Travel Path Research Articles

Ordering the confusion: a study of the impact of lens models on gravitational-wave strong lensing detection capabilities

ABSTRACT When travelling from their source to the observer, gravitational waves can get deflected by massive objects along their travel path. For a massive lens and a good source-lens alignment, the wave undergoes strong lensing, leading to several images with the same frequency evolution. These images are separated in time, magnified, and can undergo an overall phase shift. Searches for strongly lensed gravitational waves look for events with similar masses, spins, and sky location and linked through so-called lensing parameters. However, the agreement between these quantities can also happen by chance. To reduce the overlap between background and foreground, one can include lensing models. When doing realistic searches, one does not know which model is the correct one to be used. Using an incorrect model could lead to the non-detection of genuinely lensed events. In this work, we investigate how one can reduce the false alarm probability when searching for strongly lensed events. We focus on the impact of the addition of a model for the lens density profile and investigate the effect of potential errors in the modelling. We show that the risks of false alarm are high without the addition of a lens model. We also show that slight variations in the profile of the lens model are tolerable, but a model with an incorrect assumption about the underlying lens population causes significant errors in the identification process. We also suggest some strategies to improve confidence in the detection of strongly lensed gravitational waves.

Bouncing Spallation Bombs During the 2021 La Palma Eruption, Canary Islands, Spain

Incandescent pyroclasts of more than 64 mm in diameter erupted from active volcanoes are known as bombs and pose a significant hazard to life and infrastructure. Volcanic ballistic projectile hazard assessment normally considers fall as the main transport process, estimating its intensity from bomb location and impact cratering. We describe ballistically ejected bombs observed during the late October 2021 episode of eruption at La Palma (Canary Islands) that additionally travelled downhill by rolling and bouncing on the steep tephra-dominated cone. These bouncing bombs travelled for distances >1 km beyond their initial impact sites, increasing total travel distance by as much as 100%. They left multiple impact craters on their travel path and frequently spalled incandescent fragments on impact with substrate, leading to significant fire hazard for partially buried trees and structures far beyond the range of ballistic transport. We term these phenomena as bouncing spallation bombs. The official exclusion zone encompassed this hazard at La Palma, but elsewhere bouncing spallation bombs ought to be accounted for in risk assessment, necessitating awareness of an increased hazard footprint on steep-sided volcanoes with ballistic activity.

The built environment impacts on route choice from home to school for rural students: A stated preference experiment.

Rural roads and built environment in China have been developed enormously, but it is not clear whether these roads fulfill the needs of school children as they need to travel long to school every day. It is crucial to understand the influencing factors of their travel mode choices to better design future country roads and built environment, aiming to promote physical activities of school children in a safe built environment. This study thus attempts to explore the impacts of rural built environment attributes on children's school travel mode preferences. Eight rural built environment attributes are considered: distance from home to school; the number of intersections passed on the way to school; whether there are sidewalks/bicycle lanes; the traffic speed of school access routes; whether there are separation facilities between motor vehicles and non-motor vehicles; whether there are traffic lights and zebra crossings; availability of greenery such as lawns, flower ponds and street trees and whether there are shops on the way to school and at the school gate. Six hundred and thirty eight valid questionnaires were obtained through face-to-face interviews with school-age children in villages. A multinomial logit model was estimated to unravel the preferences and choices of rural school-age children in different models of school travel using the stated choice data. All the eight attributes have significant impacts on rural children's school travel choices on foot, bicycle, electric bicycle or motorbike. And four rural road design attributes have significant effects on rural children's school travel by private cars. A travel path with pavements or bike lanes, few intersections, low traffic speeds, greenery and shops can facilitate children's school travels on foot or by bike. The conclusions can provide reference for the further upgrading planning, designing and construction of rural roads, as well as enriching the theory and practice of child-friendly villages construction.

