Mathematical Programming Research Articles

An Instrument to Evaluate 4-H Cloverbud STEM Programming

Evaluation data is needed to demonstrate the impact of 4-H science, technology, engineering, and mathematics (STEM) programming on children and youth. However, collecting evaluation data from cloverbuds (ages 5-7) is particularly challenging given their developmental age. We adapted an observational Cloverbud evaluation tool to measure basic life skills, essential elements of positive youth development experiences, and, unique to this tool, STEM specific experiences. We developed the STEM items using educational science standards allowing Extension to document STEM in addition to youth development outcomes. Doing so, may increase the adoption of 4-H STEM programming by teachers in the school setting.

Overview of Distribution System Reliability Optimization Against Lightning

The reliability of the distribution system relies on the occurrence of lightning phenomena, which can significantly affect the distribution of electricity and result in power service disruptions. Therefore, ensuring the reliability of the distribution system is an ongoing challenge that necessitates continuous research for optimal solutions. Researchers have always developed solutions that are always up to date by leveraging advancements in mathematics, engineering technology, and management strategies. This paper presents a comprehensive summary and discussion of various optimization models for enhancing system reliability. It offers an overview of commonly employed mathematical programming techniques and algorithms for Lightning Protection Systems (LPSs), while also highlighting the influence of lightning phenomena on these solutions. The focus of this paper is to present the engineering aspects behind the development of modern LPSs. It encompasses historical reliability data, technical limitations, and economic considerations. By utilizing operations research and optimization theory, researchers have been able to devise more effective approaches for addressing reliability issues, even in highly intricate systems across different domains. Technological advancements have prompted researchers to adopt a new perspective on solving reliability problems, based on practical engineering requirements. In conclusion, the continuous progress in mathematics, engineering technology, and management approaches has enabled researchers to tackle the challenges associated with distribution system reliability. This paper serves as a valuable resource, providing insights into the development of modern LPSs and offering guidance on optimizing system reliability in various practical engineering scenarios.

Efficient approach to cyclic scheduling of high throughput screening systems for bioengineering

As a standard technology, high throughput screening (HTS) is widely applied for the analysis and detection of new biological substances and drugs in pharmaceutical industries and life science research. Efficient scheduling of HTS systems is a crucial issue for reducing the cost of their operations. As a typical application of high throughput screening, this work studies the scheduling problem of the enzyme-linked immunoassay (ELISA) processes in HTS systems. For this process, it requires a one-microplate cyclic schedule and a microplate visits some processing resources multiple times, making the process deadlock-prone such that its scheduling problem is very challenging. To tackle this problem, the process is modeled by a kind of Petri nets. Based on this model, by analyzing the dynamic properties of the process, it is able to directly deduce an activity sequence to form an optimal cyclic schedule. In this way, it not only efficiently solves the challenging scheduling problem without building a mathematical programming model, but also the obtained schedule is very easy to understand and implement.

Resource Extraction Evaluation Using a Mathematical Programming Framework for Surface-Underground Mining Options and Transitions Optimization

A mathematical programming framework based on Mixed Integer Linear Programming (MILP) model for surfaceunderground mining options and transition optimization for resource extraction is presented in this paper. Existing models are mainly based on a stepwise optimization approach with limited constraints which produces localized optimal solutions and are often impractical. For mineral deposits amenable to both surface and underground mining options, the MILP framework determines the most suitable mining option and associated schedule to exploit the orebody. The MILP formulation is tested and implemented on a gold deposit case study. The NPV of the optimal mining option ($ 2.515 billion) is sensitive to the gold price, ore quantity delivered from the underground mine, and delay factor associated in supporting the operational development and stopes. Positive changes in the delay factors associated with operational development support and mining stope support have more impact on the NPV than negative changes. However, the NPV is highly sensitive to the mining stope support delay than the operational development support delay

Finite termination of the optimal solution sequence in parametric optimization

This paper investigates the finite termination of the optimal solution sequence in parametric optimization as a subproblem of the equilibrium problems. By introducing an augmented mapping on the solution set of the equilibrium problems, we establish the concept of augmented weak sharpness for this set relative to the sequence of optimal solutions in parametric optimization. Augmented weak sharpness is an extension of the concepts of weak sharpness and strongly non-degeneracy. Under the condition that the solution set of the equilibrium problems is augmented weak sharpness, sufficient conditions for the finite termination of the sequence of optimal solutions in parametric optimization are provided. For some special cases of the equilibrium problems (Mathematical Programming (MP), Variational Inequality Problems (VIP), etc.), these results extend the corresponding results under weak sharpness or strongly non-degeneracy conditions in the existing literature. Additionally, they also provide weaker sufficient conditions for the finite termination of many optimization algorithms.

