrival Penalty, and Travel Cost on the Stochastic Tolled Traffic Network

In this paper, we employ a target-oriented approach to analyze the multi-attribute route choice decision of travelers in the stochastic tolled traffic network, considering the influence of three attributes, which are (stochastic) travel time, (stochastic) late arrival penalty, and (deterministic) travel cost. We introduce a target-oriented multi-attribute travel utility model for this analysis, where each attribute is assigned a target by travelers, and travelers’ objective is to maximize their travel utility that is determined by the achieved targets. Moreover, the interaction between targets is interpreted as complementarity relationship between them, which can further affect their travel utility. In addition, based on this travel utility model, a target-oriented multi-attribute user equilibrium model is proposed, which is formulated as a variational inequality problem and solved with the method of successive average. Target for travel time is determined via travelers’ on-time arrival probability, while targets for late arrival penalty and travel cost are given exogenously. Lastly, we apply the proposed model on the Braess and Nguyen–Dupuis traffic networks, and conduct sensitivity analysis of the parameters, including these three targets and the target interaction between them. The study in this paper can provide a new perspective for travelers’ multi-attribute route choice decision, which can further show some implications for the policy design.

A chance constrained programming model and an improved large neighborhood search algorithm for the electric vehicle routing problem with stochastic travel times

A chance constrained programming model and an improved large neighborhood search algorithm for the electric vehicle routing problem with stochastic travel times

Vehicle dispatching plan for minimizing passenger waiting time in a corridor with buses of different sizes: Model formulation and solution approaches

Urban public transportation agencies sometimes have to operate mixing vehicles of different sizes on their routes, due to resource limitations or historical reasons. Services with different passenger-carrying capacities are provided to passengers during a mixed-fleet operation. A fundamental question arising here is how to optimally deploy a given fleet of different bus sizes to provide services that minimize passenger waiting time. We formulate a mixed-fleet vehicle dispatching problem as a Mixed-Integer Nonlinear Programming (MINLP) model to optimize dispatching schemes (dispatching orders and times) when a given set of buses of different sizes are available to serve demand along a route. The objective is to minimize the average passenger waiting time under time-dependent demand volumes. Stochastic travel times between stops and vehicle capacity constraints (i.e., introducing extra waiting time due to denied boarding) are explicitly modeled. A Simulated Annealing (SA) algorithm coupled with a Monte Carlo simulation framework is developed to solve large real-world instances in the presence of stochastic travel times. Results show that, in addition to dispatching headway, bus dispatching sequence can strongly affect waiting times under a mixed-fleet operation. Indeed, with an optimal dispatching sequence, a more accurate adjustment of supply to demand is possible in accordance with time-dependent demand conditions, and the total savings in waiting time are mainly driven by a further reduction in the number of passengers left behind. The optimality of uneven dispatching headways stems from two elements: having a mixed fleet and having localized peaks on demand that make buses run full.

Minimum costs paths in intermodal transportation networks with stochastic travel times and overbookings

In intermodal transportation, it is essential to balance the trade-off between the cost and duration of a route. The duration of a path is inherently stochastic because of delays and the possibility of overbooking. We study a problem faced by a company that supports shippers with advice for the route selection. The challenge is to find Pareto-optimal solutions regarding the route’s costs and the probability of arriving before a specific deadline. We show how this probability can be calculated in a network with scheduled departure times and the possibility of overbookings. To solve this problem, we give an optimal algorithm, but as its running time becomes too long for larger networks, we also develop a heuristic. The idea of this heuristic is to replace the stochastic variables by deterministic risk measures and solve the resulting deterministic optimization problem. The heuristic produces, in a fraction of the optimal algorithm’s running time, solutions of which the costs are only a few percent higher than the optimal costs.

Sustainable local pickup and delivery: The case of Paris

The two-echelon distribution networks are very common in last-mile supply chains and urban logistics systems. The problem consists of delivering goods from one depot to a set of satellites and from there to a group of customers. The most common problem is known as the two-echelon vehicle routing problem (2E-VRP), which is known to be computationally difficult to solve. In real-life, uncertainty in travel times increases this complexity to actually define a delivery schedule. To deal with this stochastic behavior, this paper proposes a solution approach based on a combination of simulation and optimization, named simheuristic, to solve the 2E-VRP with stochastic travel times. The model also considers the CO2 equivalent and fine particles emissions. Experiments are run using real data of a French delivery company for the city of Paris. The performance of two scenarios for freight delivering is evaluated, and the results show that a global optimum gives better results than local optima. Policy makers need to take this into account when defining city policy on freight transport.