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19 pages, 1159 KiB  
Article
A Biased–Randomized Iterated Local Search with Round-Robin for the Periodic Vehicle Routing Problem
by Juan F. Gomez, Antonio R. Uguina, Javier Panadero and Angel A. Juan
Mathematics 2025, 13(15), 2488; https://doi.org/10.3390/math13152488 (registering DOI) - 2 Aug 2025
Abstract
The periodic vehicle routing problem (PVRP) is a well-known challenge in real-life logistics, requiring the planning of vehicle routes over multiple days while enforcing visitation frequency constraints. Although numerous metaheuristic and exact methods have tackled various PVRP extensions, real-world settings call for additional [...] Read more.
The periodic vehicle routing problem (PVRP) is a well-known challenge in real-life logistics, requiring the planning of vehicle routes over multiple days while enforcing visitation frequency constraints. Although numerous metaheuristic and exact methods have tackled various PVRP extensions, real-world settings call for additional features such as depot configurations, tight visitation frequency constraints, and heterogeneous fleets. In this paper, we present a two-phase biased–randomized algorithm that addresses these complexities. In the first phase, a round-robin assignment quickly generates feasible and promising solutions, ensuring each customer’s frequency requirement is met across the multi-day horizon. The second phase refines these assignments via an iterative search procedure, improving route efficiency and reducing total operational costs. Extensive experimentation on standard PVRP benchmarks shows that our approach is able to generate solutions of comparable quality to established state-of-the-art algorithms in relatively low computational times and stands out in many instances, making it a practical choice for real life multi-day vehicle routing applications. Full article
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29 pages, 1659 KiB  
Article
A Mixed-Integer Programming Framework for Drone Routing and Scheduling with Flexible Multiple Visits in Highway Traffic Monitoring
by Nasrin Mohabbati-Kalejahi, Sepideh Alavi and Oguz Toragay
Mathematics 2025, 13(15), 2427; https://doi.org/10.3390/math13152427 - 28 Jul 2025
Viewed by 281
Abstract
Traffic crashes and congestion generate high social and economic costs, yet traditional traffic monitoring methods, such as police patrols, fixed cameras, and helicopters, are costly, labor-intensive, and limited in spatial coverage. This paper presents a novel Drone Routing and Scheduling with Flexible Multiple [...] Read more.
Traffic crashes and congestion generate high social and economic costs, yet traditional traffic monitoring methods, such as police patrols, fixed cameras, and helicopters, are costly, labor-intensive, and limited in spatial coverage. This paper presents a novel Drone Routing and Scheduling with Flexible Multiple Visits (DRSFMV) framework, an optimization model for planning drone-based highway monitoring under realistic operational constraints, including battery limits, variable monitoring durations, recharging at a depot, and target-specific inter-visit time limits. A mixed-integer nonlinear programming (MINLP) model and a linearized version (MILP) are presented to solve the problem. Due to the NP-hard nature of the underlying problem structure, a heuristic solver, Hexaly, is also used. A case study using real traffic census data from three Southern California counties tests the models across various network sizes and configurations. The MILP solves small and medium instances efficiently, and Hexaly produces high-quality solutions for large-scale networks. Results show clear trade-offs between drone availability and time-slot flexibility, and demonstrate that stricter revisit constraints raise operational cost. Full article
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25 pages, 3182 KiB  
Article
From Efficiency to Safety: A Simulation-Based Framework for Evaluating Empty-Container Terminal Layouts
by Cristóbal Vera-Carrasco, Cristian D. Palma and Sebastián Muñoz-Herrera
J. Mar. Sci. Eng. 2025, 13(8), 1424; https://doi.org/10.3390/jmse13081424 - 26 Jul 2025
Viewed by 241
Abstract
Empty container depot (ECD) design significantly impacts maritime terminal efficiency, yet traditional evaluation approaches assess limited operational factors, constraining comprehensive performance optimization. This study develops an integrated discrete event simulation (DES) framework that simultaneously evaluates lifting equipment utilization, truck turnaround times, and potential [...] Read more.