A graph‐based optimization methodology for identifying firefighting strategies aimed at domino effects

AbstractFirefighting strategies at process plants would include simultaneous extinguishment of burning units and cooling of exposed units if firefighting resources are sufficient. This way, the fire can be contained and its propagation to the exposed units can be prevented, which would otherwise cause fire escalation and result in domino effects. However, when the firefighting resources are not sufficient to handle all the critical units—either burning or exposed—at once, firefighters need to decide which burning units to suppress first and which exposed units to cool first to minimize the risks. Making effective decisions in such situations becomes critical knowing that, by spreading the fire to adjacent units, the number of critical units grows exponentially, making the available firefighting resources even more insufficient. In the present study, after modelling fire spread in a tank terminal as a directed graph, closeness centrality—a graph centrality metric—is used to identify the critical units from the viewpoint of their contribution to potential domino effects. Knowing the critical units and considering available firefighting resources for suppression and cooling of these units, mathematical programming is applied for optimal allocation of firefighting resources. A comparison between the results of the present work and previous studies shows the effectiveness of the developed methodology.

Using Generative AI to Facilitate Data Analysis and Visualization: A Case Study of Olympic Athletes

The ability to work with data is an important skill for students enrolled in technical and professional communication programs, but students with limited mathematical and computer programming literacies might find it difficult to do basic data analysis or customize data visualizations. This article examines the extent to which ChatGPT can make data analysis and visualization more accessible for students with limited technical proficiency. The results suggest that although the tool is poised to have a substantial impact in helping students create effective data visualizations, its efficacy as a data analysis tool is more limited.

Presenting a new model for evaluating the factors affecting equipment reliability using system dynamics

AbstractThis study examines reliability of equipment (RoE) through three approaches: equipment design reliability, human reliability (HR), and maintenance‐based reliability. HR plays a key role in minimizing human error (HE) and subsequently enhancing RoE. Given that equipment reliability is influenced by numerous factors, these technologies come with various constraints, multiple outputs, and inputs. Compared to mathematical programming and analytical models, simulation methods in the field of reliability are relatively limited. However, system dynamics (SD) modeling is well‐suited to capture dynamics and complexity of systems, making it a valuable tool for long‐term strategic decision‐making. In this study, a combination of SD and regression approaches has been employed to explore the relationship between reliability and key variables such as HE and profit. Initially, the variables influencing reliability are identified, and then SD is utilized to understand the processes and interactions among these variables. Furthermore, linear regression is employed to establish the relationship between affective variables, reliability, and HE. To validate the results obtained from the proposed method, a sensitivity analysis is conducted. The results demonstrate the effectiveness of the proposed model. Simulation results indicate that implementing policies such as employee training and preventive maintenance significantly enhances RoE, leading to increased sales and profits for the organization. Therefore, managers should prioritize these variables and allocate adequate attention and resources to them.

Socioeconomic impact of agricultural water reallocation policies in the Upper Litani Basin (Lebanon): a remote sensing and microeconomic ensemble forecasting approach

