Mathematical Programming Research Articles

Bayesian Hierarchical Modelling of Student Academic Performance: The Impact of Mathematics Competency, Institutional Context, and Temporal Variability

This study explores the multifaceted factors influencing academic performance among undergraduate students enrolled in Science, Technology, Engineering, and Mathematics (STEM) programs at a South African university. Employing a Bayesian hierarchical modelling approach, this research analyses data from 630 students collected over four academic years (2019–2023). The findings indicate that high school mathematics marks and progression rates serve as significant predictors of academic success, confirming the critical role of foundational mathematical skills in enhancing university performance. Interestingly, gender and age were found to have no statistically significant impact on academic outcomes, suggesting that these factors may be less influential in this context. Additionally, socio-economic status, represented by school quintiles, emerged as a substantial determinant of performance, highlighting disparities faced by students from disadvantaged backgrounds. The results underscore the necessity for targeted educational interventions aimed at bolstering the academic capabilities of students entering university, particularly those with weaker mathematics backgrounds. Furthermore, the study advocates for a holistic admissions approach that considers various attributes beyond standardized scores. These insights contribute to the existing literature on STEM education and provide practical recommendations for educators and policymakers aiming to foster equitable academic success among all students.

Energy Distribution Effect on Bremsstrahlung Radiation Produced by \(B_{11}^{5}\) and \(Al_{27}^{13}\)

By using the Bethe-Heitler equation, this work determines the energy distribution of Bremsstrahlung radiation for \(B_{11}^{5}\) and \(Al_{27}^{13}\). We utilize the mathematical program "Mathematica" to contrast the electromagnetic impacts of photons resulting from interactions of electrons with boron and aluminum nuclei. We compare the effects of electric and magnetic cross-sections on the generation of Bremsstrahlung radiation. We will examine the impact of electric and magnetic fields on the production of Bremsstrahlung radiation using graphs. We also investigate the effect of atom mass on the emission of Bremsstrahlung radiation. According to our results, certain types of X-rays can be produced by using magnetic interactions.

Effects of uncertainty in the design parameters during the design of horizontal gravity oil, gas and water separators

The design of bulk separators for oil, gas, and water vessel-type gravity separators significantly affects the cost of topside and subsea oil- and gas-processing installations. There are often many uncertainties during the design process, such as the separator performance, fluid properties, and variation and evolution of the inlet conditions. The industry employs mechanistic models, empirical correlations, numerical studies using Computational Fluid Dynamics, and extensive and expensive experimental campaigns with separator prototypes. However, owing to time, personnel, and information integration constraints in the design phase, design evaluation, and validation are often limited to performing comprehensive sensitivity studies. This often leads to suboptimal designs and early bottlenecks. This study proposes using stochastic mathematical programming and optimization to include the effects of uncertainties in the design parameters during the separator design process. The proposed solution involves the development of a three-phase horizontal separator design model. The model was implemented using Microsoft Excel Visual Basic for Applications. The study then considered the effects of the uncertainties in the oil, gas, and water flow rates and slug volume on the optimal design using stochastic optimization. Conservative, optimistic, and ultimate design parameters (P10, P50, and P90) were obtained for each scenario. The results of this study provide a method and tool to aid topside design teams while expanding on previous research in the literature regarding separator design.

A Q-learning-based algorithm for the block relocation problem

The Block Relocation Problem (BRP), also known as the Container Relocation Problem, is a challenging combinatorial optimization problem in block stacking systems and has many applications in real-world scenarios such as logistics and manufacturing industry. The BRP is about finding the optimal way to retrieve blocks from a storage area with the objective of minimizing the number of relocations. The BRPs have been studied for a long time, and have been solved primarily using conventional optimization techniques, including mathematical programming models, as well as both exact and heuristic algorithms. For the first time, this paper tackles the problem using a reinforcement learning method. We focus on one of the major variants of the BRP—the restricted BRP with duplicate priorities (RBRP-dup). We first model the RBRP-dup as a Markov decision process and then propose a Q-learning-based algorithm to solve the problem. The Q-learning-based algorithm contains two phases. In the learning phase, two innovative mechanisms: an optimal rule-integrated behaviour policy and a heuristic-based dynamic initialization method, are incorporated into the Q-learning model to reduce the size of the state-action space and accelerate convergence. In the optimization phase, the insights obtained in the learning phase are combined with a heuristic algorithm to improve decision-making. The performance of our proposed method is evaluated against the state-of-the-art exact algorithm and a commonly used heuristic algorithm based on benchmark instances from the literature. The computational experiments demonstrate the superiority of our proposed method regarding solution quality in large and complex instances.