Time-Lapse Cross-Well Monitoring of CO2 Sequestration Using Coda Wave Interferometry

In this study, we explored the capability of coda wave interferometry (CWI) for monitoring CO2 storage by estimating the seismic velocity changes caused by CO2 injection. Given that the CWI method is highly efficient, the primary aim of this study was to provide a quick detection tool for the long-term monitoring of CO2 storage safety. In particular, we looked at monitoring with a cross-well geometry. We also expected that CWI could help to reduce the inversion errors of existing methods. Time-lapse upgoing waves and downgoing waves from two-component datasets were utilized to efficiently monitor the area between the wells and provide a quick indication of possible CO2 leakage. The resulting mean velocity changes versus the depth indicated the depth where velocity changes occurred. Combining the upgoing and downgoing wavefields provided a more specific indication of the depth range for changes. The calculated velocity changes were determined using the time shift between the time-lapse wavefields caused by CO2 injection/leakage. Hence, the resulting velocity changes were closely related to the ratio of propagation path length through the CO2 injection/leakage layer over the length of the entire travel path. The results indicated that the noise level and repeatability of the time-lapse datasets significantly influenced the results generated using CWI. Therefore, denoising and time-lapse processing were very important for improving the detectability of any change. Applying CWI to time-lapse cross-well surveys can be an effective tool for monitoring CO2 in the subsurface at a relatively low computational cost. As a highly efficient monitoring method, it is sensitive to changes in the seismic response caused by velocity changes in the subsurface and provides additional constraints on the inversion results from conventional travel time tomography and full waveform inversion.

Effect of the incident angle of a transmitting laser light on the coverage of a NLOS-FSO network

In this paper, we propose a model of the coverage and achievable data rates in No Line-of-Sight Free-Space Optical Communications (NLOS-FSOC) as a function of the angle of incidence. NLOS-FSOC uses diffuse reflected light to establish communication between two or more stations that are with or without line-of-sight to each other. Different from free-space optical communications (FSOC), NLOS-FSOC uses a diffuse reflector (DR) between a transmitter and a receiver so that LOS is not required between them but between the station and the DR. Unlike a mirror, the DR reflects the incident light to all directions but to itself and that reflection broadcast the optical channel to all receivers within LOS. The optical broadcast channel establishes a true optical local area network (OLAN). However, the reflected power and the coverage of an OLAN largely depend on the angle of incidence of transmitted laser beam. Therefore, the planning and building of an OLAN with NLOS-FSOC must consider this angle to optimize coverage, to set range, or to estimate the achievable communication data rates.The proposed model and presented analysis center on an outdoor urban setting where mobile stations, represented by cars, travel through a city street. In such scenario, we estimate the average reflected power at the DR, the received power at different locations of the covered area, and their achievable communication data rates for downlink and uplink communications. With the consideration of mobile stations, we identify different displacement configurations that represent the different traveling paths of a mobile station with respect to a DR configuration on the urban scenario. Our extensive numerical evaluations on the different traveling and location scenarios show the effect that the incidence angle has on the coverage, the achievable data rates on an OLAN, and highlight the pros and cons of each different displacement. These results also show the options for the placement and orientation of the DR and ground optical base stations for an effective and extensive coverage and the signal quality of transmissions made by mobile stations traveling through the covered area in an NLOS-FSOC OLAN.

Algorithm to Correct Measurement Offsets Introduced by Inactive Elements of Transducer Arrays in Ultrasonic Flow Metering

