Mathematics

Research

23 pages, 5532 KiB

Open AccessArticle

A Collaborative Design Method for the Cylindrical Gear Paired with Skived Face Gears Driven by Contact Performances

by Zhenyu Zhou, Yuanyuan Zhang, Mou Li, Yuansheng Zhou, Zhongwei Tang, Jinyuan Tang and Liang Zhou

Mathematics 2025, 13(7), 1180; https://doi.org/10.3390/math13071180 - 3 Apr 2025

Viewed by 238

Abstract

Skiving is an efficient method for manufacturing face gears, but theoretical machining errors may occur when face gears designed for shaping or grinding are processed by skiving. This study presents a face gear directly designed for the skiving process, eliminating theoretical machining errors. [...] Read more.

Skiving is an efficient method for manufacturing face gears, but theoretical machining errors may occur when face gears designed for shaping or grinding are processed by skiving. This study presents a face gear directly designed for the skiving process, eliminating theoretical machining errors. Additionally, a new design approach for the cylindrical gear is proposed to pair with this face gear. The tooth surface models of both the cylindrical pinion and face gear are established. For the pinion, surface modifications are applied in both profile and longitudinal directions, while the face gear’s tooth surface model is tailored for the skiving process to avoid theoretical machining errors. The contact performance, including transmission error, contact stress, and contact pattern, is evaluated through Tooth Contact Analysis (TCA). An optimization model is developed to identify the optimal cylindrical gear tooth surface parameters, targeting improved contact performance. The proposed method is validated by a case study, which shows that the optimized face gear transmission results in lower maximum contact stress and reduced transmission error amplitude. Full article

(This article belongs to the Special Issue Advanced Applications of Mathematical Modeling and Optimization in Logistics and Manufacturing)

► Show Figures

Figure 1

29 pages, 6277 KiB

Open AccessArticle

Modeling and Exploratory Analysis of Discrete Event Simulations for Optimizing Overhead Hoist Transport Systems and Logistics in Semiconductor Manufacturing

by Jin-Hyeon Sung, Seong-Hyeon Ju, Seung-Wan Cho, Hak-Jong Joo, Kyung-Min Seo and Bong-Gu Kang

Mathematics 2025, 13(7), 1167; https://doi.org/10.3390/math13071167 - 2 Apr 2025

Viewed by 277

Abstract

The optimization of overhead hoist transport (OHT) systems in semiconductor manufacturing plays a crucial role in improving production efficiency. In this study, the development of a discrete event simulation model to analyze the physical and control characteristics of an OHT system is presented, [...] Read more.

The optimization of overhead hoist transport (OHT) systems in semiconductor manufacturing plays a crucial role in improving production efficiency. In this study, the development of a discrete event simulation model to analyze the physical and control characteristics of an OHT system is presented, focusing on building a modular simulation framework for evaluating operational strategies by applying various optimization techniques. Additionally, a step-by-step analysis is introduced to optimize OHT operation using the developed model. The simulation model is broadly divided into three parts according to their purposes. The physical system encompasses the physical entities such as the equipment and vehicles. The experimental frame comprises a generator, which triggers experiments, and a result analyzer. Finally, the system controller is structured hierarchically and consists of an upper layer, known as the manufacturing control system, and subordinate layers. The subordinate layers are modularly divided according to their roles and encompass a main controller responsible for OHT control and a scheduling agent manager for dispatching and routing based on SEMI commands. The proposed simulation model adopts a structure based on the discrete event systems specification (DEVS). Since the hierarchical system controller may face challenges such as computational overhead and adaptability issues in real-world implementation, the modular design based on DEVS is utilized to maintain independence between layers while ensuring a flexible system configuration. Through an exploratory analysis using the simulation model, we adopt a step-by-step approach to optimize the OHT operation. The optimal operation is achieved by identifying the optimal number of OHT units and pieces of equipment per manufacturing zone. The results of the exploratory analysis for the three scenarios validate the effectiveness of the proposed framework. Increasing the number of OHT units beyond 17 resulted in only a 0.08% reduction in lead time, confirming that 17 units is the optimal number. Additionally, by adjusting the amount of equipment based on their utilization rates, we found that reducing the amount of equipment from 12 to five in process E-1 and from seven to three in the OUT process did not degrade performance. The proposed simulation framework was thus validated as being effective in evaluating OHT operational efficiency and useful for analyzing key performance indicators such as OHT utilization rates. The proposed model and analysis method effectively model and optimize OHT systems in semiconductor manufacturing, contributing to improved production efficiency and reduced operational costs. Furthermore, this work can bridge the gap between theoretical modeling and practical complexities in semiconductor logistics. Full article

(This article belongs to the Special Issue Advanced Applications of Mathematical Modeling and Optimization in Logistics and Manufacturing)

► Show Figures

Figure 1

28 pages, 1823 KiB

Open AccessArticle

Logistics Optimization Applied to Redesign Operations Involving Merchandise Location, Employee Ergonomics and Distribution Network

by Isidro Soria-Arguello and Esbeydi Villicaña-García

Mathematics 2025, 13(4), 639; https://doi.org/10.3390/math13040639 - 15 Feb 2025

Viewed by 591

Abstract

The growing demand for bottled beverages has led to the search for optimal configurations that represent the lowest costs. Using crossdocking techniques reduces storage costs, these costs being the main ones in the logistics of distribution of products to the consumer. However, it [...] Read more.

