Mathematical Programming Research Articles

Production Decision Model for the Cement Industry in Pursuit of Carbon Neutrality: Analysis of the Impact of Carbon Tax and Carbon Credit Costs

One of the solutions to achieve the goal of net-zero emissions by 2050 is to try to reduce the carbon emission by using the carbon tax or carbon credit (carbon right). This paper examines the impact of carbon taxes and carbon credit costs on the cement industry, focusing on ESG indicators and corporate profits. Utilizing Activity-Based Costing and the Theory of Constraints, a production decision model is developed and analyzed using mathematical programming. The paper categorizes carbon tax models into continuous and discontinuous progressive tax rates, taking into account potential government policies like emission tax exemptions and carbon trading. It finds that reducing emission caps is more effective than increasing carbon tax rates in curbing emissions. These insights can assist governments in policy formulation and provide a reference framework for establishing carbon tax systems.

Planning Courses for Student Success at the American College of Greece

We are concerned with the personalized student course plan (PSCP) problem of optimizing the plan of courses students at the American College of Greece will need to take to complete their studies. We model the constraints set forth by the institution so that we guarantee the validity of all produced plans. We formulate several different objectives to optimize the resulting plan, including the fastest completion time, course difficulty balance, and maximization of the expected student grade point average given the student’s performance in passed courses. All resulting problems are mixed-integer linear programming problems with a number of binary variables, that is, the max number of terms times the number of courses available for the student to take. The resulting mathematical programming problem is solvable in less than 10 seconds on a modern commercial off-the-shelf PC, whereas the manual process used to take more than one hour of advising time for every student and, as measured by the objectives set forth, resulted in suboptimal schedules. History: This paper was refereed.

An Optimization Approach to Berth Allocation Problems

The berth allocation problem determining the berthing time and position for incoming vessels in port operations has garnered increased attention within the global transportation network. This study focuses on the berth allocation problem with a continuous quay and dynamic vessel arrivals. With the overarching goal of enhancing service quality and optimizing berth utilization rates, this article proposes a mathematical programming model that minimizes the total waiting time of vessels and the overall completion time of vessel service. The formulated model is a mixed-integer linear programming problem that deterministic optimization techniques can globally solve. For large-scale problems, this study develops a genetic algorithm optimization approach to improve computational efficiency in reaching a near-optimal solution. Several numerical experiments are conducted to demonstrate the effectiveness and efficiency of the proposed approach.

Trapping Sets Search Using the Method of Mixed Integer Linear Programming with a Priori List of Variable Nodes

Purpose of research is to develop a new high-speed method for searching trappin sets in graph codes, ensuring the completeness of the search.Methods. There are two approaches to finding trappin sets. The first, based on the Monte Carlo method with a biased probability estimation using Importance Sampling, involves the use of a decoder. The advantage of this approach is its high performance. The disadvantages are the dependence on decoder parameters and channel characteristics and the finite probability of missing trappin sets. The second approach is based on the use of linear programming methods. The advantage of this approach is the completeness of the resulting list of trappin sets, due to its independence from the decoder parameters and channel characteristics. The disadvantage of this approach is its high computational complexity. In the article, within the framework of the second approach, a new method for searching trappin sets with less computational complexity is proposed. The method involves solving a mixed integer linear programming problem using an a priori list of code vertices participating in the shortest cycles in the code graph. Results. Using the proposed method, a search for trappin sets was performed for several low-density codes. For this purpose, the mathematical linear programming package IBM CPLEX version 12.8 was used, which was run on 32 threads of a 16-core AMD Ryzen 3950X processor with 32GB of RAM (DDR4). In the Margulis code (2640, 1320), using the proposed method, the trappin set TS(6,6) was found in a time of 0.53 s. The speedup provided by the method proposed in the paper compared to the Velazquez-Subramani method is 8252.415 times. Thanks to the high speed and completeness of the search, trappin sets were found for the first time TS(62,16) and TS(52,14) in the Margulis code (4896, 2474 ).Conclusion. The paper proposes a new method for searching trapping sets by solving a mixed integer linear programming problem with an a priori list of code. The method is fast and provides completeness of the search.

