Mathematical Programming Research Articles

To Test or Not to Test? The Graduate Record Examinations: Predictive Validity toward Graduate Study Success on Research Masters’ Programs in a Large European University

Graduate admissions committees in Europe have a challenging task of selecting students from an increasingly large pool of candidates with diverse application files. Graduate standardized testing can ease the comparison of application files. The purpose of this study was to examine whether the Graduate Record Examinations (GRE) is predictive of several dimensions of graduate success on English-taught research masters’ programs in science, technology, engineering, and mathematics at a large European university. The data from 167 masters’ students were collected. Hierarchical regression analyses were conducted. All GRE scales predicted Graduate Grade Point Average. Individual GRE scales predicted internship grade and supervisors’ assessments of students’ research performance and the content of their research report. None of the individual GRE scales predicted supervisors’ assessments of students’ practical skills, but the three GRE scales taken together improved the explanatory power of the model. The structure and style of students’ research reports was not predicted by the GRE. All relationships were held after accounting for socioeconomic status. Overall, the GRE appeared as a reasonable predictor of graduate study success. Both the benefits and drawbacks of the implementation of the GRE in European masters’ programs are discussed, as well as the legal limitations.

Matheuristic and learning-oriented multi-objective artificial bee colony algorithm for energy-aware flexible assembly job shop scheduling problem

With the increase of mass customization, flexible job shop scheduling problem considering assembly stage has widely existed in many manufacturing industries, such as die-casting mould factories. This problem is to find a reasonable machine assignment and operation sequence both in fabrication and assembly stages and simultaneously maximize production efficiency. In reality, energy shortages and environmental pollution have given an impetus to the development of energy-aware production scheduling problems. In this study, we address an energy-aware flexible assembly job shop scheduling problem (EFAJSP) with the objectives of minimizing flow time and energy consumption and first develop a mixed-integer linear programming (MILP) model to solve EFAJSP problem. Then, the model-specific characteristics are extracted and applied to a matheuristic decoding method for exploring the Pareto optimal solution. Due to the complexity of EFAJSP problem, a matheuristic and learning-oriented multi-objective artificial bee colony algorithm (MLABC), which combines the advantages of mathematical programming, reinforcement learning and meta-heuristic algorithm, is proposed. In addition, an initialization, destruction/construction operator and population update operator are proposed and work together to improve the exploration and exploitation performance of the proposed MLABC. Finally, numerical experimental results demonstrate the effectiveness of the proposed MILP model and the superiority of the MLABC over other algorithms in the literature.

Expert knowledge data-driven based actor–critic reinforcement learning framework to solve computationally expensive unit commitment problems with uncertain wind energy

With the expansion of power grid, unaffordable computational cost and time will pose serious challenges of time-efficient scheduling in unit commitment problem (UCP). However, existing optimization methods, i.e., mathematical programming methods and meta-heuristic algorithms, are powerless and time-consuming to handle computationally expensive UCP (CEUCP). Thus, reinforcement learning methods with strong inference and time-saving performances are motivated to solve the computationally expensive challenges in tackling CEUCPs. In this paper, a novel expert knowledge data-driven based actor–critic (AC) reinforcement learning methodology is proposed for solving CEUCPs. Specifically, in the proposed AC reinforcement learning methodology, expert knowledge, data-driven surrogate model, and improved meta-heuristic algorithm are integrated for further performance enhancement. Firstly, a novel action selection mechanism (based on the expert knowledge of thermal units characteristic) is integrated into AC to improve the efficiency of network training. Secondly, an improved extreme learning machine (ELM) data-driven surrogate model is proposed to build reward function in AC. In detail, original cost function in reward is replaced by a lightweight ELM model. Shape distance is integrated into ELM for enhancing accuracy. Finally, original marine predators algorithm (MPA) is improved for obtaining optimal dispatching decisions and rewards of AC method quickly and correctly. Original search pattern is replaced by quantum based representation for boosting convergence. The excellent performances of the proposed AC framework are verified by simulations of 10-units, 100-units, and 100-units with wind energy test systems.