The growing demand for bottled beverages has led to the search for optimal configurations that represent the lowest costs. Using crossdocking techniques reduces storage costs, these costs being the main ones in the logistics of distribution of products to the consumer. However, it is vitally important to consider the ergonomics of the workers who are subjected to the loading and unloading of products to meet the demands. Various ailments have been reported to the authorities, and it is imperative to address them for decision making. Likewise, the best arrangement of the products within these fast warehouses is associated with the relationship between the number of times a worker travels to pick up the product from the place where it is located to the loading area and the distance. In this work, the distribution from the production plants and the crossdocking to the distribution centers are proposed jointly and in each distribution center the best arrangement of the products is determined, as well as the ergonomics of those involved, considering the best scheme that represents the lowest cost. The results show the best distribution of products as well as the crossdocking that must be installed to meet the demands of the distribution centers. Full article

(This article belongs to the Special Issue Advanced Applications of Mathematical Modeling and Optimization in Logistics and Manufacturing)

► Show Figures

Figure 1

28 pages, 6375 KiB

Open AccessArticle

Optimization of Fresh Food Logistics Routes for Heterogeneous Fleets in Segmented Transshipment Mode

by Haoqing Sun, Manhui He, Yanbing Gai and Jinghao Cao

Mathematics 2024, 12(23), 3831; https://doi.org/10.3390/math12233831 - 4 Dec 2024

Cited by 1 | Viewed by 1183

Abstract

To address the challenges of environmental impact and distribution efficiency in fresh food logistics, a segmented transshipment model involving the coordinated operation of gasoline and electric vehicles is proposed. The model minimizes total distribution costs by considering transportation, refrigeration, product damage, carbon emissions, [...] Read more.

To address the challenges of environmental impact and distribution efficiency in fresh food logistics, a segmented transshipment model involving the coordinated operation of gasoline and electric vehicles is proposed. The model minimizes total distribution costs by considering transportation, refrigeration, product damage, carbon emissions, and penalties for time window violations. The k-means++ clustering algorithm is used to determine transshipment points, while an improved adaptive multi-objective ant colony optimization algorithm (IAMACO) is employed to optimize the delivery routes for the heterogeneous fleet. The case study results show that compared to the traditional model, the segmented transshipment mode reduces the total distribution costs, carbon emissions, and time window penalty costs by 22.13%, 28.32%, and 41.08%, respectively, providing a viable solution for fresh food logistics companies to achieve sustainable and efficient growth. Full article

(This article belongs to the Special Issue Advanced Applications of Mathematical Modeling and Optimization in Logistics and Manufacturing)

► Show Figures

Figure 1

20 pages, 2214 KiB

Open AccessArticle

Approaches for the On-Line Three-Dimensional Knapsack Problem with Buffering and Repacking

by Juan Manuel Huertas Arango, German Pantoja-Benavides, Sebastián Valero and David Álvarez-Martínez

Mathematics 2024, 12(20), 3223; https://doi.org/10.3390/math12203223 - 15 Oct 2024

Viewed by 1355

Abstract

The rapid growth of the e-commerce sector, particularly in Latin America, has highlighted the need for more efficient automated packing and distribution systems. This study presents heuristic algorithms to solve the online three-dimensional knapsack problem (OSKP), incorporating buffering and repacking strategies to optimize [...] Read more.

The rapid growth of the e-commerce sector, particularly in Latin America, has highlighted the need for more efficient automated packing and distribution systems. This study presents heuristic algorithms to solve the online three-dimensional knapsack problem (OSKP), incorporating buffering and repacking strategies to optimize space utilization in automated packing environments. These strategies enable the system to handle the stochastic nature of item arrivals and improve container utilization by temporarily storing boxes (buffering) and rearranging already packed boxes (repacking) to enhance packing efficiency. Computational experiments conducted on specialized datasets from the existing literature demonstrate that the proposed heuristics perform comparably to state-of-the-art methodologies. Moreover, physical experiments were conducted on a robotic packing cell to determine the time that buffering and repacking implicate. The contributions of this paper lie in the integration of buffering and repacking into the OSKP, the development of tailored heuristics, and the validation of these heuristics in both simulated and real-world environments. The findings indicate that including buffering and repacking strategies significantly improves space utilization in automated packing systems. However, they significantly increase the time spent packing. Full article

(This article belongs to the Special Issue Advanced Applications of Mathematical Modeling and Optimization in Logistics and Manufacturing)

► Show Figures

Figure 1

17 pages, 4904 KiB

Open AccessArticle

Development of a Digital Twin Driven by a Deep Learning Model for Fault Diagnosis of Electro-Hydrostatic Actuators

by Roman Rodriguez-Aguilar, Jose-Antonio Marmolejo-Saucedo and Utku Köse

Mathematics 2024, 12(19), 3124; https://doi.org/10.3390/math12193124 - 6 Oct 2024

Cited by 1 | Viewed by 1583

Abstract

The first quarter of the 21st century has witnessed many technological innovations in various sectors. Likewise, the COVID-19 pandemic triggered the acceleration of digital transformation in organizations driven by artificial intelligence and communication technologies in Industry 4.0 and Industry 5.0. Aiming at the [...] Read more.