The integration of remote sensing and socio-economic data is crucial for policy making in regions suffering from water scarcity and climate change. We present a framework that combines remotely sensed estimates of biomass and water use from FAO’s Water Productivity Open-access portal (WaPOR) (V2) with an ensemble of calibrated mathematical programming models to assess the impact of water reallocations on rain-fed and irrigated land use and production in water-stressed basins. We evaluated our model in the Upper Litani Basin of Lebanon using two water reallocation policies: (i) quotas that progressively reduces water allocation for irrigation up to 100%, at 1% intervals and (ii) a pricing policy that increases the agricultural water price up to 0.25 USD/m3, at 0.0025 USD/m3 intervals. Our results reveal that 1) the impacts of water availability reductions due to quotas on profit and employment are less-than-proportional when water allocation is reduced by <50%, but abruptly increase when water allocation is reduced by >50%; 2) irrigators responses to prices are inelastic until a price increase of 0.03 USD/m3, become significantly more elastic afterwards, and again become inelastic above a price increase of 0.06 USD/m3; 3) higher water prices progressively reduce profit and labor, significantly reduce water use over the elastic interval (where irrigators cultivating low value-added crops shift to rainfed agriculture), and increase tariff revenue during the inelastic interval (where irrigators largely stick to their crop portfolios and pay the higher water prices). Our results reveal nontrivial uncertainties and tipping points, thus highlighting the value of combining reliable water use data with multi-model and multi-scenario ensembles in informing robust policies.

Potential impacts of the Common Agricultural Policy's Income Stabilisation Tool on farmers' incomes and crop diversity: A French case study

AbstractThis paper analyses the potential impacts of a hypothetical implementation of the Income Stabilisation Tool (IST) in France for the field crops sector. The IST is a risk management tool available within the 2014–2020 Common Agricultural Policy (CAP) to support farmers facing a severe drop in their incomes. This analysis was conducted using a farm‐level model relying on expected utility theory and based on positive mathematical programming with risk. The model was applied to a sample of 1375 field crop farms in France derived from Farm Accountancy Data Network (FADN) data. Simulation results show that the uptake rate of the tool is relatively low, less than 37% in all scenarios. It is strongly dependent on CAP public support and on how much premium farmers have to pay. Highest uptake rates are observed in farms specialising in Other Field Crops, such as potatoes, pulses and sugar beet, and farms located in regions highly exposed to climatic risks. Previous experience with insurance favours the acceptance of the IST. Model results also show that the IST improves adopters' income and reduces income inequality. However, its impacts on crop diversity, measured by the Shannon index, are negative.

Accelerated numerical solutions for discretized Black–Scholes equations

Abstract Accepted by: Aris Syntetos This study thoroughly investigates the efficiency of advanced numerical extrapolation methods aimed at enhancing the convergence of vector sequences in the realm of mathematical finance. Our focus lies in the application of polynomial extrapolation techniques to calculate finite difference solutions for the Black–Scholes (BS) equation—an indispensable model in options pricing. The performance of our algorithms undergoes rigorous evaluation through a comprehensive analysis involving both simulated and real-world data. Notably, our experiments uncover that a stochastic scheme, incorporating two extrapolation strategies and a random relaxation parameter, outperforms other proposed methods, excelling in both convergence and stability metrics. Our findings underscore the potential of this numerical extrapolation method to enhance the efficiency of financial calculations, particularly in the realm of option pricing. This innovation holds promise for refining financial models and addressing specific challenges within the field of mathematical programming, providing effective solutions to the primary computational bottlenecks commonly encountered in financial decision-making.

Optimizing Sulfur Emission Control Areas for Shipping

The design of emission control areas (ECAs), including ECA width and sulfur limits, plays a central role in reducing sulfur emissions from shipping. To promote sustainable shipping, we investigate an ECA design problem that considers the response of liner shipping companies to ECA designs. We propose a mathematical programming model from the regulator’s perspective to optimize the ECA width and sulfur limit, with the aim of minimizing the total sulfur emissions. Embedded within this regulator’s model, we develop an internal model from the shipping liner’s perspective to determine the detoured voyage, sailing speed, and cargo transport volume with the aim of maximizing the liner’s profit. Then, we develop a tailored hybrid algorithm to solve the proposed models based on the variable neighborhood search meta-heuristic and a proposition. We validate the effectiveness of the proposed methodology through extensive numerical experiments and conduct sensitivity analyses to investigate the effect of important ECA design parameters on the final performance. The proposed methodology is then extended to incorporate heterogeneous settings for sulfur limits, which can help regulators to improve ECA design in the future. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72025103, 71831008, 72201163, 72071173, 72371221, 72394360, 72394362, 72361137001 and HKSAR RGC TRS T32-707/22-N]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0278 .

Dismantling Inequitable Structures

Four shifts needed to create mathematics programs that are equitable, just, and inclusive for each and every student.