Supplier Selection Model Considering Sustainable and Resilience Aspects for Mining Industry

Supplier selection plays a pivotal role in the mining industry, forming a key component of the supply chain management. It has been established that the integration of sustainability and resilience into this process can significantly enhance the industry’s ability to withstand economic, environmental, and social shocks. Despite a large body of literature investigating supplier selection, there is a notable gap in research specifically addressing the incorporation of sustainability and resilience criteria in the mining industry. The objective of this research is to bridge this knowledge gap and contribute to the understanding of sustainable and resilient supplier selection in the mining industry. A constructive research approach was employed, identifying both practical and theoretical problems and proposing a construction—a mathematical model. This model was developed in collaboration with industry key actors, ensuring its practical applicability and validity. The main result of this research is an optimization mathematical programming model that allows practitioners to evaluate and select suppliers considering both sustainability and resilience criteria. The model facilitates a comprehensive assessment of suppliers, incorporating a wide range of factors beyond cost, including environmental impact, social responsibility, and the ability to maintain supply under various potential disruptions.

Capacity management of forwarder with multiple carriers under uncertain flight travel time and stochastic shipment demand

AbstractConsider a freight forwarder who obtains cargo space from multiple carriers. Some capacities are reserved long term in advance through allotment contracts, while some are booked on short‐term daily basis. A unified mathematical program for both short‐ and long‐term problems under uncertainties is proposed. Demands are modeled using a probability distribution as in the stochastic program, whereas flight travel times belong to an uncertainty set as in robust optimization. In the first stage, the allotments are determined. In the second stage, the shipment demand materializes but the travel time is still unknown, the forwarder determines the daily allocation among flights, given the first‐stage allotment. The objective is to minimize the expected total cost in the two stages. We derive a closed‐form solution for a special case, propose a heuristic for a general case, and evaluate its performance via numerical experiments, whose historical records came from one of the largest Thai forwarders.

Summed Tissue Resistance of Periodontal Ligaments and Alveolar Bone in Orthodontic Distal Retraction of Maxillary Canines: Mathematical Simulation of Clinical Data and Interpretation of Results

Background: The mechanical properties of either alveolar bone or periodontal ligaments under orthodontic loading, as well as orthodontic tooth movement, have been studied in recent years using computational approaches. In previous studies, we developed a theoretical mathematical approach that uses a weighting coefficient of the summed resistance of periodontal structures, namely the bone and periodontal ligaments, in relation to apex movement, the center of rotation, orthodontic force loading, and time in order to quantify the biological response to orthodontic biomechanics. Methods: We analyzed the distal retraction of three maxillary canines and integrated the clinical data obtained in the previously developed mathematical programs. Results: The values of the (σ) weighting coefficient of the tissue resistance were interpreted in the context of the clinical data obtained: the smaller the value of (σ), the higher the actual tissue resistance, with a greater difference between the crown and root movement; also, the higher the value of (σ), the lower the actual tissue resistance, with a small difference between the crown and apex movement. Conclusions: The clinical interpretation of the results allows us to set a premise for the refinement of the mathematical programs so that we can use them in assessing the orthodontic biomechanics of larger patient groups over longer periods of time and create premises of treatment protocol simplification and adjustment.

AI-Enabled Supply Chain Optimization

As global supply chains become more intricate, the significance of supply chain risk management has significantly increased. This research delves into the utilization of artificial intelligence (AI) in managing supply chain risks, analyzing cutting-edge advancements, obstacles, and potential areas for further exploration. Through a comprehensive review of literature sources like Google Scholar, Web of Science, EI, and Scopus, this study investigates how AI methods such as machine learning, deep learning, neural networks, fuzzy logic, genetic algorithms, and evolutionary algorithms can help mitigate supply chain risks. These AI technologies have demonstrated remarkable efficacy in mitigating various risks, including forecasting, anomaly detection, image recognition, text mining, logistics optimization, and emergency response tactics. Apart from AI-driven approaches, optimization solvers and algorithms play a critical role in tackling complex supply chain dilemmas. Mathematical programming solvers, including linear programming (LP), mixed-integer programming (MIP), and quadratic programming (QP), are commonly used to model and optimize supply chain networks by considering factors like cost, capacity, and demand fluctuations. Fine-tuning solver parameters and strategies to enhance computational efficiency—known as solver tuning—has been crucial in enhancing solution quality and decreasing computation time for large-scale supply chain issues. Heuristic solvers like genetic algorithms, simulated annealing, and ant colony optimization are frequently employed to resolve conflicts in supply chains. These solvers offer practical solutions to problems where exact methods are computationally impractical, allowing for swift responses to disruptions such as production delays or spikes in demand. Pyramid classification, a hierarchical approach, further refines decision-making by categorizing risks and aligning response strategies based on priority and severity. Furthermore, the integration of AI technologies and solvers enables advanced conflict resolution techniques, including scenario-based modeling and multi-objective optimization. These approaches enable decision-makers to weigh trade-offs between conflicting objectives like minimizing costs versus maximizing service levels in real-time. The study underscores that AI technologies and optimization solvers significantly bolster risk management in supply chains. Nonetheless, challenges such as data privacy concerns, security vulnerabilities, technical intricacies, and implementation obstacles pose critical barriers to widespread adoption. The study offers practical suggestions for businesses and decision-makers while pinpointing key areas for future exploration, such as devising hybrid models that merge heuristic solvers with AI for adaptive and scalable risk management strategies.

