Travel Time Functions Research Articles

An inventory-routing optimization model for pharmaceutical supply chain with time-dependent travel time on a multi-graph network: a case study

PurposeSpurred by the high turnover in the pharmaceutical industry, locating pharmacies inside urban areas along with the high product perishability in this industry, the pharmaceutical supply chain management has recently gained increasing attention. Accordingly, this paper unveils an inventory-routing problem for designing a pharmaceutical supply chain with perishable products and time-dependent travel time in an uncertain environment.Design/methodology/approachIn this study, mathematical programming is employed to formulate a multi-graph network affected by the traffic volume in order to adapt to real-world situations. Likewise, by transforming the travel speed function to the travel time function using a step-by-step algorithm, the first-in-first-out property is warranted. Moreover, the Box–Jenkins forecasting method is employed to diminish the demand uncertainty.FindingsAn appealing result is that the delivery horizon constraint in the under-study multi-graph network may eventuate in selecting a longer path. Our analysis also indicates that the customers located in the busy places in the city are not predominantly visited in the initial and last delivery horizon, which are the rush times. Moreover, it is concluded that integrating disruption management, routing planning and inventory management in the studied network leads to a reduction of costs in the long term.Originality/valueApplying the time-dependent travel time with a heterogeneous fleet of vehicles on the multi-graph network, considering perishability in the products for reducing inventory costs, considering multiple trips of transfer fleet, considering disruption impacts on supply chain components and utilizing the Box–Jenkins method to reduce uncertainty are the contributions of the present study.

Real-Time Insertion Operator for Shared Mobility on Time-Dependent Road Networks

One of the most important challenges in shared mobility services ( e.g. , ride-sharing and parcel delivery) is planning routes for workers by considering real road conditions. To tackle this challenge, the "insertion operator", which computes the optimal route for the worker to serve ( i.e. , insert) the newly appeared delivery request, has been acted as the fundamental operation in existing solutions. However, existing works implicitly assume a static road network, hence are hard to fulfill the real-world scenario, where travel time between two locations is not constant at different times of a day. By contrast, we focus on the insertion operator over time-dependent road networks that capture the periodic pattern of road conditions. We also show that the time complexity of existing solutions would degrade into cubic time and hence such solutions can no longer satisfy the real-time requirement under this real-world setting. To satisfy the need for real-time computation, we propose a data summary to model the time-dependent travel time functions between pairs of vertices in the route. Based on the data summary, we design an efficient solution that can enumerate the best insertion position in linear time while satisfying complex spatiotemporal constraints. Finally, extensive experiments are conducted on real datasets from several applications of shared mobility. The results show that our solution is up to 44.5X faster than the state-of-the-art solution.

Correlating Access to Primary Medical Care and Veterinary Care Providers: A Novel Application of Spatial Gravity Modelling.

Increasingly, health professionals are recognizing the need for a more holistic, or One Health, approach to wellness. Companion animals share the lives and homes of many Americans, and yet little research exists on the intersection of disparities of access to veterinary care and access to human health care. This research aims to fill that gap by exploring the use of a spatial model that identifies the relationship of supply and demand while also considering reductions as a function of travel time to a care facility. Four counties in Alabama were analyzed at the census tract level to determine the supply of primary care physicians and veterinary care providers. This research provides a unique application of the Enhanced Two-Step Floating Catchment Area model by independently examining access to each type of care and then comparing both access supply values at the census level. Results indicated a statistically significant positive relationship between access to both types of care, implying areas with lower access to primary care have concomitantly low access to veterinary care. Implications for practice include the introduction of this methodological approach, identification of future parameter specification research to improve the approach, and identification of an area of significant concern in the One Health framework. Further, the results can inform solution strategies such as offering integrated care interventions for both humans and their companion animal household members with direct use for policymakers aimed at increasing equitable access to health care across the One Health spectrum.

