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Mathematics
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Optimization and Mathematical Modelling in Transport and Logistics Network
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Optimization and Mathematical Modelling in Transport and Logistics Network

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 31 December 2026 | Viewed by 7249

Special Issue Editors

Prof. Dr. Libiao Bai

E-Mail Website
Guest Editor
School of Economics and Management, Chang'an University, Xi’an 710064, China
Interests: logistics engineering; information technology and data processing; construction management
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Victor Shi

E-Mail Website
Guest Editor
Lazaridis School of Business & Economics, Wilfrid Laurier University, Waterloo, ON N2L 3C5, Canada
Interests: supply chain management; management science; inventory management; operation research
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Transport and logistics networks are fundamental to modern economies, facilitating the efficient movement of goods and people across diverse regions. However, these networks face increasing pressure from growing demand, rapid urbanization, and environmental constraints. The need for a green and smart transformation of these systems has been urgent.

Achieving this transformation requires addressing the management challenges in the planning, location, and construction of transport infrastructure, as well as optimizing interconnected transport and logistics networks.

Optimization and mathematical modeling offer tools to address these issues, providing innovative solutions for the design, management, and improvement of transport and logistics networks. The aim of this Special Issue is to collect articles with innovative methods and unique perspectives in this field.

Topics of interest for this Special Issue include, but are not limited to, the following:

Logistics project management;

Low-carbon transportation and logistics;

Intelligent transportation and logistics management;

Dynamic and stochastic modeling;

Supply chain network design and optimization;

Data-driven and machine learning approaches;

Resilience and risk management.

We encourage submissions that provide novel insights, real-world applications, or comparative analyses of existing methods. Both theoretical and empirical studies are welcome, as are interdisciplinary works combining mathematics, operations research, and computer science.

Prof. Dr. Libiao Bai
Prof. Dr. Victor Shi
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • low-carbon management
  • sustainable logistics
  • transport infrastructure
  • network optimization
  • risk management
  • data-driven models
  • dynamic modeling

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Published Papers (5 papers)