Simultaneous stochastic optimisation of mining complexes: Integrating progressive reclamation and waste management with contextual bandits

ABSTRACT Managing environmental performance of waste dump facilities in mining complexes is an integral part of long-term production planning. Sustainable long-term production scheduling solutions are desired to mitigate risk and return the environment to a productive post-mining state. A simultaneous stochastic optimisation framework for long-term production scheduling in mining complexes is developed that integrates waste management and progressive reclamation. The waste dump placement schedule is jointly optimised with the extraction sequence, destination policy, and stockpiling decisions in a single stochastic mathematical programming framework. This includes the timing of progressive reclamation activities in parallel with production to enhance waste dump rehabilitation. Uncertainty related to the production of acid rock drainage is quantified by simulating geochemical properties of waste and managing the blending of uncertain waste properties within the optimisation framework. With respect to the framework for simultaneous stochastic optimisation, contextual bandits are explored to improve the metaheuristic solution approach and solve the corresponding large-scale optimisation model. The framework is tested in a multi-mine copper-gold mining complex leading to improved environmental performance. Risk of acid rock drainage is decreased by 52.5% in the waste dump facilities. Reclamation planning activities for meeting environmental requirements are scheduled prior to closure. The solution approach more effectively improves the objective function with contextual bandits leading to a 24% improvement in the study presented.

Decision support for allocating farmed fish to customer orders using a bi-objective optimization model

Aquaculture is an important industry in certain coastal areas. Focusing on farming of salmon and trout, an operational planning problem arises with the goal of allocating supply of fish to demand expressed through customer orders. This paper provides a conceptual model of such a planning problem, defines a corresponding bi-objective mathematical programming model. The problem is novel with respect to the structure of the transportation of fish, and the rules for satisfying customer orders with respect to fish size, quality, certification, and health status. Computational experiments are conducted to gain further insights into the use of the provided model to provide support for planners involved in the operational decision making. Results indicate that the bi-objective optimization model can be useful in situations where supply is insufficient to cover all the demand within a given planning horizon.

Water Pricing and Quotas: A Quantitative Analysis from a Private and Social Perspective

AbstractThe current situation of structural water scarcity due to the rise in demand, the reduction in supply as a consequence of climate change, increasingly frequent drought periods, and overall quantitative pressure on water resources creates a need for economic instruments to reduce the amount of water used, especially in the agricultural sector. Thus, water pricing and allocation quotas (proportional reduction of allocations) may be suitable tools to reduce demand or allocate scarce water resources. For a comparative analysis of the performance of these two measures, a Positive Mathematical Programming model has been developed, using the Guadalquivir River Basin as a case study. Additionally, the analysis takes into account the revenue generated from water pricing and the marginal cost of public funds. The results indicate that, from the farmer’s perspective, quotas result in smaller losses than water pricing. However, when considering water pricing along with the revenue generated from this measure, this mechanism would be more beneficial for society as a whole, since the taxes collected could be used for other purposes, albeit with efficiency losses measured by the marginal cost of public funds and the excess burden of taxation.

Optimizing Last-Mile Delivery: A Multi-Criteria Approach with Automated Smart Lockers, Capillary Distribution and Crowdshipping

Background: This publication presents a review, multiple criteria optimization models, and a practical example pertaining to the integration of automated smart locker systems, capillary distribution networks, crowdshipping, last-mile delivery and supply chain management. This publication addresses challenges in logistics and transportation, aiming to enhance efficiency, reduce costs and improve customer satisfaction. This study integrates automated smart locker systems, capillary distribution networks, crowdshipping, last-mile delivery and supply chain management. Methods: A review of the existing literature synthesizes key concepts, such as facility location problems, vehicle routing problems and the mathematical programming approach, to optimize supply chain operations. Conceptual optimization models are formulated to solve the complex decision-making process involved in last-mile delivery, considering multiple objectives, including cost minimization, delivery time optimization, service level minimization, capacity optimization, vehicle minimization and resource utilization. Results: The multiple criteria approaches combine the vehicle routing problem and facility location problem, demonstrating the practical applicability of the proposed methodology in a real-world case study within a logistics company. Conclusions: The execution of multi-criteria models optimizes automated smart locker deployment, capillary distribution design, crowdshipping and last-mile delivery strategies, showcasing its effectiveness in the logistics sector.

