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Mathematics
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Mathematical Applications in Industrial Engineering
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Mathematical Applications in Industrial Engineering

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

Deadline for manuscript submissions: 28 February 2025 | Viewed by 7852

Special Issue Editors

Dr. Manuel Ivan Rodriguez Borbon

E-Mail Website
Guest Editor
Department of Industrial Engineering, New Mexico State University, Las Cruces, NM 88003, USA
Interests: reliability analysis; life cycle sustainability assessment; quality 4.0; data analysis; statistical data analysis; design of experiments; bayesian analysis; bayesian networks; machine learning
Dr. Hansuk Sohn

E-Mail Website
Guest Editor
Department of Industrial Engineering, New Mexico State University, Las Cruces, NM 88003, USA
Interests: mathematical programming (linear, integer, and stochastic) and dynamic programming algorithm development (optimization, heuristic, and hybrid algorithms); statistical data analysis and data mining; typical implementation areas: (a) logistics, supply chain management, and network optimization; (b) road safety; (c) fleet routing and scheduling; (d) performance measurement;(e) risk management; (f) production planning; and (g) educational

Special Issue Information

Dear Colleagues,

Industrial engineering is one of the primary fields to utilize mathematical models in research and practice. Mathematical methods in industrial engineering are essential tools to solve complex problems in areas such as operations research, reliability, sustainability, logistics, and supply chain management. To understand situations of interest in the field of industrial engineering, it is necessary to develop multifaceted mathematical formulations and thus obtain an understanding of and solution to complex applied problems.

We are pleased to invite you to contribute to this Special Issue on “Mathematical Applications in Industrial Engineering”. This Special Issue serves as a forum for articles evaluating the impact of mathematical models in several industrial engineering fields. Papers on applications of mathematical models to real-life industrial engineering problems are welcome. Application papers should cover the application of mathematical models accompanied by solutions to a particular problem. Potential topics include but are not limited to:

  • Operations research;
  • Optimization;
  • Statistics in production, manufacturing, and logistics;
  • Reliability engineering;
  • Soft computing;
  • Machine learning, artificial intelligence, and fuzzy techniques;
  • Mathematical programming;
  • Data mining;
  • Logistics and supply chain management;
  • Industry 4.0 and Quality 4.0.

Dr. Manuel Ivan Rodriguez Borbon
Dr. Hansuk Sohn
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 100 words) can be sent to the Editorial Office for announcement on this website.

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.

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Published Papers (6 papers)