Integrating Cardiovascular Engineering and Biofluid Mechanics in High School Science, Technology, Engineering, and Mathematics Education: An Experiential Approach.

Science, technology, engineering, and mathematics (STEM) education workshops and programs play a key role in promoting early exposure to scientific applications and questions. Such early engagement leads to growing not only passion and interest in science, but it also leads to skill development through hands-on learning and critical thinking activities. Integrating physiology and engineering together is necessary especially to promote health technology awareness and introduce the young generation to areas where innovation is needed and where there is no separation between health-related matters and engineering methods and applications. To achieve this, we created a workshop aimed at K-12 (grades 9-11) students as part of the Summer Youth Programs at Michigan Technological University. The aim of this workshop was to expose students to how engineering concepts and methods translate into health- and medicine-related applications and cases. The program consisted of a total of 15 h and was divided into three sections over a period of 2 weeks. It involved a combination of theoretical and hands-on guided activities that we developed. At the end of the workshop, the students were provided a lesson or activity-specific assessment sheet and a whole workshop-specific assessment sheet to complete. They rated the programs along a 1-5 Likert scale and provided comments and feedback on what can be improved in the future. Students rated hands-on activities the highest in comparison with case studies and individual independent research. Conclusively, this STEM summer-youth program was a successful experience with many opportunities that will contribute to the continued improvement of the workshop in the future.

Optimisasi Portofolio Saham Syariah dengan Pendekatan Fuzzy Goal Programming

This study discusses about solving the problem of stock portfolio optimization. The portfolio optimization problem can be modeled as a multiobjective model with two objective functions, they are maximizing return and minimizing risk. This study uses the mean-variance Markowitz model to model the portfolio. The fuzzy goal programming approach is used to solve stock portfolio problems by converting a multi-objective model into a fuzzy mathematical programming model which is solved using a nonlinear programming method. The results of implementing the model on stocks listed on the Jakarta Islamic Index show that the best investment proportion forms an optimal portfolio according to the level of aspirations. Several different optimal portfolios can be formed using the fuzzy goal programming approach. The difference in the results of these portfolios depends on the level of aspiration of investors.

Enhancing production monitoring: A back allocation methodology to estimate Well flow rates and assist Well test scheduling

Production flow rates are crucial to make operational decisions, monitor, manage, and optimize oil and gas fields. Flow rates also have a financial importance to correctly allocate production to fiscal purposes required by regulatory agencies or to allocate production in fields owned by multiple operators. Despite its significance, usually only the total field production is measured in real time, which requires an alternative way to estimate wells’ production. To address these challenges, this work presents a back allocation methodology that leverages real-time instrumentation, simulations, algorithms, and mathematical programming modeling to enhance well monitoring and assist in well test scheduling. The methodology comprises four modules: simulation, classification, error calculation, and optimization. These modules work together to characterize the flowline, wellbore, and reservoir, verify simulation outputs, minimize errors, and calculate flow rates while honoring the total platform flow rate. The well status generated through the classification module provides valuable information about the current condition of each well (i.e. if the well is deviating from the latest well test parameters), aiding in decision-making for well testing scheduling and prioritizing. The effectiveness of the methodology is demonstrated through its application to a representative offshore oil field with 14 producing wells and two years of daily production data. The results highlight the robustness of the methodology in properly classifying the wells and obtaining flow rates that honor the total platform flow rate. Furthermore, the methodology supports well test scheduling and provides reliable indicators for well conditions. By utilizing real-time data and advanced modeling techniques, this methodology enhances production monitoring and facilitates informed operational decision-making in the oil and gas industry.

Решение обратной задачи теплопередачи в конденсаторе турбоустановки со встроенным теплофикационным пучком

For power plants reduction of heat losses is one of the main ways to save energy. Energy saving issue is one of the priority areas of the development of science, engineering, and technology in the Russian Federation. Efficiency upgrading of the equipment operation are associated with the condensers of turbine units, since more than 50 percent of the fuel energy is released into the environment with cooling water. The operating efficiency of a condenser with built-in heating beams significantly affects the vacuum in the condenser and, thus, the operating efficiency of the entire unit. Diagnostics of the condition and improvement of operating modes of the condenser of a turbine unit with a built-in heating unit is an urgent scientific and practical issue. To develop a model of a condenser with a built-in heating beam, the methodology of matrix formalization of the description of heat and mass transfer processes has been used. To solve the problem of diagnosing the condition of equipment, methods of least squares and mathematical programming have been used. Within the framework of the matrix formalization methodology, the authors have developed an approach to solve inverse problems of diagnosing and designing multi-flow heat exchange equipment considering the phase transition in coolants. The authors have obtained and analyzed solutions of the inverse problem from the point of view of diagnosing the state of heat exchange equipment using the example of a turbine unit condenser with a built-in heating beam. Analysis of the calculated results has shown an adequate description by the model of the standard data for the analyzed condenser. Analysis results have shown the possibility to use the model for runtime diagnosis of the condition of power equipment and the efficient use of energy resources due to preventing ineffective modes. The proposed approach allows us to formulate and solve inverse problems of diagnosing the state of equipment of condensing units for various purposes.

Market design for ancillary service provisions of inertia and frequency response via virtual power plants: A non-convex bi-level optimisation approach

The Great Britain (GB) government is paving the path to decarbonisation by actively promoting the integration of wind power into its generation mix. This sharp transition to renewable energy, however, introduces specific challenges. The characteristics of non-synchronous wind turbines have the potential to impact grid stability and frequency security due to the reduction in system inertia. In response to these challenges, the deployment of virtual power plants (VPPs) is envisioned in deregulated power systems, which allow for the aggregation and coordinated control of diverse distributed energy resources, enhancing grid flexibility, reliability, and efficiency. Moreover, VPPs offer the provision of system inertia and frequency response services at the national level. This study drops this assumption and leverages the localised flexibility inherent in VPPs to meet the ancillary service requirements of the low-carbon power system. The formulated problem is constructed as a non-convex bi-level optimisation problem, where the upper-level problem represents the operation of a frequency-constrained unit commitment model, and the lower-level problem embodies the energy dispatches and frequency responses of a group of VPPs, guided by the dual price signals of cleared energy and ancillary services. To address the non-convex nature of the unit commitment problem, a two-fold approach is employed. First, binary commitment status decision variables are relaxed to continuous versions. Subsequently, the duality gap between the original non-convex unit commitment problem and its relaxed dual form is minimised, yielding a solution closely approximating the optimal solution of the original problem. Second, the relaxed bi-level optimisation problem is transformed into a single-level mathematical programs with equilibrium constraints by replacing the lower-level VPP problems with their equivalent Karush-Kuhn–Tucker optimality conditions. The case studies conducted in this work encompass a comprehensive scope. Initially, the study evaluates the effectiveness of VPPs in delivering ancillary services within the projected context of the GB power system for 2030. The findings reveal a substantial 28.28% decrease in system operation costs when compared to the benchmark case lacking VPP flexibility. Additionally, the integration of VPPs leads to significantly lower price signals for inertia, primary frequency response, and enhanced frequency response, reduced by 81.21%, 79.13%, and 86.27%, respectively, in contrast to the benchmark case. The analysis then delves into a sensitivity exploration, investigating the inherent flexibility of VPPs. The profit of local VPPs is expected to increase with VPP flexibility. Finally, the study illustrates how VPPs can adapt to and derive benefits from an increasing level of wind power penetration by providing a higher amount of frequency response.