Decision-Making Support in Vehicle Routing Problems: A Review of Recent Literature

The Vehicle Routing Problem (VRP) involves a set of customers with known locations, each having a certain demand for goods or services. There is also a fleet of vehicles available, each with limited capacity and often a fixed starting point. With the aid of mathematical programming tools, this paper offers an overview of the most recent VRP research. This study also examines the algorithms for solving VRP models and categorizes them in terms of their application areas. For these reasons, related publications that appeared in the international journal have been compiled and studied. According to the literature review, multi-criteria decision-making (MCDM) techniques have yet to constitute the most mathematical programming methods used to solve the VRP problem.

Implementation and Evaluation of a Team-Based Electrochemistry Module in a Large Undergraduate Class

Introductory chemistry courses at the undergraduate level offer students a foundation in chemistry principles and an opportunity to develop problem-solving skills. These principles and skill sets are widely applicable across disciplines, and thus first year chemistry courses are a gateway for many programs in science, technology, engineering, and mathematics (STEM). While first-year chemistry courses are essential for STEM students, the resulting large-enrolment classes in universities can lead to challenges in implementing active learning and in helping students to reach the course learning outcomes. The evolving field of Chemistry Education Research (CER) offers data and insight for improving teaching and learning strategies at the undergraduate level. We propose and evaluate an electrochemistry team-based problem-solving module as an active learning component of a large, first-year, blended chemistry course. In this paper, we explore the process for developing the module and evaluate this learning approach through focus groups, a large class survey, and student experience interviews. Through a preliminary case study approach, our findings suggest the interactive module is useful for enhancing conceptual understanding and problem-solving in chemistry, and improving academic confidence in electrochemistry learning outcomes. Moreover, students valued their engagement with the team-based problem-solving modules as an opportunity to build community, learn collaboratively, and successfully approach relevant problems.

The stimulating effects of international emission price fluctuations on bioenergy development of an energy-importing economy

An increase in emission price creates economic incentives because bioenergy producers could sell bioenergy and realize values attached to emission offset. Recently, the termination of the short-term goal of carbon neutrality in some European countries has skyrocketed, and demand for fossil energy has increased, as has the emission price. This situation brings challenges and opportunities to an energy-importing economy like Taiwan, which relies on fossil imports and is vulnerable to price distortions but also gets a chance to develop low-carbon energy domestically. This study proposes a mathematical programming model to investigate how such variations in emission price would affect bioenergy development from energy crops and how bioenergy producers with different production possibilities would behave in uncertain market conditions. Some insightful results are explored. First, bioenergy producers would change their production strategies from energy-focused technologies to emission-oriented ones because the gain from co-products would make emission offset more profitable. At a high emission price, biopower production declines from 11,492 GWh to about 3315 GWh. Still, more than 8.73 million tons of biochar is produced, and the total offset from bioenergy and biochar sequestration expands to 33.7 million tons of CO2. Second, the production pattern of energy crops varies substantially under market conditions. Energy crop plantation at low energy prices is 227,000–263,000 ha but expands to 638,000–798,000 ha when energy and emission prices increase. Third, reducing bioenergy production does not necessarily minimize social welfare because the gain from carbon sequestration may outweigh the loss from reduced bioenergy production at high emission prices. Potential policies that can be applied to adjust production strategies are also discussed in detail.