The first quarter of the 21st century has witnessed many technological innovations in various sectors. Likewise, the COVID-19 pandemic triggered the acceleration of digital transformation in organizations driven by artificial intelligence and communication technologies in Industry 4.0 and Industry 5.0. Aiming at the construction of digital twins, virtual representations of a physical system allow real-time bidirectional communication. This will allow the monitoring of operations, identification of possible failures, and decision making based on technical evidence. In this study, a fault diagnosis solution is proposed, based on the construction of a digital twin, for a cloud-based Industrial Internet of Things (IIoT) system contemplating the control of electro-hydrostatic actuators (EHAs). The system was supported by a deep learning model using Long Short-Term Memory (LSTM) networks for an effective diagnostic approach. The implemented study considers data preparation and integration and system development and application to evaluate the performance against the fault diagnosis problem. According to the results obtained, positive results are shown in the construction of the digital twin using a deep learning model for the fault diagnosis problem of an active EHA-IIoT configuration. Full article

(This article belongs to the Special Issue Advanced Applications of Mathematical Modeling and Optimization in Logistics and Manufacturing)

► Show Figures

Figure 1

37 pages, 6139 KiB

Open AccessArticle

A Novel Approach for Material Handling-Driven Facility Layout

by Adem Erik and Yusuf Kuvvetli

Mathematics 2024, 12(16), 2548; https://doi.org/10.3390/math12162548 - 18 Aug 2024

Viewed by 1336

Abstract

Material handling is a widely used process in manufacturing and is generally considered a non-value-added process. The Dynamic Facility Layout Problem (DFLP) considered in this paper minimizes the total material handling and re-arrangement cost. In this study, an integrated DFLP model with unequal [...] Read more.

Material handling is a widely used process in manufacturing and is generally considered a non-value-added process. The Dynamic Facility Layout Problem (DFLP) considered in this paper minimizes the total material handling and re-arrangement cost. In this study, an integrated DFLP model with unequal facility areas, assignment of material handling devices (MHD), and flexible bay structure (FBS) is considered, and it is aimed to propose fast solution approaches. Two different solution methods are proposed for the problem, which are the genetic algorithm and the simulated annealing algorithm, respectively. In both methods, a non-linear mathematical model solution was used to calculate the fitness values. Thus, the solutions in the feasible solution space are utilized. The proposed solution approaches were applied to solve four problems published in the literature. The computational experiments have validated the effectiveness of the algorithms and the quality of solutions produced. Full article

(This article belongs to the Special Issue Advanced Applications of Mathematical Modeling and Optimization in Logistics and Manufacturing)

► Show Figures

Figure 1

25 pages, 16408 KiB

Open AccessArticle

The Normalized Direct Trigonometry Model for the Two-Dimensional Irregular Strip Packing Problem

by Germán Pantoja-Benavides, David Álvarez-Martínez and Francisco Parreño Torres

Mathematics 2024, 12(15), 2414; https://doi.org/10.3390/math12152414 - 2 Aug 2024

Cited by 1 | Viewed by 1328

Abstract

Background: The Irregular Strip Packing Problem (ISPP) involves packing a set of irregularly shaped items within a strip while minimizing its length. Methods: This study introduces the Normalized Direct Trigonometry Model (NDTM), an innovative enhancement of the Direct Trigonometry Model (DTM). The NDTM [...] Read more.

Background: The Irregular Strip Packing Problem (ISPP) involves packing a set of irregularly shaped items within a strip while minimizing its length. Methods: This study introduces the Normalized Direct Trigonometry Model (NDTM), an innovative enhancement of the Direct Trigonometry Model (DTM). The NDTM incorporates a distance function that supports the integration of the separation constraint, which mandates a minimum separation distance between items. Additionally, the paper proposes a new set of constraints based on the bounding boxes of the pieces aimed at improving the non-overlapping condition. Results: Comparative computational experiments were performed using a comprehensive set of 90 instances. Results show that the NDTM finds more feasible and optimal solutions than the DTM. While the NDTM allows for the implementation of the separation constraint, the number of feasible and optimal solutions tends to decrease as more separation among the items is considered, despite not increasing the number of variables or constraints. Conclusions: The NDTM outperforms the DTM. Moreover, the results indicate that the new set of non-overlapping constraints facilitates the exploration of feasible solutions at the expense of optimality in some cases. Full article

(This article belongs to the Special Issue Advanced Applications of Mathematical Modeling and Optimization in Logistics and Manufacturing)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Advanced Applications of Mathematical Modeling and Optimization in Logistics and Manufacturing

Share This Special Issue

Special Issue Editor

Special Issue Information

Keywords

Benefits of Publishing in a Special Issue

Published Papers (8 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI