Mathematical Optimization Model Research Articles

Supply Chain Design for Waste Valorization Through High-Energy-Density Pellet Production in Chile

This study presents the development and application of a mathematical optimization model to improve decision-making in the supply chain for high-energy-density pellet (HEDP) production and commercialization. Focused on the Metropolitan Region of Chile, the research involved a detailed analysis of key supply chain components, including identifying landfills and controlled dumps, waste volume assessments, plant location analysis, technology evaluation, and market potential exploration. The model revealed that the available raw material in the region was sufficient to meet 100% of HEDP demand, with a surplus of 2,161,952 tons remaining after satisfying maximum demand. An optimization analysis of potential plant locations identified Santa Marta as the optimal choice, resulting in annual cost savings of USD 100,000 compared to other sites. This work underscores the role of mathematical optimization in enhancing supply chain efficiency for biomass-based energy products, offering valuable insights for strategic decision-making in similar contexts.

Determination of Particle Size for Optimum Biogas Production from Ouagadougou Municipal Organic Solid Waste

Anaerobic digestion’s contribution to sustainable development is well established. It is a sustainable production process that enables energy to be saved and produced and efficient pollution control processes to be implemented, thereby contributing to the sustainable development of our societies. Optimizing biogas yields from the anaerobic digestion of municipal organic waste is crucial for maximum energy recovery and has become an important topic of interest. Substrate particle size is a key process parameter in biogas production and precedes other pretreatment methods for most organic materials. This study aims to evaluate the impact of particle size and incubation period on biomethane production from municipal solid waste. Sampling of municipal solid waste was carried out in waste pre-collection in the city of Ouagadougou, Burkina Faso. Waste characterization showed lignocellulolytic green waste (grass, dead leaves), waste composed of fruit and leafy vegetables and leftover food waste. TableCurve 3D v4.0 software was used to develop an optimal mathematical model to correlate particle size and biomethane productivity to describe optimal production parameters. Particle sizes ranging from 2000 to 63 µm high biogas production values, specifically 385.33 and 201.25 L·kg−1 of MSV. PCA analysis clearly showed a high correlation between particle size and biogas production, with optimum production recorded for size 250 µm with a biomethane production value of 187.53 L·kg−1 of MSV. The average relative errors and RMSE for CH4 content were improved by 24.31% and 44.97%, respectively. The data calculated with the developed mathematical model and the existing experimental data were compared and permutated to validate the model. This work enabled the identification of a mathematical model that describes the correlations between the input parameters of an experiment and the monitored parameters, as well as the definition of the particle size that allows for the optimal production of biomethane.

Machine learning-based optimal temperature management model for safety and quality control of perishable food supply chain

The management of a food supply chain is difficult and complex because of the product's short shelf-life, time-sensitivity, and perishable nature which must be carefully considered to minimize food waste. Temperature-controlled perishable food supply chain provides the highly crucial facilities necessary to maintain the quality and safety of the product. The storage temperature is the most vital factor in maintaining both the quality and shelf-life of a perishable food. Adequate storage temperature control ensures that perishable foods are transported to the end-users in good quality and safe to consume. This paper presents perishable food storage temperature control through mathematical optimal control model where the storage temperature is regarded as the control variable and the deterioration of the perishable food’s quality follows the first-order reaction. The optimal storage temperature for a single perishable food is determined by applying the Pontryagin's maximum principle to solve the optimal control model problem. For multi-temperature commodities supply chain, an unsupervised machine learning (ML) method, called k-means clustering technique is used to determine the temperature clusters for a range of perishables. Based on descriptive analysis, it is observed that the k-means clustering technique is effective in identifying the best suitable storage temperature clusters for quality control of multi-commodity supply chain.

An Optimized Multi-Level Control Method for Wireless Power Transfer System Using the Particle Swarm Optimization Algorithm

A Wireless Power Transfer (WPT) system, known for its contactless power delivery, is extensively used for power supply in spacecraft applications. Achieving efficient and stable power transfer necessitates the integration of DC/DC converters on both the primary and secondary sides of WPT systems for power conversion and control. Traditional efficiency optimization methods primarily focus on impedance matching within the wireless power resonance network, often neglecting the overall efficiency optimization of multi-stage DC-DC and WPT systems. This oversight results in suboptimal overall system efficiency despite optimal efficiency in the wireless transmission segment. Additionally, the time-varying nature of mutual inductance and load parameters during power transmission in WPT systems presents challenges for maximum efficiency tracking and power control. This paper introduces a multi-level coordinated control efficiency optimization method for WPT systems utilizing the particle swarm optimization (PSO) algorithm. This method takes into account the transmission losses across all power conversion units within the WPT system, establishing a mathematical model for the joint optimization of overall system transmission efficiency and power. The PSO algorithm is then employed to solve this optimization model using estimated mutual inductance and load values. By adjusting the DC/DC converters on both sides, the method ensures optimal overall system efficiency and consistent power transmission. Experimental results indicate that under varying load and mutual inductance conditions, a Series–Series (SS) compensated WPT system using this method achieves a 200 W power output with maximum efficiency tracking, a power output error of 0.63%, and an average transmission efficiency of 86.2%. This demonstrates superior power transmission stability and higher efficiency compared to traditional impedance matching methods.