Mathematical Programming Formulations for the Berth Allocation Problems in Container Seaport Terminals

Background: Improving the performance of marine terminals is one of the major concerns of both researchers and decision-makers in the maritime transportation sector. The problem of container storage planning and the berth allocation problem (BAP) are the two mainstays of optimizing port operations. Methods: In this work, we address these two issues, proposing two mathematical models that operate sequentially and are applicable to both static and dynamic cases. The first developed model is a mixed-integer linear problem model aimed at minimizing vessel traffic time in the port. The second model developed is a multi-objective optimization model based on goal programming (GP) to minimize both container transfer time and the number of storage areas (minimizing container dispersion). Results: The robustness of the proposed models has been proven through a benchmark with tests using data from the literature and real port data, based on the IBM ILOG CPLEX 12.5 solver. Conclusions: The two developed mathematical models allowed the both minimization of the transfer time and the number of used storage areas, whatever the number of operations handling companies (OHCs) operating in the seaport and for both static and dynamic cases. We propose, as prospects for this work, the development of a heuristic model to deal with the major instances relating to the case of large ports.

A novel mathematical optimization method to obtain the maximum-power electrical configuration of thermoelectric generators for energy harvesting

Waste thermal energy recovery with thermoelectric generators has been widely studied as a method to make systems that produce hot exhaust gases, such as aircrafts, ground vehicles and factories, more sustainable. In this type of applications, the mismatch in hot and cold side temperatures of thermoelectric modules (TEMs) creates a mismatch in the electrical output. For each situation, there is a certain electrical interconnection between the modules that gives the maximum global power output. Three optimization models to find what is the best way of connecting the TEMs without a trial-and-error process, as usually done in previous literature, based on mathematical programming are proposed: single branch of series-connected TEMs, multiple parallel-connected branches of series-connected TEMs, and multiple groups of independent series-connected TEMs. The main novel contributions of this paper are: (i) a mathematical optimization approach that provides how to connect the thermoelectric modules one by one, (ii) the application of the above-mentioned method in a common case study: an automotive thermoelectric generator, (iii) information about how the optimal connection between modules changes if the heat source changes its operation (iv) a method for selecting a fixed optimal connection even when the heat source operation changes, e.g. different operation modes in a thermal engine, based on introducing weighting parameters in the optimization mathematical model. The optimization approach followed here is novel and has not been applied before to thermoelectric generators.

Кількісне оцінювання функціональної ефективності мережевих структур за аналізом чутливості оптимізаційної моделі до зовнішніх впливів

The real network organizational structure is constantly under the influence of external influences, which can cause unexpected consequences due to the cascading spread of relevant disturbances directed at critically important parameters. Parametric sensitivity analysis is the latest computational procedure, the results of which provide the researcher with an idea and quantitative assessment of the appropriate response of the structure in the form of an analytical platform as a composition and interaction of scenario analysis, cascade process development and optimization modeling technology. The main task is timely adaptation to expected changes in business analytics, oriented to optimal resources distribution. The generalized minimum cost problem is a typical example of widespread problems of optimal distribution and use of limited, in particular, energy resources, of any nature and purpose, using the scientific management and analysis of decisions, in its network model attention is paid to the potentials of nodes. The maximum flow problem is an example of the active and effective application of methods and models of flows optimization, where the processes and objects used a network organization, the energy systems and complexes investigated, where arc parameters are critical in its model. In the article, for these classic optimization problems, mathematical and spreadsheet models were built on concrete examples. Direct and dual mathematical programming problems were solved, the following stages were carried out - the organization of a computer experiment and the construction of an analytical platform for evaluating the behavior of the network structure under the influence of external influences and disturbances as their consequences. To take into account the specific conditions of real objects with a network structure at the stage of modification, the model supplemented with appropriate restrictions and correction of input data sets. The obtained results should be useful for planning and management personnel and top-management for discussion and decision-making regarding, for example, the optimal placement of energy equipment, the weighted distribution of energy flows in the "source-sink" system or the appointment of executors for work, automated project management using project networks, etc. Keywords: optimization modeling, maximum network flow, minimum cost flows, network organizational structures, decision making, spreadsheet modeling and analytics.