Empty container depot (ECD) design significantly impacts maritime terminal efficiency, yet traditional evaluation approaches assess limited operational factors, constraining comprehensive performance optimization. This study develops an integrated discrete event simulation (DES) framework that simultaneously evaluates lifting equipment utilization, truck turnaround times, and potential collisions to support terminal decision-making. This study combines operational efficiency metrics with safety analytics for non-automated ECDs using Top Lifters and Reach Stackers. Additionally, a regression analysis examines efficiency metrics’ effect on safety risk. A case study at a Chilean multipurpose terminal reveals performance trade-offs between indicators under different operational scenarios, identifying substantial efficiency disparities between dry and refrigerated container operations. An analysis of four distinct collision zones with varying historical risk profiles showed the gate area had the highest potential collisions and a strong regression correlation with efficiency metrics. Similar models showed a poor fit in other conflict zones, evidencing the necessity for dedicated safety indicators complementing traditional measures. This integrated approach quantifies interdependencies between safety and efficiency metrics, helping terminal managers optimize layouts, expose traditional metric limitations, and reduce safety risks in space-constrained maritime terminals. Full article
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39 pages, 17182 KiB  
Article
A Bi-Layer Collaborative Planning Framework for Multi-UAV Delivery Tasks in Multi-Depot Urban Logistics
by Junfu Wen, Fei Wang and Yebo Su
Drones 2025, 9(7), 512; https://doi.org/10.3390/drones9070512 - 21 Jul 2025
Viewed by 373
Abstract
To address the modeling complexity and multi-objective collaborative optimization challenges in multi-depot and multiple unmanned aerial vehicle (UAV) delivery task planning, this paper proposes a bi-layer planning framework, which comprehensively considers resource constraints, multi-depot coordination, and the coupling characteristics of path execution. The [...] Read more.
To address the modeling complexity and multi-objective collaborative optimization challenges in multi-depot and multiple unmanned aerial vehicle (UAV) delivery task planning, this paper proposes a bi-layer planning framework, which comprehensively considers resource constraints, multi-depot coordination, and the coupling characteristics of path execution. The novelty of this work lies in the seamless integration of an enhanced genetic algorithm and tailored swarm optimization within a unified two-tier architecture. The upper layer tackles the task assignment problem by formulating a multi-objective optimization model aimed at minimizing economic costs, delivery delays, and the number of UAVs deployed. The Enhanced Non-Dominated Sorting Genetic Algorithm II (ENSGA-II) is developed, incorporating heuristic initialization, goal-oriented search operators, an adaptive mutation mechanism, and a staged evolution control strategy to improve solution feasibility and distribution quality. The main contributions are threefold: (1) a novel ENSGA-II design for efficient and well-distributed task allocation; (2) an improved PSO-based path planner with chaotic initialization and adaptive parameters; and (3) comprehensive validation demonstrating substantial gains over baseline methods. The lower layer addresses the path planning problem by establishing a multi-objective model that considers path length, flight risk, and altitude variation. An improved particle swarm optimization (PSO) algorithm is proposed by integrating chaotic initialization, linearly adjusted acceleration coefficients and maximum velocity, a stochastic disturbance-based position update mechanism, and an adaptively tuned inertia weight to enhance algorithmic performance and path generation quality. Simulation results under typical task scenarios demonstrate that the proposed model achieves an average reduction of 47.8% in economic costs and 71.4% in UAV deployment quantity while significantly reducing delivery window violations. The framework exhibits excellent capability in multi-objective collaborative optimization. The ENSGA-II algorithm outperforms baseline algorithms significantly across performance metrics, achieving a hypervolume (HV) value of 1.0771 (improving by 72.35% to 109.82%) and an average inverted generational distance (IGD) of 0.0295, markedly better than those of comparison algorithms (ranging from 0.0893 to 0.2714). The algorithm also demonstrates overwhelming superiority in the C-metric, indicating outstanding global optimization capability in terms of distribution, convergence, and the diversity of the solution set. Moreover, the proposed framework and algorithm are both effective and feasible, offering a novel approach to low-altitude urban logistics delivery problems. Full article
(This article belongs to the Section Innovative Urban Mobility)
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20 pages, 1392 KiB  
Article
The Environmental Impact of Inland Empty Container Movements Within Two-Depot Systems
by Alaa Abdelshafie, May Salah and Tomaž Kramberger
Appl. Sci. 2025, 15(14), 7848; https://doi.org/10.3390/app15147848 - 14 Jul 2025
Viewed by 275
Abstract
Inefficient inland repositioning of empty containers between depots remains a persistent challenge in container logistics, contributing significantly to unnecessary truck movements, elevated operational costs, and increased CO2 emissions. Acknowledging the importance of this problem, a large amount of relevant literature has appeared. [...] Read more.