New weighted travel time function considering uncertainty and fuzziness based on fuzzy soft set and its application in user equilibrium assignment

New weighted travel time function considering uncertainty and fuzziness based on fuzzy soft set and its application in user equilibrium assignment

A new look at the YY CrB binary system

This study presented a new analysis for the TESS-observed W Ursae Majoris (W UMa) binary star YY Coronea Borealis (YY CrB). The light curve was analyzed by the PHysics Of Eclipsing BinariEs (PHOEBE) Python version together with the Markov chain Monte Carlo (MCMC) method. The light curve solutions required a hot spot and l3. New eclipse times from the TESS observations were extracted, and the O-C curve of primary and secondary minima showed an anti-correlated manner. In order to study the O-C curve of minima, minima times between 1991 and 2023 were collected. This investigation reported a new linear ephemeris and by fitting a quadratic function to the O-C curve of minima, calculated the orbital period rate of Ṗ≈5.786×10−8dayyear. Assuming mass conservation, a mass exchange rate of Ṁ2=2.472×10−8 calculated from the more massive component to the less massive one. Then, by using the light travel time function, the possible third body was determined in the binary and derived the mass of the third body as 0.498M⊙ with a period of ≃7351.018 days. The O-C curve analysis and the quantity of mass indicate that the presence of a third body is unlikely. This binary is expected to evolve into a broken-contact phase and is a good case to support the thermal relaxation oscillation model.

A novel road traffic flow prediction model using hybrid Particle Swarm Optimization (PSO) and Radial Basis Function Neural Network (RBFNN)

<p>Traffic congestion is a major problem in urban areas, leading to increased travel time, air pollution, and fuel consumption. Road impedance function, which describes the relationship between traffic status and travel time, plays an important role in predicting travel time and managing traffic flow. Traditional methods for estimating road impedance function rely on manual calibration and may have limitations in reflecting the complexity of traffic patterns. To address these challenges, researchers have proposed various machine learning models for predicting travel time and road impedance function. In this paper, a hybrid particle swarm optimization—radial basis function neural network model is proposed for improving the accuracy of the road impedance function. The model takes into consideration various vehicle types and is validated using travel time data collected from a road section in Huai’an City, China. The effectiveness of the proposed model is compared with the traditional road impedance function calibrated by nonlinear regression. The experimental results indicate that the Mean Relative Error (MRE) of PSORBFNN is increased by 3.89% and 6.28% respectively when compared with DPNR training samples and validation samples. When compared with DPPSO training and validation samples, the MRE of PSORBFNN is increased by 2.87% and 3.3% respectively. These findings suggest that the proposed model could guide and assist traffic engineers and practitioners in predicting travel time on road sections with improved accuracy.</p>

Hydrological and Geological Controls for the Depth Distribution of Dissolved Oxygen and Iron in Silicate Catchments

AbstractDissolved Oxygen (DO) plays a key role in reactive processes and microbial dynamics in the critical zone. Recent observations showed that fractures can provide rapid pathways for oxygen penetration in aquifers, triggering unexpected biogeochemical processes. In the shallow subsurface, DO reacts with electron donors, such as Fe2+ coming from mineral dissolution. Yet, little is known about the factors controlling the spatial heterogeneity and distribution of oxygen with depth. Here we present a reduced analytical model describing the coupled evolution of DO and Fe2+ as a function of fluid travel time in silicate catchments. Our model, validated from fully resolved reactive transport simulations, predicts a linear decay of DO with time, followed by a rapid non‐linear increase of Fe2+ concentrations up to a far‐from‐equilibrium steady‐state. The relative effects of geological and hydrological forcings are quantified through a Damköhler number (Da) and a lithological number (Λ). We use this framework to investigate the depth distribution of DO and Fe2+ in two catchments with similar environmental contexts but contrasted hydrochemical properties. We show that hydrochemical differences are explained by small variations in Da but orders of magnitude variations in Λ. Therefore, we demonstrate that the hydrological and geological drivers controlling hydrochemistry in silicate catchments can be discriminated by analyzing jointly the O2 and Fe2+ evolution with depth. These findings provide a new conceptual framework to understand and predict the evolution of DO in modern groundwater, which plays an important role in critical zone processes.