Agri-food supply chain optimization through a decentralized production process in the olive oil industry

A tactical/operational model is proposed to assist decision-making in harvest planning and olive oil production planning of the different producers in the rural sector, considering allocation and transportation decisions of the kilograms of olives to the production plant with temporary relocation decisions of the mobile olive oil mills through decentralized production activities in the agri-food supply chain. A Mixed Integer Linear Programming model is presented that maximizes the profit of small farmers in the production process of single-varietal extra virgin olive oil. The decisions are based on the geographical dispersion of the different olive growers and the oil concentration of the olive varieties in a certain period, which depends on the climatic conditions of each sector where the olives are cultivated. The mathematical programming model is applied in Coquimbo, Chile, using actual data collected from previous harvest seasons. The computational results of the optimization model indicate that transportation decisions impact olive harvesting and oil production decisions. It is concluded that cooperatives of small producers in the rural sector increase overall profits and reduce transportation costs and the number of kilometers traveled by at least 41% through a decentralized production process with mobile production plants.

Mathematical programming models for order picking in warehouses with decoupling of picker and cart

As a special Travelling Salesman Problem (TSP), the Single-Picker Routing Problem (SPRP) in warehouses is of important theoretical and practical significance. In manual order picking, the items are usually picked up by a picker with a cart. To speed up the picking process, the picker is allowed to stop the cart to pick up the items individually and return to the location of the cart. This paper proposes a mixed integer linear programming formulation for an order picking problem with the decoupling of the picker and the cart in a multi-block warehouse, where the picker capacity is at most four. And based on this model, order batching problem is also analysed. Through numerical experiments, the cost of above decoupling problems is computed under different settings of the speed ratio and the capacity of the picker while he/she is travelling alone. The results indicate how the decoupling of picker and cart leads to cost reduction. Our model shows good performance for orders of small and medium scale and hence has great potential to improve the order picking operation which is executed by decoupling containers and robots/vehicles in modern digital warehouse systems.

AN EMPLOYABILITY TRACER STUDY OF SECONDARY EDUCATION –MATHEMATICS GRADUATES FROM 2022 TO 2023

This graduate tracer study investigated the employment outcomes and career trajectories of graduates from the Bachelor of Secondary Education Major in Mathematics program at Kapalong College of Agriculture, Sciences, and Technology during the academic years 2022 to 2023. The study, based on survey responses from all 49 graduates, explored demographic characteristics, employment status, income levels, relevance of education to employment, work attitudes, and skills development. Findings revealed that most graduates were female, single, and aged between 20 to 25 years. While most graduates were employed, a significant portion remained unemployed, with a notable percentage engaged in non-teaching roles. Despite this, a substantial proportion of graduates found their college degree highly relevant to their current work. The study indicated a high level of work attitude among graduates and underscored the institutions provision of quality education and effective skills development. The employment rate stood at 73.5%, indicating a favorable outcome for many graduates. However, recommendations were proposed to address areas of concern, including the establishment of a graduate employability coordinator, offering training for graduates in non-teaching roles, enhancing technical and entrepreneurial skills through specialized workshops and partnerships, and strengthening industry partnerships to expedite job placement. Overall, the study highlighted the strengths and areas for improvement in preparing mathematics graduates for the workforce, providing valuable insights for the institution to enhance its support for graduates career development. KEYWORDS: Tracer Study, Mathematics Graduates, Teacher Education

Data-Driven Heuristic Optimization for Complex Large-Scale Crude Oil Operation Scheduling

This paper addresses the challenging scheduling of crude oil operations (SCOO) problem, characterized by the intricate sequencing of activities involving discrete events and continuous variables. Given the NP-Hard nature of scheduling problems due to their combinatorial complexity, this study employs a data-driven optimization approach. Initially, historical operational data relevant to the SCOO are scrutinized; however, due to data limitations, small-scale instances are solved using a mathematical programming model to generate data. Subsequently, operational solution data are processed using the Apriori algorithm, a renowned data mining technique. The insights gained are translated into heuristic rules, laying the groundwork for a novel data-driven heuristic algorithm tailored for the SCOO problem. This algorithm is then applied to a 45-day scheduling scenario, demonstrating the efficacy of the proposed approach.