Ultrasonic flow meters (UFMs) based on transducer arrays offer several advantages. With electronic beam steering, it is possible to tune the steering angle of the beam for optimal signal-tonoise ratio (SNR) upon reception. Moreover, multiple beams can be generated to propagate through different travel paths, covering a wider section of the flow profile. Furthermore, in a clamp-on configuration, UFMs based on transducer arrays can perform self-calibration. In this manner, userinput is minimized and measurement repeatability is increased. In practice, transducer array elements may break down. This could happen due to aging, exposure to rough environments, and/or rough mechanical contact. As a consequence of inactive array elements, the measured transit time difference contains two offsets. One offset originates from non-uniform spatial sampling of the generated wavefield. Another offset originates from the ill-defined beam propagating through a travel path different from the intended one. In this paper, an algorithm is proposed that corrects for both of these offsets. The algorithm also performs a filtering operation in the frequency-wavenumber domain of all spurious (i.e., flow-insensitive) wave modes. The advantage of implementing the proposed algorithm is demonstrated on simulations and measurements, showing improved accuracy and precision of the transit time differences compared to the values obtained when the algorithm is not applied. The proposed algorithm can be implemented in both in-line and clamp-on configuration of UFMs based on transducer arrays.

Self-replicating hierarchical modular robotic swarms

Modular robotic systems built of reconfigurable components offer an efficient and versatile alternative to traditional monolithic robots. However, as modular systems scale up, construction efficiency is compromised due to an increase in travel time and path planning complexity. Here we introduce a discrete modular material-robot system that is capable of serial, recursive (making more robots), and hierarchical (making larger robots) assembly. This is accomplished by discretizing the construction into a feedstock of simple primitive building blocks which can be re-configured to create a wide range of functionality. The discretization significantly simplifies the swarm’s navigation, error correction, and coordination. The component composition is supported by an algorithm to compile the building blocks into swarms and plan the optimal construction path. Our approach challenges the convention that larger constructions need larger machines to build them, and could be applied in areas that today either require substantial capital investments for fixed infrastructure or are altogether unfeasible.

Use of a drone-based sensor as a field-ready technique for short-term concentration mapping of air pollutants: A modeling study

While a network of low-cost sensors (LCS) boosts the capability in monitoring of air quality as covering a wide area, its fixed positioning hinders pinpointing of an unknown emitting source, its accuracy is variable over time, and its operation requires more periodic calibration than the USEPA's reference monitors. Alternatively, for short-term concentration mapping and regulatory compliance assessment, a drone equipped with a single reference sensor to detect the target air pollutant may provide a highly accurate concentration mapping tool as it offers flexibility to maneuver over hard-to-access terrains while addressing the abovementioned limitations. In this modeling study, we focused on a hypothetical point source emitting a certain air pollutant steadily inside a 1 km by 1 km study area. With respect to true concentrations generated from such source using USEPA's SCREEN3 Gaussian dispersion model and an inverse distance weighing (IDW) approach, we developed R and Python scripts to plot concentration and reliability maps for when a drone-based reference sensor/a stationary network of LCS is deployed to reconstruct the concentration maps. First, we compared the impact of the drone flight path on 1-hr-averaged concentration mapping of an air pollutant for locating a hidden point source or concentration accuracy determination at certain regions. Then, we conducted sensitivity analyses on the drone-based mapping reliability under different number of drone passes, wind speeds, and wind directions. Our results showed that compared to S-, N-, Z-, and diagonal-shape drone travel paths for the same travel total time, the time-averaged mapping accuracy of a zigzag drone flight is the best for pinpointing an unknown point source. For concentration mapping of known air polluting sources, which is intended to provide the utmost accuracy, an increase in the number of drone passes from the source to the downstream receptor points improves reliability of the projected dispersing plume. When flown under a windy condition (wind speeds above 3 m/s), concentration maps are underestimated for the most part, and the bias reduces when the drone travels in parallel to the wind direction. The outcomes of this study shed light on optimized development of the drone-based air quality sensors as proof-of-concept of a field-ready device to facilitate accurate short-term air quality monitoring or regulatory compliance of the air pollutants with hourly thresholds.