Inefficient inland repositioning of empty containers between depots remains a persistent challenge in container logistics, contributing significantly to unnecessary truck movements, elevated operational costs, and increased CO2 emissions. Acknowledging the importance of this problem, a large amount of relevant literature has appeared. The objective of this paper is to track the empty container flow between ports, empty depots, inland terminals, and customer premises. Additionally, it aims to simulate and assess CO2 emissions, capturing the dynamic interactions between different agents. In this study, agent-based modeling (ABM) was proposed to simulate the empty container movements with an emphasis on inland transportation. ABM is an emerging approach that is increasingly used to simulate complex economic systems and artificial market behaviours. NetLogo was used to incorporate real-world geographic data and quantify CO2 emissions based on truckload status and to evaluate the other operational aspects. Behavior Space was also utilized to systematically conduct multiple simulation experiments, varying parameters to analyze different scenarios. The results of the study show that customer demand frequency plays a crucial role in system efficiency, affecting container availability and logistical tension. Full article
(This article belongs to the Special Issue Green Transportation and Pollution Control)
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35 pages, 2008 KiB  
Article
From Simulation to Implementation: A Systems Model for Electric Bus Fleet Deployment in Metropolitan Areas
by Ludger Heide, Shuyao Guo and Dietmar Göhlich
World Electr. Veh. J. 2025, 16(7), 378; https://doi.org/10.3390/wevj16070378 - 5 Jul 2025
Viewed by 313
Abstract
Urban bus fleets worldwide face urgent decarbonization requirements, with Germany targeting net-zero emissions by 2050. Current electrification research often addresses individual components—energy consumption, scheduling, or charging infrastructure—in isolation, lacking integrated frameworks that capture complex system interactions. This study presents “eflips-X”, a modular, open-source [...] Read more.
Urban bus fleets worldwide face urgent decarbonization requirements, with Germany targeting net-zero emissions by 2050. Current electrification research often addresses individual components—energy consumption, scheduling, or charging infrastructure—in isolation, lacking integrated frameworks that capture complex system interactions. This study presents “eflips-X”, a modular, open-source simulation framework that integrates energy consumption modeling, battery-aware block building, depot–block assignment, terminus charger placement, depot operations simulation, and smart charging optimization within a unified workflow. The framework employs empirical energy models, graph-based scheduling algorithms, and integer linear programming for depot assignment and smart charging. Applied to Berlin’s bus network—Germany’s largest—three scenarios were evaluated: maintaining existing blocks with electrification, exclusive depot charging, and small batteries with extensive terminus charging. Electric fleets need 2.1–7.1% additional vehicles compared to diesel operations, with hybrid depot-terminus charging strategies minimizing this increase. Smart charging reduces peak power demand by 49.8% on average, while different charging strategies yield distinct trade-offs between infrastructure requirements, fleet size, and operational efficiency. The framework enables systematic evaluation of electrification pathways, supporting evidence-based planning for zero-emission public transport transitions. Full article
(This article belongs to the Special Issue Zero Emission Buses for Public Transport)
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14 pages, 4258 KiB  
Article
Implementation of Modular Depot Concept for Switchgrass Pellet Production in the Piedmont
by Jonathan P. Resop, John S. Cundiff and Shahabaddine Sokhansanj
AgriEngineering 2025, 7(6), 188; https://doi.org/10.3390/agriengineering7060188 - 12 Jun 2025
Viewed by 757
Abstract
In the bioenergy industry, highway hauling cost is typically 30%, or more, of the average cost of feedstock delivered to a biorefinery. Thus, truck productivity, in terms of Mg/d/truck, is a key issue in the design of a logistics system. One possible solution [...] Read more.