A hierarchical structure for harnessing the flexibility of residential microgrids within active distribution networks: Advancing toward smart cities

The increasing integration of Renewable Energy Sources (RESs) and the replacement of fossil fuel vehicles with electric types in distribution systems, while enhancing economic and environmental aspects, have introduced new challenges to network production-consumption balance due to the inherent randomness of these resources. This factor has magnified the significance of balancing markets in renewable-based distribution networks, as these markets address uncertainties and are vital for operational stability. Consequently, this paper introduces a two-stage multi-layer methodology for organizing local energy and balancing markets among Residential Microgrids (RMGs) within an Active Distribution Network (ADN). The AND operator organizes both energy and balancing markets.In the first stage, the intra-day energy market operates, engaging non-profit-seeking aggregators, RMGs, and ADN. Moving to the second stage, the intra-hour balancing market is conducted involving profit-seeking Flexible Load (FL) and Electric Vehicle (EV) aggregators, RMGs, and ADN. The ADN operator organizes both markets and can alter the network topology online within the energy market. The planning of profit-seeking aggregators is formulated using Karush-Kuhn-Tucker (KKT) conditions and Strong Duality Theory (SDT) in the form of Mathematical Programming with Equilibrium Constraints (MPEC), considering the correlation of aggregators' profit with the satisfaction index of end-users. The simulation results of the proposed methodology on a modified 118-bus IEEE distribution test system using GAMS indicate that this approach not only provides a significant share of balancing capacities through FLs and EVs but also ensures system stability against intra-hour fluctuations across various scenarios. The results also validate that the proposed methodology achieves a reduction of 24.8 % in power losses and 5.06 % in market costs, while simultaneously ensuring profitability for both aggregators and RMGs.

Enhancing Teachers’ Pedagogical Awareness of Teaching Early Mathematical Skills – A Mixed Methods Study of Tailored Professional Development Program

ABSTRACT The purpose of this mixed methods study was to explore changes in pedagogical awareness of teaching early mathematical skills among teachers in early childhood education (N =7) when participating in a tailored professional development (PD) program in mathematics. The program, which was designed around principles of transformative learning, was aimed at strengthening the conscious and holistic teaching of early mathematical skills to 3- to 7-year-old children. Research Findings: Thematic analysis of semi-structured interviews revealed that teachers enhanced their pedagogical awareness of teaching early mathematical skills concerning developmentally appropriate mathematical content, child-initiated mathematical learning and holistic mathematical teaching in different daily situations and play. Data obtained from pre-PD and follow-up questionnaires completed by teachers confirmed a sustainable increase in their pedagogical awareness of numerical and spatial reasoning. Recognizing children’s interests, reflecting on and examining one’s own practices individually and collaboratively, and taking actions to develop teaching and learning practices aligned with those of the PD program comprised the foundation for the transformative process. Practice or Policy: It was concluded that PD programs in mathematics enhance teachers’ pedagogical awareness of teaching early mathematical skills holistically when they are tailored to the needs of teachers, include reflective elements, and follow principles of transformative learning.

Multi-Vehicle Collaborative Trajectory Planning for Emergency Vehicle Priority at Autonomous Intersections

Emergency vehicle (EV) prioritization plays an important role in improving rescue efficiency and saving lives and property. Most existing studies have been confined to either investigating signal prioritization for EVs at intersections or focusing on clearing emergency lanes on road segments, with limited consideration for an integrated approach that combines both methods. In this study, we have developed a bi-level trajectory planning model aimed at optimizing the trajectories of EVs at intersections and road segments located within the communication range, using vehicle-to-everything technology. The upper-level model is designed to plan the entry times, speeds, and internal trajectories of vehicles within the intersection while avoiding any conflicts that may arise during their movements. In particular, to address the dimensionality of the proposed large-scale optimization problems, we introduce the equidistant discretization method to discretize the entry speeds of vehicles into a finite set of selectable values. The lower-level model focuses on optimizing the longitudinal and lateral trajectories on roadways to ensure that vehicles arrive at the stop line punctually and promptly. Both the upper- and lower-level models are formulated as mixed-integer linear programming models. The A Mathematical Programming Language and the Gurobi solver are employed for optimization. The case study demonstrates that the proposed model effectively optimizes vehicle trajectories at intersections and road segments, leading to a significant reduction in delays for EVs.