Research on travel path choice considering complex environment: theory, model and case

In this paper, considering the heterogeneity of travelers’ decision-making behavior caused by travel environment factors, thus affecting the choice of travel path, the theories and methods of travel path choice based on improved cumulative prospect theory (ICPT) in complex environment were proposed. On the basis of cumulative prospect theory (CPT), the value function was improved, and the parameter value range was enlarged. The nonlinear curve of value function and weight function of cumulative prospect theory was fitted through thousands of data tests and experiments. Then according to the decision preference, the decision makers were divided into different categories and the reference point value relationship of heterogeneous decision makers was found. In this paper, fuzzy travel time reference point and periodic dynamic risk degree reference point were set up, and a dynamic path selection model based on heterogeneous double reference point was established to improve the cumulative prospect value. Taking the highway network in Sichuan-Tibet region for example, the optimal path selection scheme of heterogeneous travel groups under the complex environmental factors such as debris flow and landslide in each time stage was studied, and the influence of preference parameter of travel time and risk degree on path choice was analyzed, and then the parameter sensitivity in the cumulative prospect theory (ICPT) was analyzed. The research results verified the rationality of the improved theory and method proposed in this study, which not only provide a new way of thinking for the study of travel path choice in complex environment but also provide theoretical guidance value for supporting regional traffic planning and construction in complex environment.

Empirical correlations between an FAS non-ergodic ground motion model and a GIT derived model for Central Italy

SUMMARY In this study, we investigate the correlation between the residuals of a neGMM (non-ergodic Ground Motion Model) and the physics-based parameters obtained using a non-parametric GIT approach (Generalized Inversion Technique) to lay the groundwork for the implementation of an ad-hoc FAS (Fourier Amplitude Spectra) neGMM for the Central Italy region. This region is particularly suitable for data-driven methodologies as those applied in this work because of the large amount of available data due to the recent multiple main shock–aftershock sequences occurred in this area. Both neGMM and GIT models are developed for Fourier spectra in the frequency range between 0.5 and 25 Hz and using the same reference sites. The comparison of the non-ergodic terms with the source, path and site spectral parameters provides interesting results. First, we find a strong correlation between the source parameters, stress drop Δσ and decay ${k}_{\mathrm{ source}}$ and the source neGMM corrective terms (the combination of the between-event δBe and the location-to-location terms δL2L). This correlation is frequency dependent and, at high frequency, is remarkably positive for Δσ and negative for ${k}_{\mathrm{ source}}$. Concerning the attenuation terms, the path-to-path residuals (δP2P) are clearly associated with the deviations from the regional Q estimates obtained from GIT analysis. This indicates that the neGMM properly captures the properties of the anelastic attenuation and that the corrective terms δP2P can be used to account for differences in travel paths across different crustal domains. Finally, adopting the same reference sites for neGMM and non-parametric GIT, we observe that the systematic site terms (δS2Ss) and the GIT-derived amplification functions are in good agreement. The next step for an appropriate modelling is to identify the physical parameters (e.g. VS,30 and ${k}_0$) describing the empirical amplification curves to be introduced as explanatory variables in the ground motion model.

An Approach for Autonomous Feeding Robot Path Planning in Poultry Smart Farm.

In order to solve the problems of poor feeding environment, untimely feeding and high labor demand in poultry smart farms, the development of feeding robots is imminent, while the research on path planning algorithms is an important part of developing feeding robots. The energy consumption of the feeding robot is one of the important elements of concern in the process of path planning. In this study, the shortest path does not mean that the feeding robot consumes the least energy, because the total mass of the feeding robot keeps changing during the feeding process. It is necessary to find the most suitable path so that the feeding robot consumes the lowest amount of energy during the feeding process. A branch and bound algorithm to calculate the minimum energy consumption travel path for small-scale buckets lacking feed is proposed. The lower bound of the branch and bound on the energy consumption is obtained by the approach of preferred selection of the set of shortest edges combined with the sequence inequality, and the upper bound could be obtained based on Christofides's Heuristic algorithm. A double-crossover operator genetic algorithm based on an upper bound on energy consumption for large-scale buckets lacking feed is proposed, and different crossover operations are performed according to the relationship between the fitness value and the upper bound of energy consumption in order to find a better path. The experiment results show that the approach proposed in this study is efficient; for small-scale buckets lacking feed, a branch and bound algorithm could calculate the minimum energy consumption path of 17 points in 300 s, and for large-scale buckets lacking feed, a double-crossover operator genetic algorithm based on an upper bound on energy consumption could calculate the minimum energy consumption travel path within 30 points in 60 s. The result is more accurate compared to the genetic algorithm with a single crossover operator.