Sequential path-equilibration algorithm for highly accurate traffic flow assignment in an urban road network

Nowadays, the issue of traffic flow assignment has become an interdisciplinary topic that concerns multiple research areas and branches of science. This work is focussed on the mathematical and computational aspects of the equilibrium traffic assignment problem in the case when route flows are considered to be decision variables. Firstly, we obtain a fixed-point mapping with the explicit contraction operator, which is proven to equilibrate the journey times on feasible routes between a single origin-destination pair of nodes with the quadratic rate. Remarkable that from mathematical perspectives, the developed operator generalizes most path-equilibration operators already exploited by researchers. Secondly, we use the obtained fixed-point procedure to run the sequential path-equilibration algorithm for traffic flow assignment on well-known test urban road networks with arc-additive travel time functions. Our computational results appear to demonstrate higher accuracy of user-equilibrium traffic assignment solutions than the best ones known to us. In other words, developed within this paper sequential path-equilibration algorithm leads to solutions with less goal function values compared to the best solutions for today, according to our knowledge.

A neural network based global traveltime function (GlobeNN)

Global traveltime modeling is an essential component of modern seismological studies with a whole gamut of applications ranging from earthquake source localization to seismic velocity inversion. Emerging acquisition technologies like distributed acoustic sensing (DAS) promise a new era of seismological discovery by allowing a high-density of seismic observations. Conventional traveltime computation algorithms are unable to handle virtually millions of receivers made available by DAS arrays. Therefore, we develop GlobeNN—a neural network based traveltime function that can provide seismic traveltimes obtained from the cached realistic 3-D Earth model. We train a neural network to estimate the traveltime between any two points in the global mantle Earth model by imposing the validity of the eikonal equation through the loss function. The traveltime gradients in the loss function are computed efficiently using automatic differentiation, while the P-wave velocity is obtained from the vertically polarized P-wave velocity of the GLAD-M25 model. The network is trained using a random selection of source and receiver pairs from within the computational domain. Once trained, the neural network produces traveltimes rapidly at the global scale through a single evaluation of the network. As a byproduct of the training process, we obtain a neural network that learns the underlying velocity model and, therefore, can be used as an efficient storage mechanism for the huge 3-D Earth velocity model. These exciting features make our proposed neural network based global traveltime computation method an indispensable tool for the next generation of seismological advances.

Evaluation of macroscopic fundamental diagram characteristics for a quantified penetration rate of autonomous vehicles

BackgroundThe availability of private vehicles with autonomous features is widespread nowadays. Various car manufacturers are providing attributes like collision warning, city automatic emergency braking, adaptive cruise control, pedestrian detection, lane-keeping assistance and lane departure warning, rear cross-traffic and blind-spot warning in their high-end models.PurposeSuch features can automatically manage the macroscopic fundamental traffic parameters such as speed, headway, etc adaptively. Consequently leading to a heterogeneous traffic stream with diverse car-following behaviour comprising completely manual/traditional (TVs) and autonomous vehicles (AVs). This questions the applicability of classic traffic flow theory relationships on such heterogeneous traffic streams.MethodologyThis paper focuses on developing the macroscopic fundamental diagram for such heterogeneous traffic streams based on the quantified penetration rate (QPR) for autonomous vehicles. The penetration rate is devised by taking into account user demographics, land usage and road network properties. QPR is used as an input for heterogeneous urban traffic stream scenarios to calculate the aggregated urban traffic network dynamics of flow and density for the same network. Travel time versus flow characteristics is evaluated based on calibrated hyperbolic urban link travel time function for both interrupted and uninterrupted flows following the aggregated speed and density output from MFDs for heterogeneous traffic streams. Also, two scenarios are generated for comparison to explain the improvement in the network characteristics together with a sensitivity analysis.ResultsCompared to the base scenario there could be 25-35% of AVs on the road networks based on the analysis in coming fifteen years. This increment in usage impacts the capacity of road networks positively by increasing it up to 59%.ConclusionsResults obtained after the application of the suggested model approach to the real network can be used to define a realistic method for multi-vehicle equilibrium assignment models for heterogeneous traffic streams including autonomous vehicles instead of approximating the penetration rates.