In the bioenergy industry, highway hauling cost is typically 30%, or more, of the average cost of feedstock delivered to a biorefinery. Thus, truck productivity, in terms of Mg/d/truck, is a key issue in the design of a logistics system. One possible solution to this problem that is being explored is the utilization of modular pellet depots. In such a logistics system, raw biomass (i.e., low-bulk-density product) is converted into pellets (i.e., high-bulk-density product) by several smaller-scale modular pellet depots instead of by a single larger-capacity pellet depot. A truckload of raw biomass (e.g., round bales) is 16 Mg and a load of pellets is 34 Mg. The distribution of depots across a feedstock production area can potentially have an impact on the total truck operating hours (i.e., raw biomass hauling to a depot + pellet hauling from the depot to the biorefinery) required to deliver feedstock for annual operation of a biorefinery. This study examined three different distributions of depots across five feedstock production areas. The numbers of depots were one, two, and four per production area for totals of five, ten, and twenty depots. Increasing the number of depots from five to ten reduced raw biomass hauling hours by 12%, and increasing from five to twenty reduced these hours by 30%. Total hauling hours (raw biomass + pellets) were reduced by less than 1% with an increase from five to ten and by about 11% with an increase from five to twenty. The modular pellet depot concept demonstrated potential for providing improvements to biorefinery logistics systems, but more research is needed to optimize this balance. Full article
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23 pages, 2072 KiB  
Article
Multi-Criteria Decision-Making of Hybrid Energy Infrastructure for Fuel Cell and Battery Electric Buses
by Zhetao Chen, Hao Wang, Warren J. Barry and Marc J. Tuozzolo
Energies 2025, 18(11), 2829; https://doi.org/10.3390/en18112829 - 29 May 2025
Viewed by 465
Abstract
This study evaluates four hybrid infrastructure scenarios for supporting battery electric buses (BEBs) and fuel cell electric buses (FCEBs), analyzing different combinations of grid power, solar energy, battery storage, and fuel cell systems. A multi-stage framework—comprising energy demand forecasting, infrastructure capacity planning, and [...] Read more.
This study evaluates four hybrid infrastructure scenarios for supporting battery electric buses (BEBs) and fuel cell electric buses (FCEBs), analyzing different combinations of grid power, solar energy, battery storage, and fuel cell systems. A multi-stage framework—comprising energy demand forecasting, infrastructure capacity planning, and multi-criteria decision-making (MCDM) evaluation incorporating total cost of ownership (TCO), carbon emissions, and energy resilience—was developed and applied to a real-world transit depot. The results highlight critical trade-offs between financial, environmental, and operational objectives. The limited rooftop solar configuration, integrating solar energy through a Solar Power Purchase Agreement (SPPA), emerges as the most cost-effective near-term solution. Offsite solar with onsite large-scale battery storage and offsite solar with fuel cell integration achieve greater sustainability and resilience, but they face substantial cost barriers. The analysis underscores the importance of balancing investment, emissions reduction, and resilience in planning zero-emission bus fleets. Full article
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30 pages, 2075 KiB  
Article
An Improved Large Neighborhood Search Algorithm for the Comprehensive Container Drayage Problem with Diverse Transport Requests
by Xuhui Yu and Cong He
Appl. Sci. 2025, 15(11), 5937; https://doi.org/10.3390/app15115937 - 25 May 2025
Cited by 1 | Viewed by 491
Abstract
Container drayage, as a pivotal element of door-to-door intermodal transportation, has garnered increasing attention due to its significant influence on container logistics costs. Although various types of transport requests have been defined in the literature, no comprehensive study has addressed all of them [...] Read more.