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Research

28 pages, 2046 KB  
Article
Game-Theoretic Optimization of Shore Power Versus Low-Sulfur Fuel Strategies in Maritime Supply Chains Under a Cap-and-Trade Mechanism
by Yan Zhou, Haiying Zhou, Wenjuan Sui and Gongliang Zhang
Mathematics 2026, 14(3), 508; https://doi.org/10.3390/math14030508 - 31 Jan 2026
Cited by 1 | Viewed by 413
Abstract
In this study, we develop a game-theoretic optimization framework to analyze competing vessels’ technology choices between shore power (SP) and low-sulfur fuel oil (LSFO) within a maritime supply chain which is regulated by a cap-and-trade mechanism. Using a Stackelberg game approach, we construct [...] Read more.
In this study, we develop a game-theoretic optimization framework to analyze competing vessels’ technology choices between shore power (SP) and low-sulfur fuel oil (LSFO) within a maritime supply chain which is regulated by a cap-and-trade mechanism. Using a Stackelberg game approach, we construct two models—one port-led and the other vessel-led—to derive closed-form equilibrium for pricing, service quantities, profits, emissions, and social welfare. The results reveal three key findings. First, the leader in either Stackelberg structure always achieves higher profits, while total supply chain profits remain identical across power structures. Second, at low carbon prices, LSFO-equipped vessels provide more services and earn higher profits due to cost advantages. As the carbon price rises—which directly incentivizes emission reduction and accelerates maritime decarbonization—SP becomes more attractive and eventually dominates in profitability despite higher initial investment. Notably, although SP has lower unit emissions, its total emissions may surpass those of LSFO at certain carbon-price thresholds because the SP-equipped vessel optimally expands output. Third, intensified competition reduces service quantities, profits, and emissions, with a more substantial reduction effect on LSFO vessels. Overall, our results provide mathematically grounded insights for optimizing low-carbon technology adoption in maritime transport and offer actionable policy implications for carbon pricing that balance environmental objectives and supply chain efficiency. This research contributes specifically to the United Nations’ Sustainable Development Goals (SDGs), specifically SDG 13 (Climate Action) and SDG 9 (Industry, Innovation and Infrastructure). Full article
(This article belongs to the Special Issue Optimization and Mathematical Modelling in Transport and Logistics Network)
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40 pages, 4623 KB  
Article
A Vehicle Routing Problem Based on a Long-Distance Transportation Network with an Exact Optimization Algorithm
by Toygar Emre and Rızvan Erol
Mathematics 2025, 13(21), 3397; https://doi.org/10.3390/math13213397 - 24 Oct 2025
Cited by 1 | Viewed by 1665
Abstract
In vehicle routing problems, long-distance transportation poses a significant challenge to the optimization of transportation costs while adhering to regulations. This study investigates a special type of logistics problem that focuses on liquid transportation systems involving full truckload delivery and the rest–break–drive periods [...] Read more.
In vehicle routing problems, long-distance transportation poses a significant challenge to the optimization of transportation costs while adhering to regulations. This study investigates a special type of logistics problem that focuses on liquid transportation systems involving full truckload delivery and the rest–break–drive periods of truck drivers over long distances according to the regulations of the United States. Based on an exact solution algorithm, this work combines a long-distance full truckload fluid transportation problem with the concept of truck driver schedules for the first time. The goal is to optimize transportation expenses while managing challenges related to the rest–break–drive periods of truck drivers, time windows, trailer varieties, customer segments, food and non-food products, a diverse fleet, starting locations, and the diverse tasks of vehicles. In order to reach optimality, a construction heuristic and the column generation method were employed, supplemented by several acceleration strategies. Performance analysis, carried out with artificial input sets mirroring real-life scenarios, indicates that low optimality gaps can be obtained in an appropriate amount of time for large-scale long-haul liquid transportation. Full article
(This article belongs to the Special Issue Optimization and Mathematical Modelling in Transport and Logistics Network)
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20 pages, 1477 KB  
Article
Dynamic Signal Timing at Urban Intersections: Cycle-Based Delay Classification and Multi-Period Optimization
by Zhao Guo, Alexander Y. Krylatov and Dan Wang
Mathematics 2025, 13(21), 3386; https://doi.org/10.3390/math13213386 - 24 Oct 2025
Cited by 1 | Viewed by 1352
Abstract
This paper addresses the optimization of traffic signal timing at urban intersections by introducing a dynamic green ratio allocation framework based on cycle-based delay classification. Conventional methods such as the Webster delay model often fail to capture the asymmetric delay characteristics and the [...] Read more.
This paper addresses the optimization of traffic signal timing at urban intersections by introducing a dynamic green ratio allocation framework based on cycle-based delay classification. Conventional methods such as the Webster delay model often fail to capture the asymmetric delay characteristics and the impact of fluctuating flows across multiple cycles. We propose a novel approach that classifies cycles into undersaturated and oversaturated states and develops dedicated optimization models for each type. For undersaturated cycles, a new delay function is derived to accurately capture the interaction between queue dissipation and green time allocation, enabling multi-period minimization of total vehicle delay. For oversaturated cycles, queue minimization at the end of each phase is adopted to accelerate congestion dissipation. The framework is validated through simulation and compared with existing methods, demonstrating superior performance in congestion clearance and delay minimization. The results show improved adaptability to changing traffic conditions and enhanced practicality for real-time signal control in smart transportation systems. Full article
(This article belongs to the Special Issue Optimization and Mathematical Modelling in Transport and Logistics Network)
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29 pages, 3101 KB  
Article
Optimizing Efficiency for Logistics Training Using Virtual Reality Movies
by Qiaoling Zou, Xinyan Jiang, Xiangling Hu, Wanyu Zheng and Dongning Li
Mathematics 2025, 13(16), 2676; https://doi.org/10.3390/math13162676 - 20 Aug 2025
Cited by 1 | Viewed by 1116
Abstract
(1) Background: Traditional logistics training faces challenges like high costs, limited scalability, and safety risks. Virtual Reality Movie Training (VRMT) enhances operational accuracy, safety, and accessibility through immersive simulation. However, adoption faces barriers including high equipment costs, immature technology, and coordination challenges among [...] Read more.
(1) Background: Traditional logistics training faces challenges like high costs, limited scalability, and safety risks. Virtual Reality Movie Training (VRMT) enhances operational accuracy, safety, and accessibility through immersive simulation. However, adoption faces barriers including high equipment costs, immature technology, and coordination challenges among logistics enterprises, design companies, and government entities. This study explores strategic interactions to optimize VRMT adoption. (2) Methods: A tripartite evolutionary game model was used to analyze strategic interactions between logistics enterprises, design companies, and government. (3) Results: System stability occurs when logistics enterprises adopt VRMT, design companies deliver high-quality solutions, and government provides active support. Simulations reveal stronger adoption coefficients through increased employee acceptance and enhanced training quality. Government incentives and brand premiums significantly influence quality design provision, though excessive subsidies may reduce governmental willingness to support initiatives. (4) Conclusions: Cost minimization and accessibility improvement require batch hardware purchasing, optimized training cycles, and shared platforms at logistics enterprises. Design companies should optimize content development for cost-effectiveness while maintaining quality standards to leverage brand benefits. Governments should establish VRMT quality certification, invest in public VR platforms for SMEs, and convert accident savings into fiscal supplements. This tripartite collaboration enables efficient, safe, and sustainable logistics training transformation. Full article
(This article belongs to the Special Issue Optimization and Mathematical Modelling in Transport and Logistics Network)
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18 pages, 1929 KB  
Article
Low-Carbon Transport for Prefabricated Buildings: Optimizing Capacitated Truck–Trailer Routing Problem with Time Windows
by Jiajie Zhou, Qiang Du, Qian Chen, Zhongnan Ye, Libiao Bai and Yi Li
Mathematics 2025, 13(7), 1210; https://doi.org/10.3390/math13071210 - 7 Apr 2025
Cited by 2 | Viewed by 1344
Abstract
The transportation of prefabricated components is challenged by the particularity of large cargo transport and urban road conditions, restrictions on parking, height, and weight. To address these challenges and to promote low-carbon logistics, this paper investigates the transportation of prefabricated components by leveraging [...] Read more.
The transportation of prefabricated components is challenged by the particularity of large cargo transport and urban road conditions, restrictions on parking, height, and weight. To address these challenges and to promote low-carbon logistics, this paper investigates the transportation of prefabricated components by leveraging separable fleets of trucks and trailers. Focusing on real-world constraints, this paper formulates the capacitated truck and trailer routing problem with time windows (CTTRPTW) incorporating carbon emissions, and designs a dynamic adaptive hybrid algorithm combining simulated annealing with tabu search (DASA-TS) to solve this model. The efficiency and robustness of the methodology are validated through two computational experiments. The results indicate that the DASA-TS consistently demonstrates excellent performance across all evaluations, with significant reductions in both transportation costs and carbon emissions costs for prefabricated components, particularly in large-scale computational instances. This study contributes to promoting the optimization of low-carbon transport for prefabricated components, offering guidance for routing design involving complex and large cargo, and supporting the sustainable development of urban logistics. Full article
(This article belongs to the Special Issue Optimization and Mathematical Modelling in Transport and Logistics Network)
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