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Mathematics Applied to Manufacturing and Logistics Systems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: closed (25 December 2025) | Viewed by 9486

Special Issue Editors


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Guest Editor
Department of Mechanical Engineering, ISEP–School of Engineering, Polytechnic of Porto, 4200-072 Porto, Portugal
Interests: tribology; coatings; manufacturing processes
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
Department of Mathematics of ISEP - School of Engineering, Polytechnic of Porto, 4200-465 Porto, Portugal
Interests: mathematics; algorithms; artificial intelligence
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This industry and the logistical operations surrounding this sector are of vital importance for the world’s economy, where competitiveness is fierce and the fight for the survival of companies hinges on innovation in terms of products and processes, as well as companies remaining at the forefront of products sought out by the market and at prices the market is willing to pay. Studies focusing on optimizing processes and operations have received particular attention from researchers as there is a pronounced lack of new solutions emerging from the industry. Mathematics plays a crucial role in this aspect, as optimization has always involved, and will certainly continue to involve, increasingly evolving mathematical models seeking to present new solutions to the industry, with ever-advancing rates of customization taking into account the specific challenges and needs of each industrial sector.

Based on these needs, this Special Issue aims to gather together highly innovative contributions in the area of mathematical modeling that responds in both more generic and more targeted ways to concrete challenges faced by the industry in its operations, which demonstrably represent added value in terms of global knowledge. Thus, works with different typologies will be accepted, including reviews of the state of the art, development of new models with a view to solving generic or specific problems faced by the industry, as well as case studies duly supported by theory and displaying innovation in the presented methodology. The aim is to concentrate a collection of contributions of high scientific quality that could form the basis for a future book that contains the most recent mathematical developments in the field of optimizing processes and operations across the most diverse sectors of industry.

Dr. Francisco J. G. Silva
Prof. Dr. Luís Pinto Ferreira
Dr. Isabel Cristina Mendes Pinto
Guest Editors

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Keywords

  • mathematical models
  • processes optimization
  • industrial management
  • logistics optimization
  • sustainability
  • costs reduction
  • quality optimization
  • process flow optimization
  • internal logistics optimization
  • external logistics optimization
  • optimization algorithms
  • industrial operations
  • robot path optimization
  • information flow optimization
  • optimization of the industry digitalization
  • case studies

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Published Papers (4 papers)