Container drayage, as a pivotal element of door-to-door intermodal transportation, has garnered increasing attention due to its significant influence on container logistics costs. Although various types of transport requests have been defined in the literature, no comprehensive study has addressed all of them together yet, due to the lack of an efficient model and corresponding algorithms. Furthermore, existing research on container drayage often neglects the simultaneous incorporation of two trucking operation modes, two empty container repositioning strategies, and the availability of empty containers across multiple depots. To address these issues, this study proposes a comprehensive container drayage problem (CDP) and mathematically formulates it as an innovative mixed integer linear programming (MILP) model, capturing the uncertainty and unpredictability inherent in empty container allocation, truck dispatching, and route planning. Given the problem’s complexity, obtaining an exact solution for large instances is not feasible. Therefore, an improved large neighborhood search (LNS) algorithm is tailored by incorporating the “Sequential insertion” and the “Solution re-optimization” operations. Extensive numerical experiments using randomly generated instances of varying scales validate the correctness of the proposed model and demonstrate the performance of the proposed algorithm. Additionally, sensitivity analysis on the number and distribution of depots and empty containers offers valuable managerial insights for the development of an effective container drayage system. Full article
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24 pages, 763 KiB  
Article
Electric Bus Scheduling Problem with Time Windows and Stochastic Travel Times
by Vladyslav Kost, Marilena Merakou and Konstantinos Gkiotsalitis
Information 2025, 16(5), 376; https://doi.org/10.3390/info16050376 - 30 Apr 2025
Viewed by 509
Abstract
This work develops a scheduling tool for electric buses that accounts for daily disruptions while minimizing the operational costs. The contribution of this study lies in the development of electric bus schedules that consider many factors, such as multiple depots, multiple charging stations, [...] Read more.
This work develops a scheduling tool for electric buses that accounts for daily disruptions while minimizing the operational costs. The contribution of this study lies in the development of electric bus schedules that consider many factors, such as multiple depots, multiple charging stations, and stochastic travel times, providing schedules resilient to extreme conditions. The developed model is a mixed-integer linear program (MILP) with chance constraints. The main decision variables are the assignment of electric vehicles to scheduled trips and charging events to ensure the improved operation of daily services under uncertain conditions. Numerical experiments and a sensitivity analysis based on the variation in travel times are conducted, demonstrating the performance of our solution approach. The results from these experiments indicate that the variant of the model with the chance constraint produces schedules with lower operational costs compared to the case where the chance constraints are not introduced. Full article
(This article belongs to the Special Issue Emerging Research in Optimization and Machine Learning)
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25 pages, 809 KiB  
Article
A Robust Optimization Approach for E-Bus Charging and Discharging Scheduling with Vehicle-to-Grid Integration
by Mingyu Kang, Bosung Lee and Younsoo Lee
Mathematics 2025, 13(9), 1380; https://doi.org/10.3390/math13091380 - 23 Apr 2025
Cited by 1 | Viewed by 564
Abstract
Electric buses (E-buses) are gaining popularity in urban transportation due to their environmental benefits and operational efficiency. However, large-scale integration of E-buses and Vehicle-to-Grid (V2G) technology introduces scheduling complexities for charging and discharging operations arising from uncertainties in energy consumption and load reduction [...] Read more.
Electric buses (E-buses) are gaining popularity in urban transportation due to their environmental benefits and operational efficiency. However, large-scale integration of E-buses and Vehicle-to-Grid (V2G) technology introduces scheduling complexities for charging and discharging operations arising from uncertainties in energy consumption and load reduction requests. While prior studies have explored electric vehicle scheduling, few have considered robust optimization for E-bus fleets under uncertain parameters such as trip energy consumption and load reduction requests. This paper proposes a robust optimization approach for the charging and discharging scheduling problem at E-bus depots equipped with V2G. The problem is formulated as a robust mixed-integer linear program (MILP), incorporating real-world operational constraints including dual-port chargers, emergency charging, and demand response. A budgeted uncertainty set is used to model uncertainty in energy consumptions and discharging requests, providing a balance between robustness and conservatism. To ensure tractability, the robust counterpart is reformulated into a solvable MILP using duality theory. The effectiveness of the proposed model is validated through extensive computational experiments, including simulation-based performance assessments and out-of-sample tests. Experiment results demonstrate superior profitability and reliability compared to deterministic and box-uncertainty models, highlighting the practical effectiveness of the proposed approach. Full article
(This article belongs to the Special Issue Mathematical Programming, Optimization and Operations Research)
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26 pages, 11513 KiB  
Article
Train-Induced Vibration Analysis and Isolation Trench Measures in Metro Depot Structures
by Shusong Zhao, Chenglin Lu, Jiaxu Shen and Mi Zhao
Appl. Sci. 2025, 15(8), 4219; https://doi.org/10.3390/app15084219 - 11 Apr 2025
Viewed by 538
Abstract
Many cities around the world are developing over-track buildings above metro depots to achieve efficient and economical land use. However, the vibrations generated by frequent train operations have a significant impact on the over-track buildings. Therefore, the analysis and control of vibrations at [...] Read more.