A Mathematical Programming Approach for Joint Optimization of Wind Farm Layout and Cable Routing Based on a Three‐Dimensional Gaussian Wake Model

ABSTRACTWind energy is currently one of the most promising alternative energy sources. The optimization of the wind farm layout and the cable layout are two important elements in the design of wind farms. Since increasing the distance between turbines can reduce wake loss but increase cable cost, these two optimizations are coupled and jointly affect the revenue of wind farms. In this paper, we propose a novel nonlinear mathematical programming model based on the 3D Gaussian wake model and use a mathematical programming approach to optimize the layout of the wind farm and the cable layout together, considering both power generation and cable cost. In this method, some of the constraints were linearized to facilitate the solution process. The optimization results show that profit increased by 9.07% when using annual economic efficiency as the objective function, compared with using energy production as the objective function.

A novel machine-learning rolling horizon heuristic for dynamic lot-sizing and job shop scheduling problems

This study introduces an innovative approach to production planning and scheduling under uncertain customer demands by integrating uncertainty directly into the algorithmic framework. We present a novel rolling horizon simulation-based constructive heuristic to minimise total costs, encompassing production, setup, inventory, and backlog costs. We leverage priority rules to enable the method to adapt in real-time to changes. Our contributions include not only a novel heuristic but also the integration of a coevolutionary genetic programming-based hyper-heuristic, significantly improving solution quality and computational efficiency. Compared to other rule-based heuristics, our method consistently outperforms with an average reduction in total costs of 1.78%. Furthermore, it outperforms deterministic and two-stage stochastic programming models within a one-hour time limit, with reductions of 18.20% and 6.53%, respectively. Incorporating mathematical programming models into a rolling horizon scheme led to slightly lower total costs, with an average reduction of 0.13% and 1.16%. However, in less than half an hour, the proposed method reached better results in two out of three cases. The results of an efficiency and robustness analysis highlight the proposed method as a robust solution for dynamic and complex real-world applications.

Optimisation of Pre-Engineered Buildings

In traditional building practice, a lot of construction material is wasted, because the structures are often grossly over-dimensioned. Inevitably, optimisation is a fundamental aspect of human life as well as a feature of nature. Although numerical optimisation methods have the potential to minimise the usage of structural materials, their application in routine design practice is limited by the absence of tailored algorithms. Structural optimisation based on mathematical computing is one of the approaches for sustainable and effective design in the field of civil engineering. It includes the formulation of the optimisation problem, defining variables, objective functions and constraints followed by a suitable optimisation method with mathematical programming to achieve structural optimisation resulting in reduced overall weight and cost of the structure. The current study includes an overview of prior research on structural optimisation and provides an analysis of the optimisation objectives, optimisation process and different methods and their limitations. The paper includes a numerical study to suggest an optimal design solution for a structural element which is part of a considered pre-engineered building. Topology optimisation of a conventional steel beam (I- section) is performed by numerical analysis along with the finite element method in ABAQUS. The topology optimisation of the beam in terms of decreasing the profile volume reduces the overall material consumed, thereby reducing the cost of the structure. The current numerical analysis helps in arriving at a cost-effective and efficient design solution for a typical pre-engineered building alternative to experimental tests and conventional trials.

Flow Shop Scheduling with Shortening Jobs for Makespan Minimization

This paper deals with a two-machine flow shop problem with shortening jobs. A shortening job means that the job’s processing time is a decreasing function of its starting time. The aim is to find a sequence that minimizes the makespan of all the jobs. several dominance properties, some lower bounds, and an initial upper bound are derived, which are applied to propose a branch-and-bound algorithm to solve the problem. We also propose some heuristics and mathematical programming. Computational experiments are conducted to evaluate the performance of the proposed algorithms.

