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16 pages, 3707 KiB

Open AccessArticle

Stochastic Final Pit Limits: An Efficient Frontier Analysis under Geological Uncertainty in the Open-Pit Mining Industry

by Enrique Jelvez, Nelson Morales and Julian M. Ortiz

Mathematics 2022, 10(1), 100; https://0-doi-org.brum.beds.ac.uk/10.3390/math10010100 - 28 Dec 2021

Cited by 4 | Viewed by 3210

Abstract

In the context of planning the exploitation of an open-pit mine, the final pit limit problem consists of finding the volume to be extracted so that it maximizes the total profit of exploitation subject to overall slope angles to keep pit walls stable. [...] Read more.

In the context of planning the exploitation of an open-pit mine, the final pit limit problem consists of finding the volume to be extracted so that it maximizes the total profit of exploitation subject to overall slope angles to keep pit walls stable. To address this problem, the ore deposit is discretized as a block model, and efficient algorithms are used to find the optimal final pit. However, this methodology assumes a deterministic scenario, i.e., it does not consider that information, such as ore grades, is subject to several sources of uncertainty. This paper presents a model based on stochastic programming, seeking a balance between conflicting objectives: on the one hand, it maximizes the expected value of the open-pit mining business and simultaneously minimizes the risk of losses, measured as conditional value at risk, associated with the uncertainty in the estimation of the mineral content found in the deposit, which is characterized by a set of conditional simulations. This allows generating a set of optimal solutions in the expected return vs. risk space, forming the Pareto front or efficient frontier of final pit alternatives under geological uncertainty. In addition, some criteria are proposed that can be used by the decision maker of the mining company to choose which final pit best fits the return/risk trade off according to its objectives. This methodology was applied on a real case study, making a comparison with other proposals in the literature. The results show that our proposal better manages the relationship in controlling the risk of suffering economic losses without renouncing high expected profit. Full article

(This article belongs to the Special Issue Optimization for Decision Making III)

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22 pages, 21198 KiB

Open AccessArticle

Fuzzy Ensemble of Multi-Criteria Decision Making Methods for Heating Energy Transition in Danish Households

by Qianyun Wen, Qiyao Yan, Junjie Qu and Yang Liu

Mathematics 2021, 9(19), 2420; https://0-doi-org.brum.beds.ac.uk/10.3390/math9192420 - 29 Sep 2021

Cited by 8 | Viewed by 2160

Abstract

More than 110 countries, including 500 cities worldwide, have set the goal of reaching carbon neutrality. Heating contributes to most of the residential energy consumption and carbon emissions. The green energy transition of fossil-based heating systems is needed to reach the emission goals. [...] Read more.

More than 110 countries, including 500 cities worldwide, have set the goal of reaching carbon neutrality. Heating contributes to most of the residential energy consumption and carbon emissions. The green energy transition of fossil-based heating systems is needed to reach the emission goals. However, heating systems vary in energy source, heating technology, equipment location, and these complexities make it challenging for households to compare heating systems and make decisions. Hence, a decision support tool that provides a generalized ranking of individual heating alternatives is proposed for households as decision makers to identify the optimal choice. This paper presents an analysis of 13 heating alternatives and 19 quantitative criteria in technological, environmental, and financial aspects, combines ideal solution-based multi-criteria decision making with 6 weighting methods and 4 normalization methods, and introduces ensemble learning with a fuzzy membership function derived from Cauchy distribution to finalize the ultimate ranking. The robustness of the proposed method is verified by three sensitive analyses from different aspects. Air-to-water heat pump, solar heating and direct district heating are the top three rankings in the final result under Danish national average data. A framework is designed to guide decision makers to apply this ranking guideline with their practical, feasible situations. Full article

(This article belongs to the Special Issue Optimization for Decision Making III)

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21 pages, 669 KiB

Open AccessArticle

Novel Methods in Multiple Criteria Decision-Making Process (MCRAT and RAPS)—Application in the Mining Industry

by Katarina Urošević, Zoran Gligorić, Igor Miljanović, Čedomir Beljić and Miloš Gligorić

Mathematics 2021, 9(16), 1980; https://0-doi-org.brum.beds.ac.uk/10.3390/math9161980 - 19 Aug 2021

Cited by 18 | Viewed by 2670

Abstract

Multiple criteria decision making (MCDM) is a supporting tool which is widely spread in different areas of science and industry. Many researchers have confirmed that MCDM methods can be useful for selecting the best solution in many different problems. In this paper, two [...] Read more.