Many cities around the world are developing over-track buildings above metro depots to achieve efficient and economical land use. However, the vibrations generated by frequent train operations have a significant impact on the over-track buildings. Therefore, the analysis and control of vibrations at metro depots are of great importance. This paper focuses on the train-induced vibration propagation law and the application of vibration isolation trench measures of the over-track building in the metro depot. To this end, a typical metro depot is taken as the research object. The train-track model, used for simulating wheel-rail force, and the track-soil-building model, used for predicting structural response, are established, respectively. Then, the vibration response of the over-track building of the metro depot is explored, and the effects of vibration isolation measures of the open trench and infilled trench in the metro depot are studied. The results show that the train-induced vibration excitation of the metro is mainly concentrated in the range of 1 to 80 Hz, and the predominant frequency range of the floor vibration is 25 to 50 Hz. The vibration response of the floor is mainly affected by the stiffness. The larger the floor area, the smaller the vertical natural frequency, and the wider the range between the train vibration excitation areas, the more prone to resonance. In addition, the vibration isolation effect of the open trench is better than that of the infilled trench. The primary factor affecting the vibration isolation performance of open trenches is their depth; the influence of trench position and width on the vibration isolation performance is weaker compared to the depth. In the predominant frequency range of floor vibration, the overall vibration isolation effect of the flexible infilled trenches is better than that of the rigid infilled trenches. The main factor affecting the vibration isolation effect of the infilled trenches is the impedance ratio of the material. Among the six kinds of filling materials selected in this paper, the barrier effect of gravel is the worst, and the barrier effect of foam is the best. Using the measure of a foam infilled trench, Z-vibration levels of floors can be reduced by 8.6–13.9 dB. Full article
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29 pages, 1986 KiB  
Systematic Review
The Vehicle-Routing Problem with Satellites Utilization: A Systematic Review of the Literature
by Raúl Soto-Concha, John Willmer Escobar, Daniel Morillo-Torres and Rodrigo Linfati
Mathematics 2025, 13(7), 1092; https://doi.org/10.3390/math13071092 - 26 Mar 2025
Cited by 1 | Viewed by 1470
Abstract
The Vehicle-Routing Problem (VRP) represents a critical challenge in logistics, encompassing numerous variations, such as time window considerations, multi-depot systems, two-echelon routing aspects, and Satellite Locations (SL). SLs are intermediate facilities that support cross-docking, storage, and transshipment operations. However, inconsistencies in defining “satellite” [...] Read more.