Data-Driven Optimization for Air Traffic Flow Management with Trajectory Preferences

In this paper, we present a novel data-driven optimization approach for trajectory-based air traffic flow management (ATFM). A key aspect of the proposed approach is the inclusion of airspace users’ trajectory preferences, which are computed from traffic data by combining clustering and classification techniques. Machine learning is also used to extract consistent trajectory options, whereas optimization is applied to resolve demand-capacity imbalances by means of a mathematical programming model that judiciously assigns a feasible four-dimensional trajectory and a possible ground delay to each flight. The methodology has been tested on instances extracted from the Eurocontrol data repository. With more than 32,000 flights considered, we solve the largest instances of the ATFM problem available in the literature in short computational times that are reasonable from the practical point of view. As a by-product, we highlight the trade-off between preferences and delays as well as the potential benefits. Indeed, computing efficient solutions to the problem facilitates a consensus between the network manager and airspace users. In view of the level of accuracy of the solutions and the excellent computational performance, we are optimistic that the proposed approach can make a significant contribution to the development of the next generation of air traffic flow management tools.

Multi Objective and Multi-Product Perishable Supply Chain with Vendor-Managed Inventory and IoT-Related Technologies

With the emergence of the fourth industrial revolution, the use of intelligent technologies in supply chains is becoming increasingly common. The aim of this research is to propose an optimal design for an intelligent supply chain of multiple perishable products under a vendor-managed inventory management policy aided by IoT-related technologies to address the challenges associated with traditional supply chains. Various levels of the intelligent supply chain employ technologies such as Wireless Sensor Networks (WSNs), Radio Frequency Identification (RFID), and Blockchain. In this paper, we develop a bi-objective nonlinear integer mathematical programming model for designing a four-level supply chain consisting of suppliers, manufacturers, retailers, and customers. The model determines the optimal network nodes, production level, product distribution and sales, and optimal choice of technology for each level. The objective functions are total cost and delivery times. The GAMS 24.2.1 optimization software is employed to solve the mathematical model in small dimensions. Considering the NP-Hard nature of the problem, the Grey Wolf Optimizer (GWO) algorithm is employed, and its performance is compared with the Multi-Objective Whale Optimization Algorithm (MOWOA) and NSGA-III. The results indicate that the adoption of these technologies in the supply chain can reduce delivery times and total supply chain costs.

The Development of a New Smart Evacuation Modeling Technique for Underground Mines Using Mathematical Programming

Navigating miners during an evacuation using smart evacuation technology can significantly decrease the evacuation time of an underground mine in case of emergency hazards. This paper presents a mathematical programming model to calculate the most efficient escape path for miners as a critical component of smart evacuation technology. In this model, the total evacuation distance of the crew is minimized and scenarios with blocked pathways and stamina categories for the miners are simulated. The findings revealed that all the tested scenarios were technically feasible. Using the feature that filters out blocked pathways has no downsides as safer routes are calculated and there is no penalty in the computation time. This paper also discusses the social and technical issues that must be resolved before the algorithm can be implemented as an actual escape solution.