Multiple criteria decision making (MCDM) is a supporting tool which is widely spread in different areas of science and industry. Many researchers have confirmed that MCDM methods can be useful for selecting the best solution in many different problems. In this paper, two novel methods are presented and applied on existing decision-making processes in the mining industry. The first method is multiple criteria ranking by alternative trace (MCRAT) and the second is ranking alternatives by perimeter similarity (RAPS). These two novel methods are demonstrated in decision-making problems and compared with the ranking of the same alternatives by other MCDM methods. The mining process often includes drilling and blasting operations as the most common activities for exploitation of raw materials. For optimal blasting design it is important to select the most suitable parameters for the blasting pattern and respect characteristics of the working environment and production conditions. By applying novel methods, how to successfully select the most proper blasting pattern respecting all conditions that must be satisfied for economic aspects and the safety of employees and the environment is presented. Full article

(This article belongs to the Special Issue Optimization for Decision Making III)

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29 pages, 17792 KiB

Open AccessArticle

Optimized Application of Sustainable Development Strategy in International Engineering Project Management

by Zhiwu Zhou, Julián Alcalá and Víctor Yepes

Mathematics 2021, 9(14), 1633; https://0-doi-org.brum.beds.ac.uk/10.3390/math9141633 - 10 Jul 2021

Cited by 3 | Viewed by 3867

Abstract

The aim of this paper is to establish an international framework for sustainable project management in engineering, to make up the lack of research in this field, and to propose a scientific theoretical basis for the establishment of a new project management system. [...] Read more.

The aim of this paper is to establish an international framework for sustainable project management in engineering, to make up the lack of research in this field, and to propose a scientific theoretical basis for the establishment of a new project management system. The article adopts literature review, mathematical programming algorithm and case study as the research method. The literature review applied the visual clustering research method and analyzed the results of 21-year research in this field. As a result, the project management system was found to have defects and deficiencies. A mathematical model was established to analyze the composition and elements of the optimized international project management system. The case study research selected large bridges for analysis and verified the superiority and practicability of the theoretical system. Thus, the goal of sustainable development of bridges was achieved. The value of this re-search lies in establishing a comprehensive international project management system model; truly integrating sustainable development with project management; providing new research frames and management models to promote the sustainable development of the construction industry. Full article

(This article belongs to the Special Issue Optimization for Decision Making III)

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19 pages, 1559 KiB

Open AccessArticle

Neutrosophic Completion Technique for Incomplete Higher-Order AHP Comparison Matrices

by Ignacio J. Navarro, José V. Martí and Víctor Yepes

Mathematics 2021, 9(5), 496; https://0-doi-org.brum.beds.ac.uk/10.3390/math9050496 - 28 Feb 2021

Cited by 7 | Viewed by 2366

Abstract

After the recent establishment of the Sustainable Development Goals and the Agenda 2030, the sustainable design of products in general and infrastructures in particular emerge as a challenging field for the development and application of multicriteria decision-making tools. Sustainability-related decision problems usually involve, [...] Read more.

After the recent establishment of the Sustainable Development Goals and the Agenda 2030, the sustainable design of products in general and infrastructures in particular emerge as a challenging field for the development and application of multicriteria decision-making tools. Sustainability-related decision problems usually involve, by definition, a wide variety in number and nature of conflicting criteria, thus pushing the limits of conventional multicriteria decision-making tools practices. The greater the number of criteria and the more complex the relations existing between them in a decisional problem, the less accurate and certain are the judgments required by usual methods, such as the analytic hierarchy process (AHP). The present paper proposes a neutrosophic AHP completion methodology to reduce the number of judgments required to be emitted by the decision maker. This increases the consistency of their responses, while accounting for uncertainties associated to the fuzziness of human thinking. The method is applied to a sustainable-design problem, resulting in weight estimations that allow for a reduction of up to 22% of the conventionally required comparisons, with an average accuracy below 10% between estimates and the weights resulting from a conventionally completed AHP matrix, and a root mean standard error below 15%. Full article

(This article belongs to the Special Issue Optimization for Decision Making III)

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16 pages, 1501 KiB

Open AccessArticle

Fuzzy Optimization Model for Decision-Making in Supply Chain Management

by Jui-Fang Chang, Chao-Jung Lai, Chia-Nan Wang, Ming-Hsien Hsueh and Van Thanh Nguyen

Mathematics 2021, 9(4), 312; https://0-doi-org.brum.beds.ac.uk/10.3390/math9040312 - 04 Feb 2021

Cited by 5 | Viewed by 2885

Abstract

Choosing a supplier is a complex decision-making process that can reduce the total cost of production inputs and increase profits without increasing the price or sacrificing product quality. However, supplier selection processes usually involve multiple quantitative and qualitative criteria which increase the complexity [...] Read more.

