Mathematical Programming Research Articles

Systematic optimization of off-grid green hydrogen production systems

In this work a novel mathematical programming formulation is presented for the simultaneous optimal design and operation of standalone, green hydrogen production systems. There is a pressing need to develop, test and commercialize technologies that can contribute in the medium term to our coordinated efforts to combat climate change. The system under study is inherently dynamic due to the stochastic and intermittent nature of meteorological data and there is a likelihood to overestimate its production capacity and economic performance. Failing to identify shortcoming in the design stage can result in expensive operational mistakes that will negatively affect the gathering race to build a massive new hydrogen economy. We present and demonstrate a systematic methodology that could be useful in decarbonizing our energy production systems by optimizing standalone, green hydrogen units and reducing the risk during their commercialization.

Decarbonizing Maritime Transport through Green Fuel-Powered Vessel Retrofitting: A Game-Theoretic Approach

Addressing the urgent global challenge of man-made greenhouse gas emissions and climate change necessitates collaborative action between shipping lines and government regulatory agencies. Aligning with the International Maritime Organization’s emissions reduction strategy, this paper presents a novel bi-level programming model that unifies these stakeholders. On the upper level of the proposed bi-level model, a number of shipping lines optimize retrofitting plans for their vessels to maximize economic benefits. On the lower level, the regulatory agency responds to the carbon reduction efforts by setting retrofitting subsidies and emission penalty rates. This framework represents a multi-leader–single-follower game involving shipping lines and the regulatory agency, and its equilibrium is determined through an equilibrium problem with equilibrium constraints (EPEC). The EPEC comprises multiple single-leader–follower problems, each of which can be formulated as a mathematical program with equilibrium constraints (MPEC). The diagonalization algorithm (DM) is employed for its solution. Simulation studies performed based on a ten-year planning period show that the proposed approach can effectively promote vessel retrofitting and the use of green fuels, which leads to an annual emission reduction of over 50%.

A critical review of analytical approaches in public bus transit network design and operations planning with focus on emerging technologies and sustainability

The Public Bus Transit Network Design and Operations Planning Problem (PBTNDOPP) is a complex transportation problem. Analytical approaches are one of the key approaches to studying this problem, often leading to optimal or near-optimal solutions with reduced computational complexity compared to mathematical programming. This article leverages the Critical Path Method (CPM) to visualize the historical applications of analytical approaches in PBTNDOPP. Then, it reviews the applications of these approaches to some of the recently emerged sub-problems identified via CPM, i.e., sustainable public bus transit network design and introducing emerging transportation technologies to these systems. Our review aims to shed light on the current state of the literature and its future direction in the selected sub-problems by analyzing published studies in the last decade from various angles, such as the problems investigated, modeling methods, decision variables, network structures, and findings. The review shows that the existing body of literature on the application of analytical approaches to the selected problems is immature and at an early stage of development. For example, most of the studies on sustainable PBTNDPPP have not included all dimensions of sustainability and have only focused on environmental sustainability, while considering social criteria such as fairness and equity in PBTNDOPP is crucial for designing a sustainable PBTS. Another important gap is related to hybrid methods based on analytical approaches that take realistic assumptions and uncertainty in various problem parameters and variables into account.

How do we prepare our youth for a world of big data?

How do we prepare our youth for a world of big data? Nancy Butler Songer, Associate Provost of STEM Education at the University of Utah, considers the importance of developing primary and secondary school programs in STEM fields that support students in developing the competencies with big data. We all know something about Big Data. This term describes massive volumes of structured and unstructured data that influence nearly every decision in our lives. A recent report by the United States National Academies of Sciences, Engineering, and Medicine stated, ‘We live in a world where nearly every interaction—both personal and professional—is mediated through data’. (1) As dedicated scientists and educators, it is our crucial responsibility to develop and evaluate primary and secondary school programs in Science, Technology, Engineering, and Mathematics (STEM) that can identify and guide students in developing the competencies with data that students need to navigate the Big Data world of the present and future. But what are these competencies?

Cost-aware workflow offloading in edge-cloud computing using a genetic algorithm

AbstractThe edge-cloud computing continuum effectively uses fog and cloud servers to meet the quality of service (QoS) requirements of tasks when edge devices cannot meet those requirements. This paper focuses on the workflow offloading problem in edge-cloud computing and formulates this problem as a nonlinear mathematical programming model. The objective function is to minimize the monetary cost of executing a workflow while satisfying constraints related to data dependency among tasks and QoS requirements, including security and deadlines. Additionally, it presents a genetic algorithm for the workflow offloading problem to find near-optimal solutions with the cost minimization objective. The performance of the proposed mathematical model and genetic algorithm is evaluated on several real-world workflows. Experimental results demonstrate that the proposed genetic algorithm can find admissible solutions comparable to the mathematical model and outperforms particle swarm optimization, bee life algorithm, and a hybrid heuristic-genetic algorithm in terms of workflow execution costs.