Model development of road performance indicator-related travel time using international roughness index: A case study national road network of Sulawesi

The International Roughness Index (IRI) is widespread in measuring road performance. However, travel time is a more critical benchmark in measuring road performance and the transportation system's performance. Therefore, new studies and models are needed to determine the relationship between IRI and travel time to obtain a segment performance function model influenced by road conditions. The study begins with a traffic condition survey to obtain vehicle travel time data on various road conditions. Assessment of road conditions uses the value of road surface flatness obtained from the results of Hawkeye measurements by carrying out actual travel throughout the national road network of Sulawesi Island. The study results show that the IRI value greatly influences the achievement of travel time as a road performance indicator in Indonesia. The equation of the relationship function of the vehicle travel time in free flow with the value of the flatness of the road surface is y=−6,062x2 +1,068x−1,0873 with R2 0,9314. At the same time, the equation of travel time as a function of road performance is ta = α1 (v/c)β + α1 (v/c) - 6,062x2 + 1,068x - 1,0873.

Half-open time-dependent multi-depot electric vehicle routing problem considering battery recharging and swapping

In order to promote green and sustainable development of the transportation industry, an increasing number of logistics companies have begun to deploy electric vehicles (EVs) to provide urban distribution services. This paper studies a Half-Open Time-Dependent Multi-Depot Electric Vehicle Routing Problem Considering Battery Recharging and Swapping (HOTDMDEVRPBRS) in last-mile delivery. Based on the calculation functions of EV energy consumption, travel time, and carbon emissions under the time-dependent road network, a mixed integer programming model is formulated. The goal of the model is to minimize the economic cost and environmental cost of logistics companies. Given the complexity of the problem, this paper designs a multi-objective simulated annealing algorithm (SAA). Finally, this paper carries out comprehensive computational experiments to verify and evaluate the performance of the proposed model and method and examines the economic and environmental benefits brought by the Half-Open Joint Distribution Mode (HOJDM). According to the results, SAA shows good performance and provides a high-quality solution. Meanwhile, the HOJDM significantly reduces the total cost and carbon emissions of logistics enterprises and provides valuable suggestions for enterprise managers and government decision-makers.

Robust optimization of train scheduling with consideration of response actions to primary and secondary risks.

Nowadays, with the rapid development of rail transportation systems, passenger demand and the possibility of the risks occurring in this industry have increased. These conditions cause uncertainty in passenger demand and the development of adverse impacts as a result of risks, which put the assurance of precise planning in jeopardy. To deal with uncertainty and lessen negative impacts, robust optimization of the train scheduling problem in the presence of risks is crucial. A two-stage mixed integer programming model is suggested in this study. In the first stage, the objective of the nominal train scheduling problem is to minimize the total travel time function and optimally determine the decision variables of the train timetables and the number of train stops. A robust optimization model is developed in the second stage with the aim of minimizing unsatisfied demand and reducing passenger dissatisfaction. Additionally, programming is carried out and the set of optimal risk response actions is identified in the proposed approach for the presence of primary and secondary risks in the train scheduling problem. A real-world example is provided to demonstrate the model's effectiveness and to compare the developed models. The results demonstrate that secondary risk plays a significant role in the process of optimal response actions selection. Furthermore, in the face of uncertainty, robust solutions can significantly and effectively minimize unsatisfied demand by a slightly rise in the travel time and the number of stops obtained from the nominal problem.

Learned Upper Bounds for the Time-Dependent Travelling Salesman Problem

Given a graph whose arc traversal times vary over time, the Time-Dependent Travelling Salesman Problem consists in finding a Hamiltonian tour of least total duration covering the vertices of the graph. The main goal of this work is to define tight upper bounds for this problem by reusing the information gained when solving instances with similar features. This is customary in distribution management, where vehicle routes have to be generated over and over again with similar input data. To this aim, we devise an upper bounding technique based on the solution of a classical (and simpler) time-independent Asymmetric Travelling Salesman Problem, where the constant arc costs are suitably defined by the combined use of a Linear Program and a mix of unsupervised and supervised Machine Learning techniques. The effectiveness of this approach has been assessed through a computational campaign on the real travel time functions of two European cities: Paris and London. The overall average gap between our heuristic and the best-known solutions is about 0.001\%. For 31 instances, new best solutions have been obtained.