Extensive hypothesis testing for estimation of crash frequency models

Estimating crash data count models poses a significant challenge which requires extensive knowledge, experience, and meticulous hypothesis testing to capture underlying trends. Simultaneous consideration of multiple modelling aspects is required including, among others, functional forms, likely contributing factors, and unobserved heterogeneity. However, model development, frequently affected by time and knowledge, can easily overlook crucial modelling aspects such as identification of likely contributing factors, necessary transformations, and distributional assumptions. To facilitate model development and an estimation that can extract as many insights as possible, an optimization framework is proposed to generate and simultaneously test a diverse array of hypothesis. The framework comprises a mathematical programming formulation and three alternative solution algorithms. The objective function involves minimizing the Bayesian Information Criterion (BIC) to avoid overfitting. The solution algorithms include metaheuristics to deal with an NP-hard problem and search through a complex and nonconvex space. The metaheuristics also enable to handle unique datasets through varying search strategies. The effectiveness of the proposed framework was ascertained using three distinct datasets, and published models used as benchmarks. The results highlighted the ability of the proposed framework to estimate crash data count models, surpassing benchmark models in terms of insights and goodness-of-fit. The framework provides several advantages, such as robust hypothesis testing, uncovering unique specifications and vital insights in the data, and leveraging existing knowledge to enhance search efficiency. The framework also exposes the vulnerability of traditional analyst efforts to fall into local optima, bias, and limitations in creating more efficient models. In a compelling example using crash data from Washington, the proposed framework unveiled insights overlooked by a benchmark published model, identifying speed, interchanges, and grade breaks as likely crash contributors, and revealing the potential danger of excessively wide shoulders. Conversely, the benchmark model identified fewer contributing factors and missed a crucial non-linear relationship between crash safety and shoulder widths. While wider shoulders are typically associated with improved safety, the proposed models suggest a safety threshold beyond which further widening could decrease safety. The introduction of random parameters in the analysis revealed a more nuanced relationship with crash frequency, thereby underlining the limitations of models incapable of capturing heterogeneity.

Addressing Carbon Storage in Forested Landscape Management Planning—An Optimization Approach and Application in Northwest Portugal

Climate change is driving worldwide efforts to mitigate and reverse the increasing anthropogenic emissions of greenhouse gases. Forests can uptake considerable amounts of carbon from the atmosphere, but management decisions and resultant silvicultural practices can largely influence these ecosystems’ carbon balance. This research presents an approach to help land managers cope with the need to ensure the provision of forest products and services while contributing to mitigating climate change via carbon sequestration. The emphasis is on combining a landscape-level resource capability model with a mathematical programming (LP) optimization method to model and solve a land management problem involving timber production, carbon sequestration, and resistance to wildfire targets. The results of an application on a forested landscape in Northwest Portugal showed that this approach may contribute to analyzing and discussing synergies and trade-offs between these targets. They revealed important trade-offs between carbon sequestration and both timber production and fire resistance.

Translanguaging in Mathematics Bilingual Classroom: Students' Perception

This research aims to investigate translanguaging in a Bilingual classroom. Hence, this research tries to know the students’ perception of translanguaging classroom interaction. This research focused on the student’s perception of translanguaging. This research applied a qualitative method, the instruments were interviews. The result of the interview was transcribed and analyzed based on the research focus. The findings of this research show that translanguaging facilitates the teaching and learning of the Mathematic bilingual program makes their English teaching in the classroom effective and makes the students understand the teaching and learning material well. The way lecturers conduct translanguaging is based on the situation of the students. If the students do not understand what the lecturers explain in English, they will use translanguaging in the classroom to make the teaching and learning process. Students have positive responses about the bilingual practice in Mathematics class.

Mathematical programming models to assist the evaluation of shipbrokers

Shipbrokers play a key role in maritime industry by acting as intermediates between shipping companies and the market. They undertake various chartering, buying or selling operations. In this paper, we propose a mathematical programming approach for the evaluation and selection of shipbrokers. Specifically, the score of each ship broker is a composite measure that is derived by aggregating a set of performance criteria, e.g., reputation, etc. The developed mathematical programming models enable the aggregation and weighting of the criteria. We employ three optimization models to explore the effect of different weighting schemes on the scores and ranking of the shipbrokers. The models that provide a common set of weights for all the shipbrokers establish the appropriate ground for comparisons among them. Also, our models facilitate the incorporation of user priorities over the criteria in the form of weight restrictions. The proposed approach is illustrated by assessing seven shipbroker offers for selling a dry-bulk ship using four criteria, namely revenue, brokerage fee, brokerage time and terms & conditions.