Multi-Stage Mathematical Programming Models and Their Applications in Agriculture

The article presents multi-stage parametric programming models, the characteristics of which depend on time and seasonality. The first model took into account the impact on the yield of agricultural crops of predecessors. In the second model, related to the distribution of sales of products by seasons, at the first stage, a point and interval forecast of the task parameters is carried out, at the second stage, optimal coefficients are determined that characterize the volume of sales of crop products depending on the season. Then, based on the obtained forecasts and optimal coefficients, the parametric programming problem is solved. The described tasks are implemented on real objects of the Irkutsk region. Logistic and asymptotic dependences are used to predict crop yields, and the price trend is a seasonal model. It should be noted that the presented models can be refined with the help of expert assessments, which will improve the adequacy of planning the activities of agricultural producers.

Формирование оптимального кредитного портфеля с использованием нечётко-множественного подхода

The problem of profit maximization from lending to a financial organization is considered. A set of loan con-tracts forms a loan portfolio, which makes it possible to use the portfolio theory in the study of the designated problem. We will consider the formation of a loan portfolio as the formation of an investment portfolio. The problem arises of redistributing the funds of the investment portfolio in order to minimize its possible risk and maximize profitability. This problem in classical formulation can be solved according to Markowitz risk diversification. Thus, the problem of risk minimization and profitability maximization from lending to a financial institu-tion can be represented as a fuzzy mathematical programming problem, and more specifically, as a fuzzy linear programming problem. The resulting problem is solved by considering discrete α-levels and is reduced to a set of linear programming problems constructed for each of them. A clear expected optimal solution can be obtained by applying the defuzzification method, which allows you to convert a fuzzy set into a crisp number.

Оптимізація будівельних конструкцій

In the field of the theory of calculation of building structures, there is a constant refinement of the actual operation of these structures, i.e. design schemes are created that most accurately correspond to actual operating conditions. Creating optimal structures is a very urgent task facing designers. Therefore, it is quite natural to try to solve this problem using mathematical programming methods, which involve: selecting dependent and independent variables, constructing mathematical models and establishing criteria for the effectiveness of the selected model. In this case, the model should be a function that fairly accurately describes the research being carried out using mathematical apparatus (various types of functions, equations, systems of equations and inequalities, etc.). In mathematical programming, any set of independent (controlled) variables is called a solution. Optimal solutions are those that, for one reason or another, are preferable to others. The preference (effectiveness) of the study is quantified by the numerical value of the objective function. “Solution Search” is an add-in for Microsoft Excel that is used to solve optimization problems. Simply put, with the Solver add-in, you can determine the maximum or minimum value of one cell by changing other cells. Most often, this add-in is used to find optimal solutions to problems economically. There are not enough results of using this approach for calculating building structures in the public domain. Therefore, it is quite logical to try to use this add-on in problems of optimization of building structures. In this work, an attempt was made to use mathematical programming methods and this add-on to optimize the geometric dimensions of the structure, when the numerical value of the bending moment in a specific section was chosen as an optimization criterion.

Design of metamaterial-based heat manipulators using isogeometric level-set topology optimization

We exploit level-set topology optimization to find the optimal material distribution for metamaterial-based heat manipulators. The level-set function, geometry, and solution field are parameterized using the Non-Uniform Rational B-Spline (NURBS) basis functions to take advantage of easy control of smoothness and continuity. In addition, NURBS approximations can produce conic geometries exactly and provide higher efficiency for higher-order elements. The values of the level-set function at the control points (called expansion coefficients) are utilized as design variables. For optimization, we use an advanced mathematical programming technique, Sequential Quadratic Programming. Taking into account a large number of design variables and the small number of constraints associated with our optimization problem, the adjoint method is utilized to calculate the required sensitivities with respect to the design variables. The efficiency and robustness of the proposed method are demonstrated by solving three numerical examples. We have also shown that the current method can handle different geometries and types of objective functions. In addition, regularization techniques such as Tikhonov regularization and volume regularization have been explored to reduce unnecessary complexity and increase the manufacturability of optimized topologies.