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Research

20 pages, 6939 KiB  
Article
A Steepest Ascent Analysis Based on an Experimental Approach for the Hardening Process of a Steel Alloy
by Paulo Eduardo García-Nava, Gabriel Plascencia-Barrera, Luis Alberto Rodríguez-Picón, Roal Torres-Sánchez and Rafael García-Martínez
Mathematics 2024, 12(22), 3563; https://doi.org/10.3390/math12223563 - 14 Nov 2024
Viewed by 516
Abstract
A significant number of alloyed metals applied for different purposes are currently available in industry. The hardness of a piece is an important parameter to consider. The tempering process is widely used to change a metal’s hardness, which is obtained using a hardness [...] Read more.
A significant number of alloyed metals applied for different purposes are currently available in industry. The hardness of a piece is an important parameter to consider. The tempering process is widely used to change a metal’s hardness, which is obtained using a hardness test. Once the response is obtained, a way to evaluate the system is by performing an analysis of variance to verify the significance of terms and obtain a regression equation to improve the response. The aim of this work is to illustrate the implementation of an experimental approach based on the steepest ascent method and stopping rules for optimization purposes by considering the hardening process of the steel alloy 4140. The regression coefficients obtained from an experimental design were used to build the steepest path of improvement. The Myers and Khuri stopping rule and the enhanced parabolic stopping rule were applied to determine the best value while individual experimentation is developed. The obtained results, discussion, and a conclusive analysis are disclosed in this document. Full article
(This article belongs to the Special Issue Mathematical Applications in Industrial Engineering)
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19 pages, 10806 KiB  
Article
Mathematical and Statistical Analysis of Fused Filament Fabrication Parameters for Thermoplastic Polyurethane Parts via Response Surface Methodology
by Wajdi Rajhi, Ali B. M. Ali, Dheyaa J. Jasim, Omid Mehrabi, Lotfi Ben Said and Mahmoud Moradi
Mathematics 2024, 12(19), 3146; https://doi.org/10.3390/math12193146 - 8 Oct 2024
Viewed by 673
Abstract
This work aims to analyze the effects of the main process parameters of fused filament fabrication (FFF) on the mechanical properties and part weight of 3D-printed thermoplastic polyurethane (TPU). Raster angle (RA), infill percentage (IP), and extruder temperature (FFF) in the ranges of [...] Read more.
This work aims to analyze the effects of the main process parameters of fused filament fabrication (FFF) on the mechanical properties and part weight of 3D-printed thermoplastic polyurethane (TPU). Raster angle (RA), infill percentage (IP), and extruder temperature (FFF) in the ranges of 0–90°, 15–55%, and 220–260 °C, respectively, were considered as the FFF input parameters, and output variables part weight (PW), elongation at break (E), maximum failure load (MFL), ratio of the maximum failure load to part weight (Ratio), and build time (BT) were considered as responses. The Response Surface Methodology (RSM) and Design of Experiments (DOE) were applied in the analysis. Subsequently, the RSM approach was performed through multi-response optimizations with the help of Design-Expert software. The experimental results indicated a higher maximum failure load is achieved with an increased raster angle and decreased extruder temperature. ANOVA results show that ET has the most significant effect on elongation at break, with elongation at break decreasing as ET increases. The raster angle does not significantly affect the part weight of the TPU samples. The ratio of the maximum failure load to part weight of samples decreases with an increase in IP and ET. The results also indicated that the part weight and build time of FFF-printed TPU samples increase with an increase in IP. An ET of 220 °C, RA of 0°, and IP of 15% are the optimal combination of input variables for achieving the minimal part weight; minimal build time; and maximum elongation at break, maximum failure load, and ratio of the maximum failure load to part weight. Full article
(This article belongs to the Special Issue Mathematical Applications in Industrial Engineering)
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22 pages, 5366 KiB  
Article
A Statistical Evaluation Method Based on Fuzzy Failure Data for Multi-State Equipment Reliability
by Jingjing Xu, Qiaobin Yan, Yanhu Pei, Zhifeng Liu, Qiang Cheng, Hongyan Chu and Tao Zhang
Mathematics 2024, 12(9), 1414; https://doi.org/10.3390/math12091414 - 6 May 2024
Cited by 1 | Viewed by 956
Abstract
For complex equipment, it is easy to over-evaluate the impact of failure on production by estimating the reliability level only through failure probability. To remedy this problem, this paper proposes a statistical evaluation method based on fuzzy failure data considering the multi-state characteristics [...] Read more.
For complex equipment, it is easy to over-evaluate the impact of failure on production by estimating the reliability level only through failure probability. To remedy this problem, this paper proposes a statistical evaluation method based on fuzzy failure data considering the multi-state characteristics of equipment failures. In this method, the new reliability-evaluation scheme is firstly presented based on the traditional statistical analysis method using the Weibull distribution function. For this scheme, the failure-grade index is defined, and a fuzzy-evaluation method is also proposed by comprehensively considering failure severity, failure maintenance, time, and cost; this is then combined with the time between failures to characterize the failure state. Based on the fuzzy failure data, an improved adaptive-failure small-sample-expansion method is proposed based on the classical bootstrap method and the deviation judgment between distributions of the original and newborn samples. Finally, a novel reliability-evaluation model, related to the failure grade and its membership degree, is established to quantify the reliability level of equipment more realistically. Example cases for three methods of the scheme (the failure-grade fuzzy-evaluation method, the sample-expansion method, and the reliability-evaluation modeling method) are presented, respectively, to validate the effectiveness and significance of the proposed reliability-evaluation technology. Full article
