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Axioms
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Applied Optimization for Solving Real-World Problems
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Applied Optimization for Solving Real-World Problems

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (20 December 2023) | Viewed by 12111

Special Issue Editors

Prof. Dr. Rafael Bernardo Carmona Benítez

E-Mail Website
Guest Editor
Facultad de Economía y Negocios, Universidad Anahuac Mexico, Huixquilucan 52786, Mexico
Interests: operations research; optimization; mathematical modeling; supply chain management; forecasting; financial optimization
Dr. João Lemos Nabais

E-Mail Website
Co-Guest Editor
Marketing and Logistics Department, Instituto Politécnico de Setúbal, 2910-761 Setúbal, Portugal
Interests: supply chain operations management; transportation; synchromodality; port community systems; physical internet; digital transformation
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We invite you to submit your research in the area of optimization and its application in business to the Special Issue, "Applied Optimization for Solving Real-World Problems" in Axioms.

On a daily basis, many enterprises face decision-making problems that can be solved with optimization. However, many enterprises prefer to use other decision-making approaches such as simulation to overcome such problems because, in general, optimization solutions are more difficult to debug, even when optimization delivers higher-quality analytical solutions. Applying optimization to solve real-world problems is difficult because the complexity of the problems varies from many features that make them difficult to solve that depends on how the real-world problem is translated to a mathematical formulation with its parameters, variables, constraints, and objectives. The combination of multiple variables, constraints, and input data make real-world problems have unknown search spaces with many difficulties that demean the performance of optimization algorithms. Hence, real-world optimization problems require a deep understanding of the problem, its parameters, its variables, its constraints, and its objectives to design mathematical formulations that are as non-complex possible but that are capable of solving all their required decisions.

This Special Issue aims to seek out high-quality articles from industry-related scholars and researchers in the areas of applied optimization in mathematics, economics, business, logistics, production, transportation, supply chain, finance, etc. We are interested in publishing articles that solve the problems of real companies through the development of optimization models. The results of their applications in real practice should be shown, discussed, and analysed. High-quality papers are solicited to address practical issues in the development of efficient mathematical models to represent real-world business problems and their applications along with the solution of a particular problem. Submissions that present new business models with solutions methods and their applications are welcome. Potential topics include, but are not limited to, applications of mathematical economics, business analytics models, financial optimization, supply chain optimization, and business optimization.

Prof. Dr. Rafael Bernardo Carmona Benítez
Dr. João Lemos Nabais
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. Axioms is an international peer-reviewed open access monthly 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 2400 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

  • optimization
  • applied optimization
  • mathematical economics
  • business analytics models
  • financial optimization
  • transportation
  • supply chain optimization
  • business optimization

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Published Papers (5 papers)