A Stochastic Dynamic Traffic Assignment Model for Emergency Evacuations That Considers Background Traffic

In this work, we present a stochastic dynamic traffic assignment model for emergency evacuations that considers background traffic. First, the equilibrium functions of the entry time and path choice are formulated based on the logit model. The constraints of this formulation include the state equation, propagation function, and conservation. The proposed equilibrium functions are formulated as a variational inequality problem, which is solved by the dynamic traffic network demand loading iterative method. Based on a case study in Wenling, China, we verify the proposed model on the basis of iterative evolution, path assignment, and model comparison. In addition, we perform sensitivity analysis of four relevant parameters, namely, the length of the time interval, total number of evacuation vehicles, perception error parameters of the total travel cost, and path travel cost. The results make it evident that the proposed model assists evacuation planners to effectively understand real-time dynamic changes of evacuation vehicles and the influence of background vehicles and to generate optimal emergency plans.

Unity Engine 기반 수중 로봇 3차원 포지셔닝 프로그램 구현

A number of studies related to underwater robots are being conducted to utilize marine resources. However, unlike ordinary drones, underwater robots have a problem that it is not easy to locate because the medium is water, not air. The monitoring and positioning program of underwater robots, an existing study for identifying underwater locations, has difficulty in locating and monitoring in small spaces because it aims to be utilized in large spaces. Therefore, in this paper, we propose a three-dimensional positioning program for continuous monitoring and command delivery in small spaces. The proposed program consists of a multi-dimensional positioning monitoring function and a ability to control the path of travel through a three-dimensional screen so that the depth of the underwater robot can be identified. Through the performance evaluation, a robot underwater could be monitored and verified from various angles with a 3D screen, and an error within the assumed range was verified as the difference between the set path and the actual position is within 6.44 m on average.

HUMAN MACHINE INTERFACING VIA PERIPHERAL SENSORY NEURON STIMULATION

Electronics Travels Aids (ETAs) are electronic devices that are created to help the blind navigate their environment. To help the visually impaired people to navigate the environment, this paper seeks to address the following goals: • Detect object in path of travel • Detect motion of object • Detect horizontal • Detect vertical location of object • Detect shape of object Brail Vision consists of a belt of vibro-motor actuators which will be mounted to user’s head, and an android phone as the processing unit and camera. The ETA was mainly developed to enable experimentation with the algorithm proposed which is described in detail in this paper. The proposed system managed to meet 80% of the targets. The paper details how the proposed system was implemented and tested.

A Hybrid DNN Model for Travel Time Estimation from Spatio-Temporal Features

Due to recent advances in the Vehicular Internet of Things (VIoT), a large volume of traffic trajectory data has been generated. The trajectory data is highly unstructured and pre-processing it is a very cumbersome task, due to the complexity of the traffic data. However, the accuracy of traffic flow learning models depends on the quantity and quality of preprocessed data. Hence, there is a significant gap between the size and quality of benchmarked traffic datasets and the respective learning models. Additionally, generating a custom traffic dataset with required feature points in a constrained environment is very difficult. This research aims to harness the power of the deep learning hybrid model with datasets that have fewer feature points. Therefore, a hybrid deep learning model that extracts the optimal feature points from the existing dataset using a stacked autoencoder is presented. Handcrafted feature points are fed into the hybrid deep neural network to predict the travel path and travel time between two geographic points. The chengdu1 and chengdu2 standard reference datasets are used to realize our hypothesis of the evolution of a hybrid deep neural network with minimal feature points. The hybrid model includes the graph neural networks (GNN) and the residual networks (ResNet) preceded by the stacked autoencoder (SAE). This hybrid model simultaneously learns the temporal and spatial characteristics of the traffic data. Temporal feature points are optimally reduced using Stacked Autoencoder to improve the accuracy of the deep neural network. The proposed GNN + Resnet model performance was compared to models in the literature using root mean square error (RMSE) loss, mean absolute error (MAE) and mean absolute percentile error (MAPE). The proposed model was found to perform better by improving the travel time prediction loss on chengdu1 and chengdu2 datasets. An in-depth comprehension of the proposed GNN + Resnet model for predicting travel time during peak and off-peak periods is also presented. The model’s RMSE loss was improved up to 22.59% for peak hours traffic data and up to 11.05% for off-peak hours traffic data in the chengdu1 dataset.