A mathematical model for potash supply chain management with a strategic logistics perspective

Abstract Accepted by: M. Zied Babai This paper introduces a novel Integer Linear Programming model designed to enhance the efficiency and sustainability of the potash supply chain, a crucial element supporting global agriculture. The developed mathematical optimization model focuses on fleet selection (private/outsource) and incorporates the concept of ‘inter-warehouse collaboration’, which addresses key logistics considerations. Integrating mining, processing, storage and transportation, the model encompasses decision variables like extracted carnallite amount, production, storage levels and shipped potash amount. Illustrated through a case study on the Arab Potash Company in Jordan, the results showcase the model’s proficiency in meeting local and international market demands. The model ensures resilient and sustainable supply chain performance by emphasizing logistics optimization, particularly in fleet selection. The study attains the highest ‘warehouse-to-warehouse’ support for Standard and Granular potash types in the international demand scenario, contributing to efficient production planning and fleet management. In conclusion, the presented mathematical model is a valuable tool for potash industry stakeholders, offering insights for strategic decision-makers involved in production planning and fleet management.

Research on charging scheduling optimization of pure electric buses considering peak-valley time-of-use electricity prices and battery loss costs

In recent years, with the accelerated progress of pure electric buses in my country, the charging scheduling and operation plan of pure electric buses urgently needs to be rationalized and scientific. This study takes the charging scheduling operation in the daily operation of pure electric buses as the starting point, and effectively describes the battery loss cost function by analyzing the optimal fluctuation range of the state of charge of the power battery of pure electric buses. Combined with the analysis of the characteristics of peak and valley time-of-use electricity prices during the charging period, the problem is refined into a pure electric bus charging scheduling decision with controllable operation completion, and the parallel machine scheduling theory is used to characterize and solve the mathematical optimization model, with the aim of minimizing the operating cost of bus companies. At the same time, an immune optimization algorithm based on random key encoding and a greedy algorithm based on the idea of avoiding peaks and filling valleys are developed to solve large-scale problems. In addition, the effectiveness of the algorithm and the applicability of the method are verified through the real bus network in Shanghai.

Comparison of desirability function (DF) and overall equipment effectiveness (OEE) with mathematical model for optimization in fruit juice production process

Comparison of desirability function (DF) and overall equipment effectiveness (OEE) with mathematical model for optimization in fruit juice production process

Research on multi-objective topology optimization of unmanned sightseeing vehicle frame based on Analytic Hierarchy Process

To optimize the frame of a sightseeing vehicle, this paper proposes a multi-objective topology optimization method combining Analytic Hierarchy Process (AHP) and topology optimization. Firstly, the edges of the unmanned sightseeing car are statically analyzed. The rectangular steel frame structure of the original frame is replaced with square plates, the basic model of the unmanned sightseeing car frame is established, and a single-objective topology optimization mathematical model of the frame is established to optimize the topology design of the frame. Then, in order to design a frame structure that meets all the working conditions at the same time, a mathematical model of multi-working condition topology optimization is established, and the weights of each working condition are determined by using AHP, and the multi-working condition topology optimization design of the frame is carried out. Finally, a comparison of the comprehensive performance of the frame before and after optimization shows that the proposed method enables the optimized frame to meet the strength requirements under various working conditions, resulting in a weight reduction of 16.5 kg.