Choosing a supplier is a complex decision-making process that can reduce the total cost of production inputs and increase profits without increasing the price or sacrificing product quality. However, supplier selection processes usually involve multiple quantitative and qualitative criteria which increase the complexity of the problem and may decrease the accuracy and effectiveness of the process. Such complex decision-making problems can be supported by using multicriteria decision-making (MCDM) models. While there have been multiple MCDM models to support supplier selection processes in different industries and sectors, only a few are developed to support the supplier selection processes in the garment industry, especially under uncertain decision-making environment. This paper presents an integrated mathematical model under a fuzzy environment and applies it to the supplier selection process in the garment industry. In this research, the authors utilize the Buckley extension based fuzzy Analytical Hierarchical Process (FAHP) method in combination with linear normalization based fuzzy Grey Relational Analysis (F-GRA) method to develop a MCDM approach to the supplier selection process under a fuzzy environment. As a result, supplier 08 (SA08) is the optimal supplier. The contribution of this work is to propose an MCDM model for ranking potential suppliers in the garment industry under a fuzzy environment. The proposed approach can also be applied to support complex decision-making processes under a fuzzy environment in different industries. Full article

(This article belongs to the Special Issue Optimization for Decision Making III)

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28 pages, 3031 KiB

Open AccessArticle

Analyzing Operational Efficiency in Real Estate Companies: An Application of GM (1,1) and DEA Malmquist Model

by Chia-Nan Wang, Thi-Ly Nguyen and Thanh-Tuan Dang

Mathematics 2021, 9(3), 202; https://0-doi-org.brum.beds.ac.uk/10.3390/math9030202 - 20 Jan 2021

Cited by 14 | Viewed by 4269

Abstract

Real estate management and its operation play a crucial role in supporting company operation. Going hand-in-hand with the rapid growth of companies, the real estate portfolio has expanded dramatically, attracting large numbers of domestic and foreign investors. This paper studied the top 12 [...] Read more.

Real estate management and its operation play a crucial role in supporting company operation. Going hand-in-hand with the rapid growth of companies, the real estate portfolio has expanded dramatically, attracting large numbers of domestic and foreign investors. This paper studied the top 12 real estate companies listed on Vietnam’s stock market to develop a method that combines the Grey methodology and the Data Envelopment Analysis (DEA) Malmquist model, intending to predict and evaluate their performances in two periods: 2015–2018 and 2019–2022. The proposed model considered three input factors, namely total assets, cost of sales, and cost of goods sold, and two output factors, namely total revenue and gross profit. Findings revealed that drastic efficiency changes in some companies should be observed at the beginning of the process, even if the technological efficiency in the period is stable. In the future period, most companies achieved relatively stable productivity. This study serves as a reference for policymakers and strategy makers by analyzing insights for the operational status of real estate businesses and providing an overview in the future toward sustainable development. Full article

(This article belongs to the Special Issue Optimization for Decision Making III)

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32 pages, 3548 KiB

Open AccessEditor’s ChoiceReview

Nature-Inspired Metaheuristic Techniques for Combinatorial Optimization Problems: Overview and Recent Advances

by Md Ashikur Rahman, Rajalingam Sokkalingam, Mahmod Othman, Kallol Biswas, Lazim Abdullah and Evizal Abdul Kadir

Mathematics 2021, 9(20), 2633; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202633 - 19 Oct 2021

Cited by 23 | Viewed by 4881

Abstract

Combinatorial optimization problems are often considered NP-hard problems in the field of decision science and the industrial revolution. As a successful transformation to tackle complex dimensional problems, metaheuristic algorithms have been implemented in a wide area of combinatorial optimization problems. Metaheuristic algorithms have [...] Read more.

Combinatorial optimization problems are often considered NP-hard problems in the field of decision science and the industrial revolution. As a successful transformation to tackle complex dimensional problems, metaheuristic algorithms have been implemented in a wide area of combinatorial optimization problems. Metaheuristic algorithms have been evolved and modified with respect to the problem nature since it was recommended for the first time. As there is a growing interest in incorporating necessary methods to develop metaheuristics, there is a need to rediscover the recent advancement of metaheuristics in combinatorial optimization. From the authors’ point of view, there is still a lack of comprehensive surveys on current research directions. Therefore, a substantial part of this paper is devoted to analyzing and discussing the modern age metaheuristic algorithms that gained popular use in mostly cited combinatorial optimization problems such as vehicle routing problems, traveling salesman problems, and supply chain network design problems. A survey of seven different metaheuristic algorithms (which are proposed after 2000) for combinatorial optimization problems is carried out in this study, apart from conventional metaheuristics like simulated annealing, particle swarm optimization, and tabu search. These metaheuristics have been filtered through some key factors like easy parameter handling, the scope of hybridization as well as performance efficiency. In this study, a concise description of the framework of the selected algorithm is included. Finally, a technical analysis of the recent trends of implementation is discussed, along with the impacts of algorithm modification on performance, constraint handling strategy, the handling of multi-objective situations using hybridization, and future research opportunities. Full article

(This article belongs to the Special Issue Optimization for Decision Making III)

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