Integrating virtual resequencing with car resequencing via selectivity banks for mixed-model assembly lines

Physical resequencing and virtual resequencing are two general forms of sequence adjustment in the context of mixed-model assembly lines. Selectivity banks can be used to physically change the production sequences on a mixed-model assembly line. Virtual resequencing can be incorporated into this process in order to improve the reordering outcomes. This paper introduces a problem of car resequencing before final assembly via selectivity banks that incorporates virtual resequencing. A mathematical programming formulation is presented to describe this integrated resequencing problem. The objective is to minimize the number of violations of sequencing rules within the downstream sequence. Several heuristic approaches for the car storage and retrieval processes are proposed, based on which nine integrated resequencing algorithms are developed. Computational experiments show that incorporating virtual resequencing nearly always obtains noticeably better results than pure physical resequencing. In addition, one of the presented algorithms, denoted by IR9, which jointly applies a chromosome based fill procedure and an integrated release procedure, performs best.

A Survey on Optimization Algorithms: Challenges and Future Opportunities

This paper conducts a comprehensive exploration of contemporary optimization algorithms, addressing challenges and outlining potential avenues for future research. The survey encompasses a wide spectrum of optimization techniques employed in various domains, ranging from mathematical programming to machine learning and artificial intelligence. It systematically analyses the inherent challenges faced by existing algorithms, including scalability issues, convergence speed, and adaptability to diverse problem spaces. Furthermore, the paper critically examines the impact of optimization algorithms on real-world applications, considering their effectiveness and limitations. The survey identifies emerging trends, such as hybrid approaches and metaheuristic methods that offer promising directions for overcoming current challenges. By synthesizing the state-of-the-art in optimization algorithms, this paper provides a valuable resource for researchers, practitioners, and decision-makers, guiding them towards addressing existing limitations and unlocking new opportunities in the evolving landscape of optimization research.

A two-stage real world serial batching scheduling problem: a case study

This paper concerns a real-life production management problem composed of two stages, which includes interdependent batch scheduling problems. Moreover, both stages require setup operations at the beginning and between the subsequent batches. From the optimisation point of view, this production management problem is complying with customers’ deadlines and hence minimising total lateness. To achieve this objective, the production planner must identify optimum or near-optimum batch schedules for both stages. Correspondingly, this paper aims to develop a methodology to manage the related production problem as accurately as possible. We formulate an optimisation model that employs the mathematical programming method in line with this. Afterwards, an algorithmic proposal based on the simulated annealing algorithm is also developed to solve the problem in realistic sizes. The computational capabilities of the developed model and the algorithm are evaluated on the randomly generated problem sets. A direct comparison between the mathematical model and the algorithm shows how efficiently the proposed algorithm solves real-world problems. Also, computational results indicate that the proposed algorithm satisfactorily solves the related real-world batch scheduling problem.

Energy-efficient scheduling model and method for assembly blocking permutation flow-shop in industrial robotics field

Implementing green and sustainable development strategies has become essential for industrial robot manufacturing companies to fulfill their societal obligations. By enhancing assembly efficiency and minimizing energy consumption in workshops, these enterprises can differentiate themselves in the fiercely competitive market landscape and ultimately bolster their financial gains. Consequently, this study focuses on examining the collaborative assembly challenges associated with three crucial parts: the body, electrical cabinet, and pipeline pack, within the industrial robot manufacturing process. Considering the energy consumption during both active and idle periods of the industrial robot workshop assembly system, this paper presents a multi-stage energy-efficient scheduling model to minimize the total energy consumption. Two classes of heuristic algorithms are proposed to address this model. Our contribution is the restructuring of the existing complex mathematical programming model, based on the structural properties of scheduling sub-problems across multiple stages. This reformation not only effectively reduces the variable scale and eliminates redundant constraints, but also enables the Gurobi solver to tackle large-scale problems. Extensive experimental results indicate that compared to traditional workshop experience, the constructed green scheduling model and algorithm can provide more precise guidance for the assembly process in the workshop. Regarding total energy consumption, the assembly plans obtained through our designed model and algorithm exhibit approximately 3% lower energy consumption than conventional workshop experience-based approaches.