A spatiotemporal disparity of transit and automobile access gap and its impact on transit use

This research empirically evaluates the access gap between transit and automobile to examine the extent of auto-access-orientation within and between the 50 American Metropolitan Areas. The Modal Access Gap (MAG) index is calculated over space and travel time to test three hypotheses: (1) MAG is a function of space and travel time, (2) MAG is CBD-centric, and (3) MAG is associated with transit use. Results indicate that (1) MAG merely possesses negative values ranging between −0.98 and −0.79, regardless of the travel-time thresholds or metropolitan areas, and the travel time lag between transit and automobile ranges from 35 minutes in New York to 51 minutes in Riverside for a 60-minute commute, (2) MAG decreases as one moves away from the central area, and (3) a 1% increase in MAG increases transit use by 1.37% on average.

Method of Distributions for Two‐Phase Flow in Heterogeneous Porous Media

AbstractMultiscale heterogeneity and insufficient characterization data for a specific subsurface formation of interest render predictions of multi‐phase fluid flow in geologic formations highly uncertain. Quantification of the uncertainty propagation from the geomodel to the fluid‐flow response is typically done within a probabilistic framework. This task is computationally demanding due to, for example, the slow convergence of Monte Carlo simulations (MCS), especially when computing the tails of a distribution that are necessary for risk assessment and decision‐making under uncertainty. The frozen streamlines method (FROST) accelerates probabilistic predictions of immiscible two‐phase fluid flow problems; however, FROST relies on MCS to compute the travel‐time distribution, which is then used to perform the transport (phase saturation) computations. To alleviate this computational bottleneck, we replace MCS with a deterministic equation for the cumulative distribution function (CDF) of travel time. The resulting CDF‐FROST approach yields the CDF of the saturation field without resorting to sampling‐based strategies. Our numerical experiments demonstrate the high accuracy of CDF‐FROST in computing the CDFs of both saturation and travel time. For the same accuracy, it is about 5 and 10 times faster than FROST and MCS, respectively.

P-, SV- and SH-wave eikonal approximations for HTI media based on perturbation theory

SUMMARY The eikonal equation for transversely isotropic media is a complex quartic partial differential equation that causes instability in traveltime inversion. The phenomenon of shear wave splitting in a transversely isotropic model with a horizontal symmetry axis (HTI) provides information for inversion. However, the involvement of shear waves makes the computation of forward modelling and inversion more time-consuming than when only using Pwaves. Most studies of traveltime approximation based on the eikonal equation are based on an acoustic assumption, which does not work for shear waves. Therefore, based on perturbation theory, we derive approximate solutions of the eikonal equation in a heterogeneous elastic HTI model for P, SV and SH waves to improve the traveltime computation efficiency. The approximate solutions of linear, quadratic and Shanks forms are based on the linearization of the traveltime function in terms of fracture weaknesses in an isotropic background, which are suitable for joint P-, SV- and SH-wave traveltime inversion and tomography for fracture parameters. When applied for a homogenous model, the proposed formulation results in a simple and accurate traveltime approximation. The first- and second-order perturbation coefficients are used to analyse the sensitivity of the traveltime to fracture weakness. To improve the accuracy of our approximation, we also expand the approximation of the P-wave traveltime with respect to the anellipticity parameter η in an elliptic background, which is evaluated by performing an error test. Based on the accuracy and stability of the perturbation, we select a set of linear equations with respect to the fracture weaknesses and a set of more accurate nonlinear equations to serve different needs.

Dynamic Programming for the Time-Dependent Traveling Salesman Problem with Time Windows