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Research

36 pages, 3900 KiB  
Article
Efficient Formulation for Vendor–Buyer System Considering Optimal Allocation Fraction of Green Production
by Adel A. Alamri
Axioms 2023, 12(12), 1104; https://doi.org/10.3390/axioms12121104 - 7 Dec 2023
Viewed by 1432
Abstract
The classical joint economic lot-sizing (JELS) policy in a single-vendor single-buyer system generates an equal production quantity in all cycles, where the input parameters remain static indefinitely. In this paper, a new two-echelon supply chain inventory model is developed involving a hybrid production [...] Read more.
The classical joint economic lot-sizing (JELS) policy in a single-vendor single-buyer system generates an equal production quantity in all cycles, where the input parameters remain static indefinitely. In this paper, a new two-echelon supply chain inventory model is developed involving a hybrid production system. The proposed model simultaneously focuses on green and regular production methods with an optimal allocation fraction of green and regular productions. Unlike the classical mathematical formulation, cycles do not depend on each other, and consequently, each model parameter can be adjusted to be responsive to the dynamic nature of demand rate and/or price fluctuation. A rigorous heuristic approach is used to derive a global optimal solution for a joint hybrid production system. This paper accounts for carbon emissions from production and storage activities related to green and regular produced items along with transportation activity under a multi-level emission-taxing scheme. The results emphasize the significant impact of green production on emissions. That is, the higher the allocation fraction of green production, the lower the total amount of emissions generated by the system, i.e., the system becomes more sustainable. Adopting a hybrid production method not only decreases the greenhouse gas (GHG) emissions dramatically, but also reduces the minimum total cost per unit time when compared with regular production. One of the main findings is that the total system cost generated by the base closed-form formula of the proposed model is considerably lower in the first cycle (subsequent cycles) than that of the existing literature, i.e., 33.59% (16.13%) when the regular production method is assumed. Moreover, the optimal production rate generated by the proposed model is the one that minimizes the emissions production function. In addition, the system earns further revenue by utilizing a mixed transportation policy that combines the Truck Load (TL) and Less than Truck Load (LTL) services. Illustrative examples and special cases that reflect different realistic situations are compared to outline managerial insights. Full article
(This article belongs to the Special Issue Applied Optimization for Solving Real-World Problems)
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46 pages, 2854 KiB  
Article
The Branch-and-Bound Algorithm in Optimizing Mathematical Programming Models to Achieve Power Grid Observability
by Nikolaos P. Theodorakatos, Rohit Babu and Angelos P. Moschoudis
Axioms 2023, 12(11), 1040; https://doi.org/10.3390/axioms12111040 - 8 Nov 2023
Cited by 6 | Viewed by 3509
Abstract
Phasor Measurement Units (PMUs) are the backbone of smart grids that are able to measure power system observability in real-time. The deployment of synchronized sensors in power networks opens up the advantage of real-time monitoring of the network state. An optimal number of [...] Read more.
Phasor Measurement Units (PMUs) are the backbone of smart grids that are able to measure power system observability in real-time. The deployment of synchronized sensors in power networks opens up the advantage of real-time monitoring of the network state. An optimal number of PMUs must be installed to ensure system observability. For that reason, an objective function is minimized, reflecting the cost of PMU installation around the power grid. As a result, a minimization model is declared where the objective function is defined over an adequate number of constraints on a binary decision variable domain. To achieve maximum network observability, there is a need to find the best number of PMUs and put them in appropriate locations around the power grid. Hence, maximization models are declared in a decision-making way to obtain optimality satisfying a guaranteed stopping and optimality criteria. The best performance metrics are achieved using binary integer, semi-definite, and binary polynomial models to encounter the optimal number of PMUs with suitable PMU positioning sites. All optimization models are implemented with powerful optimization solvers in MATLAB to obtain the global solution point. Full article
(This article belongs to the Special Issue Applied Optimization for Solving Real-World Problems)
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12 pages, 235 KiB  
Article
Solving Feasibility Problems with Infinitely Many Sets
by Alexander J. Zaslavski
Axioms 2023, 12(3), 273; https://doi.org/10.3390/axioms12030273 - 6 Mar 2023
Cited by 4 | Viewed by 1223
Abstract
In this paper, we study a feasibility problem with infinitely many sets in a metric space. We present a novel algorithm and analyze its convergence. The algorithms used for the feasibility problem in the literature work for finite collections of sets and cannot [...] Read more.
In this paper, we study a feasibility problem with infinitely many sets in a metric space. We present a novel algorithm and analyze its convergence. The algorithms used for the feasibility problem in the literature work for finite collections of sets and cannot be applied if the collection of sets is infinite. The main feature of these algorithms is that, for iterative steps, we need to calculate the values of all the operators belonging to our family of maps and even their sums with weighted coefficients. This is impossible if the family of maps is not finite. In the present paper, we introduce a new algorithm for solving feasibility problems with infinite families of sets and study its convergence. It turns out that our results hold for feasibility problems in a general metric space. Full article
(This article belongs to the Special Issue Applied Optimization for Solving Real-World Problems)
18 pages, 7054 KiB  
Article
Optimising the Optic Fibre Deployment in Small Rural Communities: The Case of Mexico
by Luis A. Moncayo-Martínez and Ante Salcedo
Axioms 2023, 12(3), 269; https://doi.org/10.3390/axioms12030269 - 5 Mar 2023
Viewed by 1896
Abstract
Over the years, connection or access to the Internet has shown a positive impact on users in their everyday activities, such as entertainment, online education, online business, and productivity increments in their communities. Unfortunately, rural communities, which usually are far away from cities, [...] Read more.
Over the years, connection or access to the Internet has shown a positive impact on users in their everyday activities, such as entertainment, online education, online business, and productivity increments in their communities. Unfortunately, rural communities, which usually are far away from cities, cannot enjoy these benefits due to inefficient or inexistent Internet access. We propose an algorithm to select which communities to connect to maximise the number of people connected to the Internet while minimising the length of the network, or while maximising the number of connected communities, or while maximising the linked people per kilometre of fibre. The algorithm estimates the shortest driving distance and the minimum spanning tree. Then, the algorithm creates a subset of linked communities to select the next one to connect based on one of the three criteria described above. To test the algorithm, we used data from a set of rural communities in Mexico. The results showed that the minimum length of the network to connect the 597 rural communities (with 454,514 people) in our test case was 949.09 km. Moreover, there was a difference of 204.1 km in the network length to connect 90% of the total population depending on the selected criterion to connect the communities. If the decision-maker wants to connect 90% of the population, the maximum number of connected communities was 507 using the PC criterion. Full article
(This article belongs to the Special Issue Applied Optimization for Solving Real-World Problems)
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14 pages, 2367 KiB  
Article
Impact of Goodwill on Consumer Buying through Advertising in a Segmented Market: An Optimal Control Theoretic Approach
by Pradeep Kumar, Kuldeep Chaudhary, Vijay Kumar and Sudipa Chauhan
Axioms 2023, 12(2), 223; https://doi.org/10.3390/axioms12020223 - 20 Feb 2023
Cited by 2 | Viewed by 1949
Abstract
Market segmentation is one of the key marketing activities to target the potential market for a product, which allows the firm to have a better understanding of their customers. This paper considers an optimal control problem to determine the dynamic price and advertising [...] Read more.
Market segmentation is one of the key marketing activities to target the potential market for a product, which allows the firm to have a better understanding of their customers. This paper considers an optimal control problem to determine the dynamic price and advertising policies of a new product introduction in a segment-specific market incorporating advertising-based goodwill. Under differentiated advertising and single-channel advertising, advertising efforts increase the stock of goodwill in each segment. Single-channel advertising starts in all segments with a fixed segment spectrum, while the differentiated advertising process deals with each segment independently. The explicit optimal dynamic advertising effort and price strategies are obtained by applying Pontryagin’s maximum principle, and local stability of equilibria have also been examined. The effectiveness of the proposed method is validated through numerical examples, and a local sensitivity analysis is performed to find the sensitive parameters that can affect the optimal values of price and advertising effort rates. Full article
(This article belongs to the Special Issue Applied Optimization for Solving Real-World Problems)
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