Image-domain DAS 3D VSP elastic transmission tomography

SUMMARY Full-wavefield elastic imaging of active-source seismic data acquired by downhole receivers commonly offers higher-resolution subsurface images in the vicinity of a borehole compared to conventional surface seismic data sets, which can lack higher-frequency wavefield components due to longer travel paths and increased attenuation. An increasingly used approach for downhole acquisition is vertical seismic profiling (VSP), which has become more attractive when coupled with distributed acoustic sensing (DAS) using optical fibres installed in wells. The main difficulty for generating high-quality images with full-wavefield imaging tools for DAS VSP data, though, is the need for an accurate velocity model. To build plausible velocity models using active-source DAS VSP data, we adopt a 3-D image-domain elastic transmission tomography technique, originally developed for surface-recorded passive (microseismic) data, by exchanging the source and receiver positions (i.e. reciprocity) to mimic a passive-seismic surface monitoring scenario. The inversion approach exploits various images for each source constructed through time-reverse imaging (TRI) of downgoing P- and S-wave first-arrival waveforms. The TRI process uses the kinetic term of the (extended) PS energy imaging condition that exhibits sufficient sensitivity to velocity model errors. The method automatically updates the P- and S-wave velocity models to optimize image focusing via adjoint-state inversion. We illustrate the efficacy of the adopted elastic inversion technique using an active-source DAS 3-D VSP field data set acquired in the North Slope of Alaska. The numerical experiments demonstrate that the inverted elastic velocity models can be further used in full-wavefield acoustic/elastic imaging algorithms to obtain accurate subsurface images.

Influential factors to aircraft taxi time in airport

Operation of aircraft in the airport movement area is a major source of fuel combustion and emission, and has a great influence on aircraft exit time, fuel cost, and labor cost. Slots are calculated according to runway capacity, mooring capacity, terminal capacity, and control capacity, but aircraft flow in climate or mobile areas is not considered. This study proposes a model to explain a taxi time in an airport with influential factors such as airport weather (wind direction, wind speed, visibility, air pressure, precipitation), number of take-off and landing flights, number of aircraft moving in the moving area, runway occupation time for arrival, runway occupation time for departure, take-off and landing direction, and terminal location. In this study, the factors influencing aircraft movement are analyzed using data from Gimpo Airport and Jeju Airport in 2019. Result shows that taxi-in-time and taxi-out time are affected by wind speed, air pressure, and precipitation, especially among weather variables, the number of arrival flights by time, and departure flights before takeoff. The runway occupancy time, the take-off and landing direction, and the terminal location shows a significant factor to taxi hours. Gimpo Airport and Jeju Airport show a significant difference in taxi in and taxi out time. It is expected that these results can contribute to systematically and scientifically calculating aircraft flow while considering moving areas and weather. This study can help optimize the landing runway, landing direction, and travel path and time of the aircraft.