The time-dependent traveling salesman problem with time windows (TDTSPTW) is a variant of the well-known traveling salesman problem with time windows, in which travel times are not assumed to be constant. The TDTSPTW accounts for the effects of congestion at the planning level, being particularly suited for distribution problems in large cities. In this paper we develop a labeling-based algorithm for the TDTSPTW that incorporates partial dominance and generalizes several state-of-the-art components from the time-independent related literature. We propose a framework general enough to be applied to the TDTSPTW and its variant without time windows, with the objective of minimizing the duration or the makespan. As part of the framework, we introduce a new state-space relaxation specifically designed for the time-dependent context. Extensive computational experiments show the effectiveness of the overall approach and the impact of the new relaxation, outperforming several recent algorithms proposed for these variants on more than 9,000 benchmark instances. In addition, we frame the minimum tour duration problem within the time-dependent literature and include it as a benchmark for our algorithm, obtaining improved computation times and 31 new optimal solutions. Summary of Contribution: In this paper, we study the time-dependent traveling salesman problem with time windows (TDTSPTW), a difficult single-vehicle routing problem that incorporates more realistic travel time functions than its classic time-independent counterpart. As a result, the TDTSPTW is harder to solve, as it requires more complex models and algorithms. Using state-of-the-art optimization techniques, we propose an efficient solution approach for the TDTSPTW and some related variants that outperforms the previous approaches in the literature. Our paper emphasizes the importance of algorithmic design and efficient implementations to tackle relevant practical combinatorial optimization problems—in particular, for time-dependent problems. Moreover, the resulting algorithm fosters a new research direction regarding exact algorithms for time-dependent problems using dynamic programming and relaxation techniques. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This research has been funded by Fondo para la Investigación Científica y Tecnológica (FONCyT) [Grants PICT-2016-2677 and PICT-2018-2961] from the Ministry of Science, Argentina, and by the Google Latin America Research Award (LARA) 2019. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.1236 .

PAHUTE MESA TRAVEL TIMES AT KURIL–KAMCHATKA SEISMIC STATIONS

This research fulfills additional information about the lithosphere below Southeastern Asia and the northern Pacific. The area is interesting for researchers because of the Kuril–Kamchatka subducted lithosphere. The availability to study an underground structure is complicated, because of Pacific Ocean. The significance of this research concerns epicentral distances ~54°–70° or ~6000–7000 km. During the Cold War of the 20th century and the classification of information between the largest nuclear states the Soviet Union (USSR) and the United States of America (USA), data on the registration of nuclear explosions were not published, however, underground nuclear explosions (UNE) were recorded. Thanks to an employee of the laboratory 5-s of the Institute of Physics of the Earth named after O.Yu. Schmidt of the USSR Academy of Sciences Kh.D. Rubinstein is kept at the Institute for the Dynamics of Geospheres of the Russian Academy of Sciences named after Academician M.A. Sadovsky (IDG RAS). Only after 1985 reports from some seismic stations of the former USSR began to be published in the operational reports of the United Geophysical Survey of the Russian Academy of Sciences (GS RAS). As it has not been yet published anywhere, we collect them and obtain the travel times were by revising seismograms from the archives IDG RAS and GS RAS for five Kuril–Kamchatka seismic stations (Bering, Esso, Severo-Kurilsk, Kurilsk). The 48 Unites States UNE at Pahute Mesa (at Nevada Test Site) from 1968 to 1990 are used for travel time curve building. We measure P waves travel times (tp) on historical seismograms for the ray travel path between Pahute Mesa tests and Kuril–Kamchatka stations. The body-waves magnitudes (mb) vary from 5.3 to 6.5. We obtain arrivals for: 1 UNE at Bering station, 7 UNE at Esso station, 45 UNE at Petropavlovsk, 18 UNE at Severo-Kurilsk and 12 at Kurilsk. We build a travel time function using linear regression algorithm as tp=k·Δ°+b, where Δ° is the epicentral distance, k and b are arbitrary constants. We show that travel time deviations, associated with nonlinearity of the Earth. We estimate the effective velocities of P waves for the Pahute Mesa – Kuril–Kamchatka travel path as coefficient k in the linear equation. Effective velocity is equal to 7.5 km/s.

NP-hardness of shortest path problems in networks with non-FIFO time-dependent travel times

We study the complexity of earliest arrival problems on time-dependent networks with non-FIFO travel time functions, i.e. when departing later might lead to an earlier arrival. In this paper, we present a simple proof of the weak NP-hardness of the problem for travel time functions defined on integers. This simplifies and reproduces an earlier result from Orda and Rom. Our proof generalizes to travel time functions defined on rational numbers and also implies that, in this case, the problem becomes harder, i.e. is strongly NP-hard. As arbitrary functions are impractical for applications, we also study a more realistic problem model where travel time functions are piecewise linear and represented by a sequence of breakpoints with integer coordinates. We show that this problem formulation is strongly NP-hard, too. As an intermediate step for this proof, we also show the strong NP-completeness of SubsetProduct on rational numbers.