The Vehicle-Routing Problem (VRP) represents a critical challenge in logistics, encompassing numerous variations, such as time window considerations, multi-depot systems, two-echelon routing aspects, and Satellite Locations (SL). SLs are intermediate facilities that support cross-docking, storage, and transshipment operations. However, inconsistencies in defining “satellite” have hindered precise research and implementation. This study presents a systematic review of the use of satellites for VRP, employing the PRISMA methodology to ensure a comprehensive and reproducible analysis. The findings indicate that about 50% of the reviewed papers include a path-splitting variant. At the same time, there is a notable gap in addressing random demands and pickup and delivery within cross-docking environments. A major limitation is the lack of a well-known public dataset, as about 50% of the datasets are created or adapted for specific studies. Additionally, the analysis reveals significant gaps in dataset standardization and the integration of dynamic routing under uncertainty. These findings underscore the potential of satellite-based systems to optimize urban logistics and supply chains while pointing to critical avenues for future research. Full article
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38 pages, 6647 KiB  
Article
Collaboration and Resource Sharing for the Multi-Depot Electric Vehicle Routing Problem with Time Windows and Dynamic Customer Demands
by Yong Wang, Can Chen, Yuanhan Wei, Yuanfan Wei and Haizhong Wang
Sustainability 2025, 17(6), 2700; https://doi.org/10.3390/su17062700 - 18 Mar 2025
Cited by 2 | Viewed by 761
Abstract
With increasingly diverse customer demands and the rapid growth of the new energy logistics industry, establishing a sustainable and responsive logistics network is critical. In a multi-depot logistics network, adopting collaborative distribution and resource sharing can significantly improve operational efficiency. This study proposes [...] Read more.
With increasingly diverse customer demands and the rapid growth of the new energy logistics industry, establishing a sustainable and responsive logistics network is critical. In a multi-depot logistics network, adopting collaborative distribution and resource sharing can significantly improve operational efficiency. This study proposes collaboration and resource sharing for a multi-depot electric vehicle (EV) routing problem with time windows and dynamic customer demands. A bi-objective optimization model is formulated to minimize the total operating costs and the number of EVs. To solve the model, a novel hybrid algorithm combining a mini-batch k-means clustering algorithm with an improved multi-objective differential evolutionary algorithm (IMODE) is proposed. This algorithm integrates genetic operations and a non-dominated sorting operation to enhance the solution quality. The strategies for dynamically inserting customer demands and charging stations are embedded within the algorithm to identify Pareto-optimal solutions effectively. The algorithm’s efficacy and applicability are verified through comparisons with the multi-objective genetic algorithm, the multi-objective evolutionary algorithm, the multi-objective particle swarm optimization algorithm, multi-objective ant colony optimization, and a multi-objective tabu search. Additionally, a case study of a new energy logistics company in Chongqing City, China demonstrates that the proposed method significantly reduces the logistics operating costs and improves logistics network efficiency. Sensitivity analysis considering different dynamic customer demand response modes and distribution strategies provides insights for reducing the total operating costs and enhancing distribution efficiency. The findings offer essential insights for promoting an environmentally sustainable and resource-efficient city. Full article
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23 pages, 1053 KiB  
Article
Task Planning of Multiple Unmanned Aerial Vehicles Based on Minimum Cost and Maximum Flow
by Xiaodong Shi, Xiangping Zhai, Rui Wang, Yi Le, Shuang Fu and Ningzhong Liu
Sensors 2025, 25(5), 1605; https://doi.org/10.3390/s25051605 - 5 Mar 2025
Viewed by 1029
Abstract
With the rapid development of UAV technology, UAV delivery has gained attention for its potential to reduce labor costs. However, limitations in load capacity and energy restrict UAVs’ distribution capabilities. This paper proposes a cooperative delivery scheme combining traditional trucks and UAVs to [...] Read more.
With the rapid development of UAV technology, UAV delivery has gained attention for its potential to reduce labor costs. However, limitations in load capacity and energy restrict UAVs’ distribution capabilities. This paper proposes a cooperative delivery scheme combining traditional trucks and UAVs to extend UAV coverage and improve delivery completion rates. For densely distributed depots in wide-area regions, we develop algorithms for task allocation and path planning in a truck-independent UAV system. Specifically, a minimum-cost, maximum-flow model is constructed to obtain sub-paths covering all delivery tasks, and resource tree-based algorithms are used to construct global paths for UAVs and trucks. Simulation results show that our algorithms reduce total energy consumption by 11.53% and 9.15% under different task points, which suggests that our proposed method can significantly enhance delivery efficiency, offering a promising solution for future logistics operations. Full article
(This article belongs to the Special Issue AI-IoT for New Challenges in Smart Cities)
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