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Research

27 pages, 919 KB  
Article
A Mixed-Integer Linear Programming Framework for Multi-Period Offshore Wind Personnel Logistics: Integrating Routing, Scheduling, and Personnel Inventory Management
by Yunxiang Shu, Yu Guo, Yuquan Du and Shuaian Wang
Mathematics 2026, 14(6), 978; https://doi.org/10.3390/math14060978 - 13 Mar 2026
Cited by 1 | Viewed by 499
Abstract
The offshore wind energy sector faces significant logistics costs due to complex maritime environments. This study addresses the multi-period Crew Transfer Vessel routing within offshore wind farms and scheduling problems through a novel mixed-integer linear programming framework. The model integrates personnel inventory management [...] Read more.
The offshore wind energy sector faces significant logistics costs due to complex maritime environments. This study addresses the multi-period Crew Transfer Vessel routing within offshore wind farms and scheduling problems through a novel mixed-integer linear programming framework. The model integrates personnel inventory management with dynamic service times. It determines optimal routing and scheduling plans to minimise total operational costs. Numerical experiments demonstrate the effectiveness of the approach. The results indicate that increasing vessel capacity from 8 to 20 reduces total expenses by approximately 80%. Moreover, shifting from single-trip to multi-trip operations decreases fixed charter costs by 30%. The computational performance is efficient, and the solver achieves optimal solutions within an average of 5.67 s. This framework provides operators with precise decision support for complex offshore wind farm maintenance scenarios. Full article
(This article belongs to the Special Issue Mathematics Applied to Manufacturing and Logistics Systems)
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33 pages, 2618 KB  
Article
Strategic Fleet Planning Under Carbon Tax and Fuel Price Uncertainty: An Integrated Stochastic Model for Fleet Deployment and Speed Optimization
by Weilin Sun, Ying Yang and Shuaian Wang
Mathematics 2026, 14(1), 66; https://doi.org/10.3390/math14010066 - 24 Dec 2025
Viewed by 662
Abstract
This paper presents a two-stage stochastic programming model for the joint optimization of fleet deployment and sailing speed in liner shipping under fuel price volatility and carbon tax uncertainty. The integrated framework addresses strategic fleet planning by determining optimal fleet composition in the [...] Read more.
This paper presents a two-stage stochastic programming model for the joint optimization of fleet deployment and sailing speed in liner shipping under fuel price volatility and carbon tax uncertainty. The integrated framework addresses strategic fleet planning by determining optimal fleet composition in the first stage, while the second stage optimizes operational decisions, including vessel assignment to routes and sailing speeds on individual voyage legs, after observing stochastic parameter realizations. The model incorporates nonlinear fuel consumption functions that are approximated using piecewise linearization techniques, with the resulting formulation being solved using the Sample Average Approximation (SAA) method. To enhance computational tractability, we employ big-M methods to linearize mixed-integer terms and introduce auxiliary variables to handle nonlinear relationships in both the objective function and constraints. The proposed model provides shipping companies with a comprehensive decision-support tool that effectively captures the complex interdependencies between long-term strategic fleet planning and short-term operational speed optimization. Numerical experiments demonstrate the model’s effectiveness in generating optimal solutions that balance economic objectives with environmental considerations under uncertain market conditions, highlighting its practical value for resilient shipping operations in volatile fuel and carbon pricing environments. Full article
(This article belongs to the Special Issue Mathematics Applied to Manufacturing and Logistics Systems)
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30 pages, 1039 KB  
Article
Enabling Sustainable Diffusion in Supply Chains Through Industry 5.0: An Impact Analysis of Key Enablers for SMEs in Emerging Economies
by Chih-Hung Hsu, Jian-Cen Liu, Xue-Qing Cai, Ting-Yi Zhang and Wan-Ying Lv
Mathematics 2024, 12(24), 3938; https://doi.org/10.3390/math12243938 - 14 Dec 2024
Cited by 9 | Viewed by 3084
Abstract
Industry 5.0 (I5.0) builds upon Industry 4.0 by emphasizing the role of workers in production processes and prioritizing socio-economic-environmental sustainability. It has been shown that I5.0 can enhance sustainability within supply chains (SCs). However, companies in emerging economies, especially small and medium-sized manufacturing [...] Read more.
Industry 5.0 (I5.0) builds upon Industry 4.0 by emphasizing the role of workers in production processes and prioritizing socio-economic-environmental sustainability. It has been shown that I5.0 can enhance sustainability within supply chains (SCs). However, companies in emerging economies, especially small and medium-sized manufacturing enterprises (SMEs), which are crucial to developing economies, face challenges in implementing these concepts. These SMEs are in the early stages of adopting I5.0 to foster sustainability in their SCs and require urgent identification of key I5.0 enablers. Unfortunately, the current literature lacks research on this topic specifically within the context of SMEs in emerging economies. To bridge this gap, this study identifies the enablers of I5.0 that promote sustainability diffusion in SCs, using China’s SME manufacturing sector as a case study. The integrated framework for applying multiple criteria decision-making (MCDM) techniques in this study aims to assist decision-makers in evaluating different options and making optimal choices in a systematic and structured manner when faced with complex situations. The study employs the fuzzy Delphi method (FDM) to identify 15 key I5.0 enablers and categorize them into three clusters. Grey-DEMATEL is subsequently utilized to determine the causal relationships, rank the importance of the enablers, and construct an interrelationship diagram. This study found that ‘availability and functionality of resources’; ‘top management support, active participation, and effective governance’; ‘support from government, regulators, and financial resources’; and ‘introduction of safer and more efficient robotic systems for human–robot interaction and collaboration’ serve as the primary means of resolving issues. Overall, this study helps managers, practitioners, and policymakers interested in I5.0 applications to promote sustainability in the supply chain. Full article
(This article belongs to the Special Issue Mathematics Applied to Manufacturing and Logistics Systems)
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17 pages, 2553 KB  
Article
Pallet Loading Problem: A Case Study in the Automotive Industry Applying a Simplified Mathematical Model
by Naiara P. V. Sebbe, Francisco J. G. Silva, Alcinda M. S. Barreiras, Isabel M. Pinto, Rita C. M. Sales-Contini, Luis P. Ferreira and Ana B. M. Machado
Mathematics 2024, 12(7), 984; https://doi.org/10.3390/math12070984 - 26 Mar 2024
Cited by 2 | Viewed by 3763
Abstract
Logistics and the supply chain are areas of great importance within organizations. Due to planning gaps, an increase in extra and unnecessary transport costs is usually observed in several companies due to their commercial commitments and need to comply with the delivery time [...] Read more.
Logistics and the supply chain are areas of great importance within organizations. Due to planning gaps, an increase in extra and unnecessary transport costs is usually observed in several companies due to their commercial commitments and need to comply with the delivery time and the batch quantity of products, leading to a negative economic impact. Thus, the objective of this work was to adjust an optimization model to maximize the shipments usually carried out by the companies. To validate the model, an automotive components manufacturer was selected, allowing us to apply the model to a real case study and evaluate the advantages and drawbacks of this tool. It was found that the company to validate the model exports most of its products, and most pallets sent are not fully optimized, generating excessive expense for the company in terms of urgent transport. To solve this problem, two mathematical optimization models were used for the company’s current reality, optimizing the placement of boxes per pallet and customer. With the use of the new tool, it was possible to determine that five pallets should be sent to the customer weekly, which correspond to their needs, and that have the appropriate configurations so that the pallet is sent completely. Full article
(This article belongs to the Special Issue Mathematics Applied to Manufacturing and Logistics Systems)
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