Hospital selection for suspected stroke: risk-averse approach considering the minimal risk of exceeding the therapeutic time window

BackgroundTimely treatment within the therapeutic window is critical for patients with stroke. This study adopts a risk-averse optimization approach to maximize the likelihood of receiving treatment within this window.MethodsWe developed...

Low-glycemic load muffin production process for flour confectionery products expansion for people suffering from diabetes mellitus

Introduction. The relevance of the article is associated with the limited assortment of specialized products with low glycemic load for one of the common diseases, i.e. diabetes mellitus. In the age of accelerated pace of life, unhealthy diet, quick snacks, including products with easily digestible carbohydrates, lead to increased blood sugar, metabolic disorders, excess weight and, as a result, diabetes mellitus. The goal of the research. The goal was to develop recipes and technology for low-glycemic load muffins, since the range of flour confectionery products made from non-traditional raw materials was insufficiently represented. Plant-based raw materials - different types of flour with a low glycemic index, chicory, pectin, fructose, and muffins were the objects of the research. Despite the limited consumption of flour confectionery products, this product group is popular and demanded. During the research, the authors studied the characteristics of raw materials to justify the choice of recipe ingredients,their optimal ratios for the maximum possible organoleptic value, nutrient balance and minimum glycemic load. The Methods. The studies were conducted using the laboratory base of the KubSTU for conducting generally accepted instrumental methods for assessing the quality and safety of raw materials and finished products, as well as regression analysis and mathematical programming methods, focusing onthe principles of food combinatorics. The Results. During the experimental studies, the authors developed recipes for muffins with a low glycemic load - oatmeal “Azalea”, oatmeal-amaranth “Althea” and “Anemone”, the nutritional value of which was higher than the control sample due to the increased content of the main functional ingredients. The developed samples meet the requirements of regulatory documents based on the results of physicochemical studies conducted by the authors. Permissible shelf life is determined based on microbiological studies. The Conclusion. The developed recipes and technology allow obtaining muffins with increased nutritional value, low calorie content and glycemic load, which determines the possibility of recommending them in the diet of patients with diabetics.

Optimisation of Embodied Carbon and Thermal Performance of Roof Material Selections for Australian Residential Housing

This research is responding to the latest sustainable development policy for residential housing in Australia, which mandates a minimum R6.0 for roof insulation and a requirement of reporting the embodied carbon footprint for new build residential houses before obtaining development approval. The requirement of thermal resistance (R-value) results in thicker roof material to be used, and inevitably increases the total embodied carbon. This condition has drawn the need for an optimised design to balance the embodied carbon with the required thermal performance. In this paper, a multi-objective, mixed-integer, non-linear mathematical programming model is adopted to perform the optimisation. While mathematical programming is a well-established method in optimisation, a research gap has been observed in its application in optimising roof material selection under the simultaneous constraints of the R-value and volumetric heat capacity (thermal mass). Using a common conventional pitched roof with a timber frame, the study demonstrates how the model identifies material combinations that minimise the total embodied carbon within the specified thermal performance ranges. The unique contribution of this research is integrating thermal mass into the optimisation of roof material selections alongside thermal resistance, and embodied carbon. The findings provide practical recommendations for sustainable material selections across varying R-value and thermal mass ranges, offering a new perspective on roof material selections.

Teaching geometry in school: Digital resources to develop students' spatial thinking

Good school geometry education not only develops logical thinking but also the spatial imagination and thinking of students. The main means of developing spatial thinking is solving stereometric problems and especially making drawings for these problems. In current practice, teaching students how to construct images of geometric shapes is a challenging task. Weaknesses in geometric preparation are manifested primarily in the inability to accurately depict geometric figures, perform additional constructions and analyze the constructed drawing. Therefore, creating precise and correct drawings, fostering a culture of working with visual effects and developing spatial thinking skills are all vital skills to teach students in geometry courses. In this regard, digital resources and specialized mathematics programs serve as powerful learning tools. The purpose of this study is to identify the significance of digital resources in solving geometric problems for the development of students' spatial thinking. This paper discusses the relationship between the type of spatial thinking and geometric problems for reasoning and digital technologies, presents digital educational materials and resources and provides recommendations for their integration into the educational program. The research methods of this study include observation, study and generalization of teaching experience, interviewing, surveying and testing students, development of methodology and digital resources. A pedagogical experiment was conducted to test the effectiveness of the developed methodology. The results showed the effectiveness of digital resources in the learning process with a noticeable improvement in students' spatial thinking skills observed due to the introduction of digital education.