Economic impact and food security effects of trade disruptions in agricultural products for Sweden

The COVID-19 pandemic and geopolitical conditions in 2022–2023 highlighted the vulnerabilities of food supply chains to trade disruptions in agricultural inputs and foods, with the ensuing economic effects on producers and consumers. This study calculated the impact of various disruptions in the trade of agricultural inputs and outputs for Swedish producers and consumers and for food security. To this end, a mathematical programming model of the food sector with a spatial dimension was applied, which accounts for adjustments and interactions between producers and consumers of food. Food security is measured in terms of the self-sufficiency ratio, the ability to produce minimum dietary needs, and economic access for low-income households. The trade scenarios included disruptions to imports of agricultural inputs (fertilisers, fuel, feed, pesticides and foreign labour) and foods. The results showed that the economic effects for producers can be considerable, with a reduction in producer surplus by up to 75%. The decrease in consumer surplus is smaller, amounting to a maximum decrease of 21%. The self-sufficiency ratio and the ability to produce minimum dietary needs can be reduced by 55% and 61%, respectively, but may rise if the disruption to feed imports increases. Economic access to foods is slightly decreased in all scenarios. These results showing different impacts of trade disruptions on producers and consumers and food security metrics highlight the need to undertake extensive assessments to determine whether and how to prevent and mitigate their effects. The economic effects on producers and consumers and the associated impacts on food security are likely to differ, which affects the selection and targeting of policies, such as compensation for economic losses and promotion of food security.

Integrating freshness and profitability in horticultural supply chain design

AbstractThe freshness at sale for horticultural products sold in retailers is increasingly valued because of its impact on the environmental and social sustainability of the agri-food sector. To ensure this maximum freshness, it is necessary to consider it when planning planting, harvesting, packing, holding, and transporting of horticultural products. These tactical decisions are constrained by the configuration of the supply chain, which makes it relevant to ascertain if maximising the freshness at sale for horticultural products during chain design influences its configuration. Given the gap in the literature in this area, this paper proposes a mathematical programming model with multiple objectives that supports the design of agri-food supply chains by simultaneously maximising their economic benefits and the average freshness at sale for horticultural products. To this end, the model incorporates strategic decisions concerning supply chain design and tactical decisions concerning the production and transport planning of horticultural products to ensure their freshness. The model’s validity is confirmed through its application to a realistic case study of Argentina, considering scenarios with different weight distribution among the optimized objectives. The results reveal that the distribution of weights among the objectives significantly determines the design of the supply chain and its subsequent management, showing the relevance of considering the freshness of the horticultural products in this process. In addition, the impact this has on the supply chain economic benefits, the average freshness at sale for horticultural products, the wastage of products and the unsatisfied demand are analysed, finding interesting trade-offs among these factors.

Integrating freshness and profitability in horticultural supply chain design

AbstractThe freshness at sale for horticultural products sold in retailers is increasingly valued because of its impact on the environmental and social sustainability of the agri-food sector. To ensure this maximum freshness, it is necessary to consider it when planning planting, harvesting, packing, holding, and transporting of horticultural products. These tactical decisions are constrained by the configuration of the supply chain, which makes it relevant to ascertain if maximising the freshness at sale for horticultural products during chain design influences its configuration. Given the gap in the literature in this area, this paper proposes a mathematical programming model with multiple objectives that supports the design of agri-food supply chains by simultaneously maximising their economic benefits and the average freshness at sale for horticultural products. To this end, the model incorporates strategic decisions concerning supply chain design and tactical decisions concerning the production and transport planning of horticultural products to ensure their freshness. The model’s validity is confirmed through its application to a realistic case study of Argentina, considering scenarios with different weight distribution among the optimized objectives. The results reveal that the distribution of weights among the objectives significantly determines the design of the supply chain and its subsequent management, showing the relevance of considering the freshness of the horticultural products in this process. In addition, the impact this has on the supply chain economic benefits, the average freshness at sale for horticultural products, the wastage of products and the unsatisfied demand are analysed, finding interesting trade-offs among these factors.