A generalized Benders decomposition approach for the optimal design of a local multi-energy system

A local multi-energy system (LMES) is a decentralized energy system producing energy under multiple forms to satisfy the energy demand of a set of buildings located in its neighborhood. We study the problem of optimally designing an LMES over a multi-phase horizon. This problem is formulated as a large-size mixed-integer linear program with a block-decomposable structure involving mixed-integer sub-problems. We propose a new way to adapt a recently published framework for generalized Benders decomposition to our problem. This is done by exploiting the fact that the constraint matrix appearing in front of the first-stage variables in the coupling constraints is non-negative. The obtained generalized Benders decomposition algorithm relies on the use of a new type of non-convex Benders cuts involving indicator functions. We first prove that, under the assumption that all first-stage decision variables are integer and bounded, the finite and optimal convergence of our algorithm is guaranteed in theory. We then investigate how to obtain a good numerical performance in practice. Finally, we report the results of a computational study carried out on a real-life case study. These results show that the proposed algorithm clearly outperforms both a mathematical programming solver directly solving the problem as a whole and a state-of-the art hierarchical decomposition algorithm.

Optimised Congestion Management Using Curative Measures in Combined AC/DC Systems with Flexible AC Transmission Systems

Due to the increasing demand for transport of electrical energy, measures for power flow control, congestion management, and higher utilisation of the existing grid play a decisive role in the transformation of the power system. Hence, enormous efforts must be undertaken using measures of congestion management. Modelling and integration of corresponding measures in optimisation tools to support grid and system operation and therewith reduce the resulting efforts become more important. This is especially true because of the high intermittency and decentralisation of renewable generation leading to increased complexity of the power system, higher loading of assets, and a growing need for control over flexible alternating current transmission systems (FACTS) and high-voltage direct current (HVDC) converters. This work therefore describes the implementation of optimised congestion management in an A Mathematical Programming Language (AMPL)-based nonlinear optimisation problem. AMPL is an effective tool to deal with highly complex problems of optimisation and scheduling. Therefore, the modelling of assets and flexibilities for power flow control in AC/DC systems in combination with an innovative grid operation strategy using predefined curative measures for the optimised use of the existing grid is introduced. The nonlinear mathematical optimisation aims at the optimal cost selection of flexibility measures. The application of the optimisation technique in a combined AC/DC system shows the optimal preventive and curative use of measures in operational congestion management. Simulation results prove that, by using predefined curative measures, the volume of cost-intensive preventive measures can significantly be reduced, especially in association with power flow control.

Novel process optimization based on machine learning: A study on biohydrogen production from waste resources

The biomass poultry litter and sewage sludge co-gasification is a good thermochemical method to produce hydrogen energy meanwhile to mitigate the consumption of fossil fuels. However, the operation optimization in the complex process system is important while computationally difficult because of high nonlinearity and many first-principle constraints. To address the optimization of this biohydrogen production process, a methodology framework for achieving the optimal operations is thus presented. The complete process system is first simulated and decomposed into upstream gasification process and downstream hydrogen purification for reducing computational complexity through the thermodynamic equilibrium-based simulation. Totally 1400 data points by pairing total 15 operating conditions with a composite sustainability index objective are generated through the random sampling and data classification strategies, which are then used for the construction of the artificial neural network (ANN)-based prediction models. ANN models of two subprocesses demonstrate the satisfactory prediction accuracy with R2 value of 0.98 and 0.99, respectively, which are then integrated with mixed-integer linear programming (MILP) for the optimization of upstream process and downstream process step-by-step. The MILP problems based on the ANN models are solved with lower optimization time of 45∼100 s compared to the heuristic algorithm optimization (3–6 h) based on the thermodynamic equilibrium-based simulation. The optimal sustainability index values of two processes are 0.80 and 0.91 which are both improved compared to the existing optimization results (0.79 and 0.84). This study emphasizes the optimization potential of the integration approach of machine learning-based modelling and mathematical programming for developing the optimal waste-to-energy processes.