(This article belongs to the Special Issue Mathematical Applications in Industrial Engineering)
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24 pages, 6540 KiB  
Article
Transient Response of Homogenous and Nonhomogenous Bernoulli Production Lines
by Neven Hadžić, Viktor Ložar, Tihomir Opetuk and Robert Keser
Mathematics 2023, 11(24), 4945; https://doi.org/10.3390/math11244945 - 13 Dec 2023
Viewed by 847
Abstract
The transient response of production systems is of significant importance especially if present advancements in Digital Twinning technology are taken into account. While the steady-state response enables long-term strategic decision making, the transient response enables more detailed simulation concerning aspects like production losses [...] Read more.
The transient response of production systems is of significant importance especially if present advancements in Digital Twinning technology are taken into account. While the steady-state response enables long-term strategic decision making, the transient response enables more detailed simulation concerning aspects like production losses and preventive maintenance. This is especially relevant if nonhomogenous aspects of production systems are taken into account. An analytical and approximative solution to the problem of the transient response of homogenous and nonhomogenous Bernoulli production systems is developed in this paper based on the eigendecomposition of transition matrices, the eigenvalue problem, and the finite-state method. In particular, sub-resonant and resonant nonhomogeneous production lines are introduced for the first time. Also, the most significant key performance indicators are developed as functions of the time elapsed from the first cycle. Finally, the relationship between the number of eigenvalues and the accuracy of the results is inspected by employing a sensitivity analysis. The presented theoretical framework was employed in the case of a wood processing facility to present the potential application of the theory in the case of long- and short-term management of production systems. Full article
(This article belongs to the Special Issue Mathematical Applications in Industrial Engineering)
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19 pages, 2394 KiB  
Article
The Chen–Perks Distribution: Properties and Reliability Applications
by Luis Carlos Méndez-González, Luis Alberto Rodríguez-Picón, Manuel Iván Rodríguez Borbón and Hansuk Sohn
Mathematics 2023, 11(13), 3001; https://doi.org/10.3390/math11133001 - 5 Jul 2023
Cited by 4 | Viewed by 1788
Abstract
In this paper, a statistical distribution is presented that possesses the ability to describe failure rates exhibiting both monotonic and non-monotonic behaviors, and the bathtub curve, which represents the performance of a device in reliability engineering. The proposed distribution is based on the [...] Read more.
In this paper, a statistical distribution is presented that possesses the ability to describe failure rates exhibiting both monotonic and non-monotonic behaviors, and the bathtub curve, which represents the performance of a device in reliability engineering. The proposed distribution is based on the sum of the hazard functions of the Chen distribution and the Perks distribution, thus presenting the Chen–Perks distribution (CPD). Statistical properties of the CPD focused on reliability engineering are presented to make the model attractive to practitioners of the discipline. The parameters of the CPD were calculated via the maximum likelihood estimator. On the other hand, a comparative analysis was conducted in three study cases to determine the behavior of the CPD relative to other distributions that can describe failure times with the shape of a bathtub curve. The results show that the CPD can offer competitive results, which practitioners can consider when conducting reliability analysis. Full article
(This article belongs to the Special Issue Mathematical Applications in Industrial Engineering)
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35 pages, 16288 KiB  
Article
An Underground Mine Ore Pass System Optimization via Fuzzy 0–1 Linear Programming with Novel Torricelli–Simpson Ranking Function
by Dževdet Halilović, Miloš Gligorić, Zoran Gligorić and Dragan Pamučar
Mathematics 2023, 11(13), 2914; https://doi.org/10.3390/math11132914 - 29 Jun 2023
Cited by 5 | Viewed by 1442
Abstract
In this work, we propose a 3D dynamic optimization model that enables the design of an underground mine ore pass system with uncertainties. Ore transportation costs and ore pass development costs are quantified by triangular fuzzy numbers. Transportation costs are treated as production [...] Read more.
In this work, we propose a 3D dynamic optimization model that enables the design of an underground mine ore pass system with uncertainties. Ore transportation costs and ore pass development costs are quantified by triangular fuzzy numbers. Transportation costs are treated as production costs, and they vary over the duration of mining operation, while development costs of ore passes are treated as an investment, and they are treated as constant. The developed model belongs to the class of fuzzy 0–1 linear programming models, where the fuzzy objective cost function achieves a minimum value, with respect to given set of techno-dynamic constraints. Searching for optimal value in the fuzzy environment is a hard task, and because of that, we developed a new ranking function which transforms the fuzzy optimization model into a crisp one. A triangular fuzzy number can be presented as a triangular graph G(V,E) composed of vertices and edges. The x-coordinate of the Torricelli point of a triangular graph presents the crisp value of a triangular fuzzy number. The use of this model lets us know the optimal number of ore passes, optimal location of ore passes, and optimal dynamic ore transportation plan. Full article
(This article belongs to the Special Issue Mathematical Applications in Industrial Engineering)
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