RESEARCH ON EMERGENCY RESCUE RESPONSE IN WENCHUAN COUNTY IN CHINA BASED ON BAIDU MAP NAVIGATION DATA

Abstract. Earthquake disasters often cause massive casualties and property losses, so it is essential to achieve rapid emergency rescue response. Although many scholars have studied the speed of emergency rescue response from different perspectives, there are still many problems in the impact of road congestion on travel paths and distances, as well as the timeliness of the road network. Therefore, this study calculated the travel distance from the rescue point to the disaster point using the path planning method based on the Baidu map navigation data, and obtained the distribution map of the emergency rescue response level in Wenchuan County, Sichuan Province, China. The results show that :(1) the path planning method based on Baidu map navigation data is more realistic and accurate than the traditional method. (2) there are apparent spatial differences in the emergency rescue response in Wenchuan County, and the emergency rescue response level in Weizhou town in the north is higher than that in Wolong and Sanjiang town in the southwest. The research results have significant reference value for planning emergency rescue routes and improving rescue speed in Wenchuan County and similar counties.

Optimization of multi-type sensor locations for simultaneous estimation of origin-destination demands and link travel times with covariance effects

This paper investigates the multi-type traffic sensor location problem for simultaneous estimation of origin-destination (OD) demands and link travel times while also considering the two sources of spatial covariance effects on a road network with uncertainties. The first source is the statistical correlation of the vehicular traffic demands for different OD pairs in a typical hourly period (e.g., morning peak hour) on a daily scale, as the travel demand patterns vary daily, weekly, and seasonally over the year. The second source is the stochastic nature of the link travel times on different road links during the peak hour period and their correlation with adjacent links in congested conditions. By considering these aspects, a novel model is formulated to optimize the number and locations of multi-type traffic sensors for simultaneous estimation of stochastic OD demands and link travel times during the same peak-hour period over a year. This estimation is supported by the data recorded by multi-type traffic sensors such as point sensors and automatic vehicle identification sensors, which yield the link speed/flow and path travel time information, respectively. Based on the integrated observations from multi-type traffic sensors, a novel Kullback–Leibler divergence-based model is developed to accommodate different probability distributions of OD demands and link travel times in different traffic conditions. Moreover, an improved firefly algorithm is developed to solve the multi-type sensor location problem. Specifically, the search strategy of this algorithm is enhanced by considering the mean and covariance of the OD demands and link travel times. Numerical examples of synthetic and real-world road networks are used to illustrate the applications and merits of the developed multi-type sensor location model for simultaneously estimating the OD demands and link travel times while also considering covariance effects.

Optimal shape for a rectangular warehouse with a lateral receive/ship dock

Purpose: This technical note provides the mathematical demonstration for obtaining the optimal aspect ratio for a rectangular storage area with a lateral receive/ship dock, representing the standard configuration of modern distribution centers and logistic warehouses. The proposed aspect ratio is the one that minimizes the travel times of operators, keeping the common assumption of a storage area having a uniform access probability.Design/methodology/approach: To obtain the optimal aspect ratio of the storage area we model the entry point of the uniformly distributed dock with a random variable with a continuous uniform distribution, and we consequently evaluate the average travel path of the operator as a function of the latter. Successively, we estimate and minimize the average roundtrip length of the operator, leading to the optimal aspect ratio of the storage area.Findings: We find that the optimal aspect ratio between the warehouse width (U) and length (V) equals 1.5. The obtained result shows that the operators’ travel times are minimized with a storage area where .Research limitations/implications: Warehouses with a dock on one side now represent modern distribution centers' standard configuration. However, no optimal aspect ratio for the storage area has been discussed. For this reason, the paper fills this lack of scientific literature in the warehouse optimization research field by providing indications on how to design this class of warehouses.Practical implications: Distribution managers may find here guidance for defining a proper design of logistics centers and evaluating the operators' actual travel times to perform a roundtrip within the storage area.Originality/value: Traditional warehouse shape optimization models assume a single input/output point to the storage area. To our knowledge, no formal demonstration has been proposed for a warehouse with a dock on one entire side.