Pricing heterogeneous products to heterogeneous customers who buy sequentially

AbstractThis paper considers optimal pricing in a system with limited substitutable resources, such as certain goods or services. Prices for the different resources have to be set and then customers with heterogeneous preferences show up sequentially. Customers, of n types, select an item from the m available resources, depending on their valuations of the resources and the prices. The goal is to analyze this optimization problem, characterize a set of candidates to optimal solutions and provide methods for solving it. We prove that this problem is NP-hard to approximate within a factor $$O(n^{1-\varepsilon })$$ O ( n 1 - ε ) for any fixed $$\varepsilon >0$$ ε > 0 . Another important contribution is to prove that, the space of prices (which in principle is a continuous domain in $${\mathbb {R}}^m$$ R m ), can be reduced to a finite set of vectors of cardinality $$m^{m-2}n^m2^m$$ m m - 2 n m 2 m . For a deterministic version of the problem, where the customer types are known to the firm, we provide a mathematical program that chooses the best set of prices. We report extensive computational results showing the usefulness of our exact approach to solve medium size problems with up to 200 customers and different assortments of products and customer types. We then show how to approximate the stochastic model by a small number of solutions of deterministic scenarios solved using a mixed-integer linear program.

Characterization of the Competencies of Future Mathematics Teachers in Ecuador

Objective: To analyze the graduation profile of teacher training programs to identify and describe the specific skills that teachers should acquire during their initial training. Theoretical Framework: The study is grounded in the theory of teacher training competencies, which asserts that teachers must possess cognitive abilities to adapt to different educational contexts, procedural skills to address specific professional challenges, and ethical attitudes to guide their educational practice. Method: An ex post facto study was conducted with a mixed exploratory and descriptive approach, using as the study population the 13 Ecuadorian universities that offer teacher training in mathematics. Results and Discussion: A total of 198 competencies grouped into 17 categories were identified. The most frequent category pertains to mathematical knowledge. Variations among the universities analyzed were observed, with some focusing more on content knowledge and others on competencies directly related to teaching practice. Research Implications: The results can be used to enhance teacher training programs by integrating key competencies and developing more effective educational strategies. Additionally, they could influence the formulation of educational policies that establish clear standards, thereby improving educational quality and preparing teachers for current challenges. Originality/Value: This study provides a mixed exploratory and descriptive approach to examine the graduation profile of teacher training programs in mathematics in Ecuador. It also offers guidance for the preparation of future teachers, ensuring alignment with current and future educational demands.

Resiliency Analysis of Role-Based Access Control via Constraint Enforcement and Mathematical Programming

Resiliency Analysis of Role-Based Access Control via Constraint Enforcement and Mathematical Programming

Synthesis of heat-integrated water networks considering detailed heat exchanger design

This paper introduces a mathematical programming approach for synthesising heat-integrated water networks (HIWNs) with a detailed heat exchanger design. A common assumption of constant heat capacities of water streams is relaxed. The specific heat capacity of water is now considered as a nonlinear function of temperature to avoid errors in calculating energy balances. In addition, most previous works have assumed constant individual heat transfer coefficients for water streams and utilities when estimating heat transfer areas. This assumption can lead to significant over- or under-estimation of heat transfer areas. In this research, individual and overall heat transfer coefficients for heat exchangers are calculated based on the detailed design of plate heat exchangers for heat recovery. The objective function of the proposed mixed integer nonlinear programming (MINLP) model is to minimise the total annualised cost (TAC). The TAC includes operating costs for freshwater and utilities, pumping costs for overcoming pressure drops in heat exchangers, and investment costs for heat exchangers. Three examples are solved in this work to verify the proposed model.

Approximation Methods for a Class of Non-Lipschitz Mathematical Programs with Equilibrium Constraints

Approximation Methods for a Class of Non-Lipschitz Mathematical Programs with Equilibrium Constraints

METHOD OF TRUCK CREW WORK COORDINATION ON INTERNATIONAL ROUTES

The article deals with the problem of increasing the productivity of trucks in the performance of international road freight transportation in Eastern Europe and the European Union. There are restrictions on cabotage transportation (domestic cabotage), as well as time limits for the execution of orders and penalties for the execution of the entire volume of transportation in this case in addition to the restrictions of the European Agreement E/ECE/TRANS/564. The task of optimizing the required number of vehicles, drivers/driving crews, and route configuration was formulated and solved by mathematical programming with time constraints. At the same time, a variable method of organizing the work of drivers on adjacent routes was applied, by which drivers/crews are not assigned to a specific vehicle but are changed after a certain number of work hours. This minimized the non-productive idling of trucks, ensured compliance with the work and rest regulations of drivers, and minimized truck mileage on routes. In contrast to known methods and research results, the problem is solved with a guaranteed achievement of the optimum in an acceptable search time. This result was achieved due to the appropriate formulation of the solution conditions. The results can be applied in the logistic planning of transport processes.