Accelerating Benders Decomposition for sustainable food closed-loop supply chain network under uncertainty: a case study

PurposeThe purpose of this study was to address waste management in the food supply chain (FSC) through the integration of inspection processes in production and distribution centers under uncertain conditions, aiming to enhance sustainability across environmental, economic and social dimensions. The study introduces a sustainable forward and reverse FSC network using a closed-loop supply chain network approach to prevent the transfer of spoiled products, ultimately providing competitive advantages to stakeholders.Design/methodology/approachA robust multi-objective mathematical programming model is proposed, incorporating inspection processes to manage perishable products effectively. The model is solved using the Augmented Epsilon Constraint technique implemented in GAMS software, providing Pareto-optimal solutions tailored to decision-makers’ preferences. Furthermore, the methodology is applied in a real-world case study and solved with the Benders Decomposition algorithm to validate its practicality and effectiveness.FindingsThe proposed methodology effectively minimizes waste and enhances sustainability in the FSC by optimizing decision-making processes under uncertainty. The illustrative examples and real case study demonstrate the efficiency of the model and solution approach, highlighting the significant role of inspection in improving all three dimensions of sustainability.Practical implicationsThe study offers valuable insights into and tools for food industry managers to make informed strategic and tactical decisions. By addressing waste management through advanced supply chain modeling, the research helps organizations reduce costs, improve sustainability and gain a competitive edge in the market.Originality/valueThis research is novel in its focus on integrating inspection into the FSC network and addressing uncertainty through robust mathematical modeling. It contributes to the existing literature by demonstrating the impact of inspection on sustainability in FSCs and providing practical solutions for real-world implementation.

Net present value comparison of different mathematical programming models for multi-element open pit mines

ABSTRACT This paper compares two well-known mathematical programming approaches aiming to maximise multi-element open-pit mines’ net present value (NPV). The first approach, called production scheduling-based (PS-based), decides the optimum schedule of the individual blocks within the pit limit, whereas the second approach, called cut-off grade-based (COG-based), decides the partial extraction of bins derived from a reprehensive grade-tonnage curve of the orebody. A modified COG-based approach is also presented to accentuate the importance of blending requirements in multi-element deposits. The blending constraints in the PS-based model are also considered selectively to understand the paramount effect of the accessibility rules and to compare the two types of strategy fairly. The models were then applied to the Chadormalu iron ore open-pit mine in central Iran. The results were almost identical for those deposits with low stripping ratios and where excessive mining capacity is available. On the other hand, the results were entirely different for deposits with high stripping ratios and insufficient mining capacity. It was also shown that the COG-based models overestimate the NPV, in this special case, about 4.3%, and discriminate the ore-waste untruly. Also, the conventional COG-based models consistently violate the rigid bounds of elements at destinations. This comparison provides a guideline for knowing where the fast COG-based approaches can be used for the project evaluations instead of time-consuming PS-based approaches.

A knowledge graph-based intelligent planning method for remanufacturing processes of used parts

Intelligent remanufacturing process planning is crucial for the efficient and high-quality remanufacturing of used parts with complex failure characteristics. However, due to the varied failure characteristics of used parts, the diversity of remanufacturing processes, and complex non-linear relationships among remanufacturing process elements, relying solely on mathematical programming or manual empirical is difficult to effectively model and optimise the remanufacturing process planning. To this end, a knowledge graph-based intelligent planning method for remanufacturing processes is proposed to enhance efficiency and quality by combining mathematical programming and knowledge reuse. Firstly, with failure characteristics as decision nodes, a full-element remanufacturing process ontology model is constructed, linking used parts, failure characteristics, and corresponding process plans. The BERT-BiLSTM-CRF model extracts remanufacturing process entities, and a remanufacturing process knowledge graph (RPKG) is constructed. Secondly, an intelligent decision-making model based on graph multi-node path retrieval is proposed. Aim to minimise carbon emissions, time, and cost, combining feature similarity calculations and nearest neighbour search (NNS) to efficiently retrieve the optimal process plan for each failure characteristic. Then, the optimal process plans are merged based on process constraints to create the complete plan. Finally, a concrete case is given to verify the effectiveness and advantages of this method.

A mathematical programming approach for a wildfire suppression problem

A mathematical programming approach for a wildfire suppression problem