Thermal request optimization of a smart district heating system

This paper proposes a solution approach to manage the heating plans of tenants served by a district heating plant located in Sweden. To do that, the daily temperature request of each household in the associated pilot region is obtained, and the daily temperature profile of each household is optimized with the help of the proposed decision support system and smart valves. The hot water inflow rates of radiators are remotely controlled via smart valves at each flat to minimize the total energy consumption, carbon emission and cost associated with the energy consumption of the district heating plant. We aim to shave the peak demands while fully satisfying the temperature requests of households without violating their thermal comfort. Peak demand shaving is achieved by generating preheating schedules via mathematical optimization and using the thermal storage potential of the insulated flats. The resulting mathematical optimization model presents significant computational challenges that cannot be efficiently solved using optimization solvers within a reasonable time limit. To this end, we develop three genetic algorithm approaches that are computationally scalable for realistically-sized instances and verified to yield near-optimal solutions for the test instances. Extensive numerical analyses show the effectiveness of the proposed approach and the genetic algorithm since we yield significant carbon emission reduction and cost savings compared with the method that the experts of the utility company propose.

Maximizing virtual power plant profit: A two-level optimization model for energy market participation

Managing dispersed generation via virtual power plants (VPPs) is crucial for maximizing profits in electricity markets. This paper presents a model aimed at maximizing VPP profit through participation in the energy market. The proposed model addresses grid and security constraints of units using deterministic programming, formulated as an equilibrium-constrained, two-level mathematical optimization model. The first level focuses on maximizing VPP profit, while the second optimizes social welfare. Applying duality theory transforms this two-level model into a mixed-integer linear programming model, further refined using Karush–Kuhn–Tucker (KKT) optimality conditions. Given the inherent conflict in these objectives, a novel algorithm employing water flow dynamics is proposed for solving the model. To enhance method performance, the Pareto criterion and fuzzy decision-making are incorporated. Model tests are conducted on a standard 24-bus IEEE grid, demonstrating its efficiency. For the single-objective problem without line congestion, the solving time was 12 s. Introducing line congestion increased the profit by 13.4 %, from $40,413.21 to $45,837.32. In the two-objective problem without congestion, the profit ranged between $36,928.72 and $42,813.28, and emissions ranged from 275.21 to 2,916.32 pounds. With congestion, the profit range increased by a maximum of 8.7 %, and emissions were reduced by up to 4.6 %.

Analysis and optimal design of forging preforming for I-shaped forgings

Abstract The optimal design of forging preforming is the key to improving forging quality and productivity. Taking an I-shaped forging as a research object, an approach to optimize two-dimensional preform shape is employed. The mathematical model of multi-objective optimization in forging forming simulation is established, and the forming load and die wear are used as the objective functions to optimize the design. Two forms of straight line and circular arc are designed for the shape of the deformation area of the preforming die. With the aid of the finite element simulation software, the process of preforming and finishing forging by using the preformed die with different design variables and different parameters is simulated. Simulation results show that the best optimization results can be achieved when the linear angle is 53.5° and the circular arc radius is 66 mm. After optimization, the load drops by about 36 percent by adopting the circular arc shape, and by about 76 percent by adopting the straight-line shape. The die wear depth decreases and the wear zones become more balanced after optimization. Numerical results prove that this approach is effective in designing the optimal preform shape in forging.

Technician assignment in multi-shift maintenance schedules in an offshore wind farm

Offshore wind farms are becoming more and more important to sustainable energy strategies, yet their maintenance presents unique logistical challenges. The focus of this research is the Technician Assignment Problem (TAP) which involves a complicated and fluctuating scheduling problem. The key objective is to determine the most effective assignment of technicians to maintenance tasks to maximize operational efficiency and ensure reliable service. This study introduces a mathematical optimization model that processes numerous variables—technician availability, skill sets, and temporal constraints—to minimize unmet maintenance needs and ensure equitable workload distribution. The model is based on assumptions derived from actual operational conditions and human resource practices, guaranteeing that its results are not only theoretically valid but also practically feasible. TAP adheres to labor regulations, employs human resource capabilities, and aims for a smart assignment of workforce. It complies with restrictions that prevent excessive work, require breaks, and ensure that technicians are assigned tasks that match their skills, thus promoting the well-being of the workforce and the efficiency of operations. The computational investigation of the model shows that it has a remarkable ability to improve scheduling decisions which effectively reduce unassigned positions and uniformly distribute work hours. In essence, this research contributes a methodologically robust framework to the field of workforce scheduling, with the potential to inform the maintenance strategies of offshore wind farms and similar complex service systems.