Методы и информационная система автоматизированного подбора лица, принимающего решения

The effectiveness of management activities is largely determined by the degree of reasonableness and efficiency of selecting a decision-maker and delegating the necessary powers to him. To solve this problem, it is advisable to use mathematical methods and information technologies that ensure the specified selection in an automated mode. This approach involves the creation of a DSS using unpopulated decision-making technologies. This allows you to identify employees or groups of employees who are most suitable for the implementation of managerial functions in terms of certain quality indicators. The use of unpopulated decision-making technologies in the interests of economic entities makes it possible to reduce the time and cost of their adoption by automating the transit management level. The purpose of the study considered in this article is to solve the problem of organizing the effective selection of a decision maker (DPR), or a group of people, as well as transferring the task to be performed automatically. To achieve this goal, the mathematical modeling of the LPR selection algorithm (LPR group) was carried out by performing operations on sets containing significant indicators and solving a mathematical programming problem. The proposed mathematical apparatus makes it possible to create a subsystem of the DSS responsible for the selection of a DSS (group of DSS) capable of making a high-quality management decision under given constraints, and transferring tasks to it for execution. The specified restrictions contain the type of task to be solved, the possibility of its implementation with the help of unpopulated decision-making technologies, competence limitations of LPR (groups of LPR), time constraints. The DSS subsystem, created on the basis of the proposed mathematical apparatus containing the task of optimizing the selection of LPR (LPR group) according to the cost criterion, makes it possible to minimize the cost of decision-making.

THE IMPACT OF DIFFERENTIATED PEDAGOGY ON THE IMPROVEMENT OF HIGHER-ORDER THINKING SKILLS AMONG YEAR 5 STUDENTS IN THE SCIENCE SUBJECT AT SK. ST. AUGUSTINE (M), MERADONG

Higher-order thinking skills (HOTS) are a vital aspect in the transformation of the education system in Malaysia. However, thinking skills are less effectively implemented in the Malaysian education system, leading to a lack of Higher- Order Thinking (HOT) skills among Malaysian pupils. One of the factors contributing to this problem is the teaching approach used by teachers during teaching and learning sessions in the classroom. The presence of students with a variety of learning styles, interests, and levels of ability in a classroom has been a challenge for teachers to undertake teaching and learning activities and subsequently the established teaching and learning objectives. According to the 2022 International Student Assessment Programme Report (PISA), Malaysia is ranked 53rd out of 81 participating countries, which is the lowest ranking when compared to other countries. This is the result of the student's inability to answer assessment questions that require high-level thinking skills. The same situation also occurred where Malaysia’s performance in the Trend in International Mathematical and Scientific Studies (TIMSS) programme in 2019 showed that Malaysia was ranked 26th out of 39 participating countries. (TIMSS 2019). Differentiated Pedagogy (DP) is proposed as a solution, as it meets the learning needs and backgrounds of students who are different from the abilities aspect. The purpose of this study was to examine the impact of different pedagogy methods on the improvement of higher-order thinking skills within 5th-year primary school pupils in science subjects. The study was conducted using an experimental method by implementing differentiated pedagogical learning on a sample of 40 pupils selected purposefully from a school in the Meradong district. The sample of this study was divided by class, which was Year 5 of St. Thomas (n = 20) was used as a control group taught using conventional teaching methods, and Year 5 of St. Matthew (n = 20) was assigned to an experimental group taught using Differentiated Pedagogy method. The sample was given a high-level thinking skills test to determine the performance of pupils before and thereafter the implementation of differentiated pedagogy in learning the unit of 'Matter'. The results of this study indicated an improvement in higher-order thinking skills (HOTs) application in the treatment group that was taught utilizing differentiated pedagogy compared to that of the control group. This study suggests the use of this differentiated pedagogy in other schools as well as in other subjects.

Perinatal influences on academic achievement and the developing brain: a scoping systematic review.

In this PRISMA-compliant systematic review, we identify and synthesize the findings of research in which neuroimaging and assessments of achievement have been used to examine the relationships among aspects of developmental programming, neurodevelopment, and achievement in reading and mathematics. Forty-seven studies met inclusion criteria. The majority examined the impact of prematurity (n = 32) and prenatal alcohol exposure (n = 13). Several prematurity studies reported a positive correlation between white-matter integrity of callosal fibers and executive functioning and/or achievement, and white matter properties were consistently associated with cognitive and academic performance in preterm and full-term children. Volumetric studies reported positive associations between academic and cognitive abilities and white and gray matter volume in regions such as the insula, putamen, and prefrontal lobes. Functional MRI studies demonstrated increased right-hemispheric language processing among preterm children. Altered activation of the frontoparietal network related to numerical abilities was also reported. Prenatal alcohol exposure studies reported alterations in white matter microstructure linked to deficits in cognitive functioning and academic achievement, including mathematics, reading, and vocabulary skills. Volumetric studies reported reductions in cerebral, cerebellar, and subcortical gray matter volumes associated with decreased scores on measures of executive functioning, attention, working memory, and academic performance. Functional MRI studies demonstrated broad, diffuse activation, reduced activation in canonical regions, and increased activation in non-canonical regions during numeric tasks. A preponderance of studies linked prematurity and prenatal alcohol exposure to altered neurodevelopmental processes and suboptimal academic achievement. Limitations and recommendations for future research are discussed. Identifier: DOI 10.17605/OSF.IO/ZAN67.

A mathematical programming model integrating waste pickers in urban area recycling practice

Urbanization has resulted in a significant accumulation of waste in densely populated areas. Effective household waste separation practices within urban areas are crucial for advancing the concept of circular economy. The informal system has contributed remarkably to urban material circulation, but it has not been appropriately valued. Through the partnership among the municipal solid waste authorities, condominium building residents, and waste pickers, the latter can be engaged in the community to assist in household waste separation. This initiative would not only enhance their income and reduce probable occupational risks but also augment the recycling rate in the community. Based on the insights from the current waste picker assignment policy in Taichung City, this study has established a mathematical programming model by considering the overall waste separation volume and proximal distance to the neighborhood, facilitating the assignment of individual waste picker to multiple communities within the neighborhood area. Consequently, concerned waste pickers may increase their income and avoid the constraints of picking up recyclables in high-occupational-risk areas. Additionally, it may reduce the volume of unsorted garbage in the community. According to the findings of case studies, the developed model could obtain an optimal solution or acceptable approximate solution in a short timeframe. In contrast to the outcomes from the existing waste picker assignment policy, the application of the developed model could increase the total volume of sorted recyclables, which was directly proportional to the income of waste pickers, by 2.3–2.6 times.

Integrated transmission expansion planning incorporating fault current limiting devices and thyristor-controlled series compensation using meta-heuristic optimization techniques

Transmission expansion planning (TEP) is a vital process of ensuring power systems' reliable and efficient operation. The optimization of TEP is a complex challenge, necessitating the application of mathematical programming techniques and meta-heuristics. However, selecting the right optimization algorithm is crucial, as each algorithm has its strengths and limitations. Therefore, testing new optimization algorithms is essential to enhance the toolbox of methods. This paper presents a comprehensive study on the application of ten recent meta-heuristic algorithms for solving the TEP problem across three distinct power networks varying in scale. The ten meta-heuristic algorithms considered in this study include Sinh Cosh Optimizer, Walrus Optimizer, Snow Geese Algorithm, Triangulation Topology Aggregation Optimizer, Electric Eel Foraging Optimization, Kepler Optimization Algorithm (KOA), Dung Beetle Optimizer, Sea-Horse Optimizer, Special Relativity Search, and White Shark Optimizer (WSO). Three TEP models incorporating fault current limiters and thyristor-controlled series compensation devices are utilized to evaluate the performance of the meta-heuristic algorithms, each representing a different scale and complexity level. Factors such as convergence speed, solution quality, and scalability are considered in evaluating the algorithms’ performance. The results demonstrated that KOA achieved the best performance across all tested systems in terms of solution quality. KOA’s average value was 6.8% lower than the second-best algorithm in some case studies. Additionally, the results indicated that WSO required approximately 2–3 times less time than the other algorithms. However, despite WSO’s rapid convergence, its average solution value was comparatively higher than that of some other algorithms. In TEP, prioritizing solution quality is paramount over algorithm speed.

Partial reformulation-linearization based optimization models for the Golomb ruler problem

In this paper, we provide a straightforward proof of a conjecture proposed in \cite{Duxbury2021} regarding the optimal solutions of a non-convex mathematical programming model of the Golomb ruler problem. Subsequently, we investigate the computational efficiency of four new binary mixed-integer linear programming models to compute optimal Golomb rulers. These models are derived from a well-known nonlinear integer model proposed in \cite{Kocuk2019}, utilizing the reformulation-linearization technique. \modif{Finally, we provide the correct outputs of the greedy heuristic proposed in \cite{Duxbury2021} and correct some false conclusions stated or implied therein.}