Managing the patient portfolio using mathematical programming: decision support guidelines using a real-world use case at a university hospital

AbstractMany hospitals in Germany are facing escalating economic pressures. After several years of stagnation, the number of inpatient hospital treatments dropped by $$\:13\%$$ in 2020 compared to the previous year. This negative tendency can also be seen in operating theaters (OTs). Strategic management of the case mix in hospital OTs now necessitates a solid data foundation. The case mix and the case mix index have become central economic indicators in contemporary hospital operations. In this work, we develop a mathematical model for case mix optimization at Augsburg University Hospital in Germany, which is based on an extensive data analysis with descriptive methods. The optimization model is subject to rigorous testing and evaluation through an extensive series of scenario analyses. The primary objective is to calculate a revenue-maximizing patient mix while respecting the available scarce personnel resources in the OT and intensive care unit. This research marks a pioneering effort in delineating the practical integration of case mix planning into a hospital’s routine operations using mathematical optimization. The analyses reveal a strong correlation between an upsurge in revenue and an increased number of cases. Furthermore, the results demonstrate that strategic planning of the patient mix has the potential to enhance revenue with existing resources. Even though the optimal patient mix may not be directly implementable in practice, the findings yield valuable insights for managerial decision-making. A critical examination of these results also fosters a nuanced discourse on the utilization of optimization models as decision support tools within hospital management.

A time-space network-based model for transportation service optimization of China Railway Express

This paper describes the development and optimization plans for the China Railway Express (CR Express). As a new type of international land transport organization, CR Express has emerged with the continuous expansion of China toward European investment and trade, and in particular, has expanded with the continuous progress of the One Belt and One Road (OBOR) initiative. In addition to improving the service quality of CR Express, the operating costs must be reduced for developing “smart railways” that serve “smart cities”. We propose a dual-objective-based function mathematical optimization model; the satisfaction of the cargo owner is considered, and the timeliness, transportation capacity, and goods category constraints of CR Express transportation are designed. Moreover, we present the normalized equivalent method of the two-objective function of the model. Finally, a case study is conducted against the background of certain trains in the western corridor of CR Express to validate the effectiveness of the model and research methods proposed in this study.

Multidisciplinary Reliability Design Optimization Modeling Based on SysML

Model-Based Systems Engineering (MBSE) supports the system-level design of complex products effectively. Currently, system design and optimization for complex products are two distinct processes that must be executed using different software or platforms, involving intricate data conversion processes. Applying multidisciplinary optimization to validate system optimization often necessitates remodeling the optimization objects, which is time-consuming, labor-intensive, and highly error-prone. A critical activity in systems engineering is identifying the optimal design solution for the entire system. Multidisciplinary Design Optimization (MDO) and reliability analysis are essential methods for achieving this. This paper proposes a SysML-based multidisciplinary reliability design optimization modeling method. First, by analyzing the definitions and mathematical models of multidisciplinary reliability design optimization, the SysML extension mechanism is employed to represent the optimization model based on SysML. Next, model transformation techniques are used to convert the SysML optimization model generated in the first stage into an XML description model readable by optimization solvers. Finally, the proposed method’s effectiveness is validated through an engineering case study of an in-vehicle environmental control integration system. The results demonstrate that this method fully utilizes SysML to express MDO problems, enhancing the efficiency of design optimization for complex systems. Engineers and system designers working on complex, multidisciplinary projects can particularly benefit from these advancements, as they simplify the integration of design and optimization processes, facilitating more reliable and efficient product development.

Optimization Method of Mine Ventilation Network Regulation Based on Mixed-Integer Nonlinear Programming

Mine ventilation is crucial for ensuring safe production in mines, as it is integral to the entire underground mining process. This study addresses the issues of high energy consumption, regulation difficulties, and unreasonable regulation schemes in mine ventilation systems. To this end, we construct an optimization model for mine ventilation network regulation using mixed-integer nonlinear programming (MINLP), focusing on objectives such as minimizing energy consumption, optimal regulation locations and modes, and minimizing the number of regulators. We analyze the construction methods of the mathematical optimization model for both selected and unselected fans. To handle high-order terms in the MINLP model, we propose a variable discretization strategy that introduces 0-1 binary variables to discretize fan branches’ air quantity and frequency regulation ratios. This transformation converts high-order terms in the constraints of fan frequency regulation into quadratic terms, making the model suitable for solvers based on globally accurate algorithms. Example analysis demonstrate that the proposed method can find the optimal solution in all cases, confirming its effectiveness. Finally, we apply the optimization method of ventilation network regulation based on MINLP to a coal mine ventilation network. The results indicate that the power of the main fan after frequency regulation is 71.84 kW, achieving a significant energy savings rate of 65.60% compared to before optimization power levels. Notably, ventilation network can be regulated without adding new regulators, thereby reducing management and maintenance costs. This optimization method provides a solid foundation for the implementation of intelligent ventilation systems.

Biorefinery superstructure optimization under carbon pricing policies using stochastic programming

The growing utilization of biomass feedstocks for climate change mitigation has led to increased research on biorefineries. Concurrently, environmental policies are evolving as crucial tools to address these global concerns. Cap-and-trade, carbon tax, and carbon cap policies have been established to reduce carbon dioxide emissions. In this work, a mathematical optimization model is developed to integrate biorefinery process design with carbon pricing policies and crediting mechanisms. A two-stage stochastic mixed integer linear programming model is proposed to account for emissions, feedstock supply, chemical demand, and pricing uncertainties. A bi-objective optimization framework is employed to consider economic and environmental metrics. The framework is a valuable tool for governments and businesses to determine pareto-optimal investment strategies under environmental policies. It is applicable for evaluating prospective chemical technologies with carbon pricing policies beyond biorefineries. The results indicate that carbon crediting mechanisms can minimize the financial penalty by up to 50% under a carbon tax policy. Implementing chemical demand constraints within a cap-and-trade policy reduces potential profits, especially when the carbon prices are high. The stochastic programming approach revealed that underestimating the expected carbon cap leads to lower expected profits. Despite the financial implications of these policies, profitable process designs are achievable.

Design of gravity assisted heat exchanger and its application on enhanced waste heat recuperation utilizing organic Rankine and LNG system

Waste heat recovery involves capturing and reusing heat from a system that would typically be discarded. In industries like manufacturing and power generation, this method is gaining importance due to its potential to reduce greenhouse gas emissions and fuel consumption. This paper discusses a novel heat exchanger system that utilizes gravity to extract heat from exhaust gas, providing an alternative solution to the difficulties encountered by the conventional heat recovery techniques. Moreover, by adding both the ORC (Organic Rankine Cycle) and LNG (Liquefied Natural Gas) cycle to this system, excess heat can be used more efficiently, allowing for better energy recovery. The gravity-pipe heat exchanger and two cycles are used in the combined energy recovery system to extract useful heat from a low-grade waste stream. Energy performance is measured by using heat transfer analysis, energy efficiency testing, and exergy analysis followed by a comprehensive parametric analysis. To identify the optimal operating parameters for maximizing energy recovery and minimizing energy losses including economic analysis of GPHE with conventional HE, mathematical optimization models are developed. The heat exchanger demonstrates good effectiveness, close to 52.3 %, at an optimum temperature of approximately 275 °C to 280 °C for a 35 kg/s air flow rate. The ORC cycle is most efficient with optimum operating condition when pentane's mass flow rate is 3.3 kg/s. The maximum work output is obtained at a condenser pressure of 0.21 MPa, reaching 280 kW. When using pentane, the cycle's maximum efficiency is 36.8 %. However, the system's exergy efficiency drops by 4.94 % when the pinch temperature goes up by 7 °C. The output of ORC turbine increases from 220 kW to 240 kW, and the output of LNG turbine increases from 25 kW to 40 kW, as the condenser pressure rises. From economic analysis it's attain that the designed GPHE is economically viable for waste heat recovery from dirty exhaust gas. This paper develops a theoretical model to evaluate several cycles for extracting energy from waste heat, which could reduce fuel use and greenhouse gas emissions in industries.

The effect of stope size and cut-off grade on the design and scheduling of an underground mining operation in the presence of a pre-concentration system

ABSTRACT Stope layout optimisation is considered one of the main steps in the design and strategic planning of underground mining operations. This paper investigates the influence of stope size and cut-off grade in an underground sublevel stoping operation in the presence of a preconcentration system using a newly developed mathematical optimisation model. The utilisation of a bulk ore sorting system, its effects on the resource utilisation, and the final discounted cash flow of a case study are presented. Results show that incorporating a bulk sorting system to a sublevel stoping operation can significantly increase the viability of a deposit.

A dimensionality reduction optimization method for thin-walled parts to realize mass center control and lightweight design

Structural lightweight design has attracted growing attention. However, most studies have ignored the impact of lightweight design on the location of mass centres, which is an important factor affecting the dynamic performance of structures. This article proposes a structural optimization method for thin-walled parts to achieve both mass centre control and lightweight design. First, mass centre and volume are taken as the constraints for structural optimization, and a mathematical model for multi-constrained topology optimization is developed. Secondly, a dimensionality reduction method based on a 3D spatial filter is introduced for the optimization of thin-walled parts. The maximum error between the mass centre of the optimized structure and the target mass centre is only 1.03%, which indicates that the method has high accuracy in mass centre control. Numerical analysis shows that adjusting the mass centre can achieve regulation of the moment of inertia and can also suppress flutter.