Economic Optimization Research Articles

An Introduction to Lagrange Multipliers: Theory and Applications in Economics

The purpose of this paper is to explore the basic applications of the Lagrange multiplier method in economics and to help beginners build their understanding of this mathematical tool. Tesla Inc. is used as a case study to examine how it maximizes profits by optimizing pricing and marketing expenses under given market conditions and constraints. The context of the study includes the importance of maintaining Tesla’s leadership position as the world’s leading electric car manufacturer in a competitive market. In this paper, the Lagrange multiplier method is used to incorporate specific market share and marketing expense constraints into the profit function and to find the extreme values by constructing the Lagrange function and solving for the derivatives. However, the results of the study show that the solutions obtained are extreme minima rather than the expected maxima. This result highlights the possible limitations of the Lagrange multiplier method in economic optimization problems. Nonetheless, this paper provides valuable lessons for understanding and applying the Lagrange multiplier method and points the way for further research on the application of optimization methods in economic decision making.

Real-Time Control of Thermal Synchronous Generators for Cyber-Physical Security: Addressing Oscillations with ANFIS

This paper introduces a novel real-time ANFIS controller, specifically designed for thermal synchronous generators, to mitigate the risks associated with cyber-physical attacks on power systems. The controller integrates the dynamic model of the turbine’s thermomechanical components, such as the boiler and heat transfer processes, within the synchronous generator. In contrast to previous studies, this model is designed for practical implementation and addresses often-overlooked areas, including the interaction between electrical and thermomechanical components, real-time control responses to cyber-physical attacks, and the incorporation of economic considerations alongside technical performance. This study takes a comprehensive approach to filling these gaps. Under normal conditions, the proposed controller significantly improves the management of industrial turbines and governors, optimizing existing control systems with a particular focus on minimizing generation costs. However, its primary innovation is its ability to respond dynamically to local and inter-area power oscillations triggered by cyber-physical attacks. In such events, the controller efficiently manages the turbines and governors of synchronous generators, ensuring the stability and reliability of power systems. This approach introduces a cutting-edge thermo-electrical control strategy that integrates both electrical and thermomechanical dynamics of thermal synchronous generators. The novelty lies in its real-time control capability to counteract the effects of cyber-physical attacks, as well as its simultaneous consideration of economic optimization and technical performance for power system stability. Unlike traditional methods, this work offers an adaptive control system using ANFIS (Adaptive NeuroFuzzy Inference System), ensuring robust performance under dynamic conditions, including interarea oscillations and voltage deviations. To validate its effectiveness, the controller undergoes extensive simulation testing in MATLAB/Simulink, with performance comparisons against previous state-of-the-art methods. Benchmarking is also conducted using IEEE standard test systems, including the IEEE 9-bus and IEEE 39-bus networks, to highlight its superiority in protecting power systems.

Conceptual Design and Economic Optimization of Different Valorization Routes for Orange Peel Waste: The Application of the Biorefinery Concept for an Integral Use of Raw Material

Biorefineries are novel biotechnological routes designed to generate sustainable processes from renewable raw materials. The valorization of orange peel waste (OPW) provides high-value products based on their composition. The economic optimization of biorefineries through conceptual design and generation of superstructures based on the analysis of processing units is a topic of great interest. This work aimed to obtain the most profitable biorefinery through economic optimization strategies based on high-value-added products from OPW. Two stages were considered: The first stage consisted of the conceptual design of multiple OPW processing units (production of essential oil, mucic acid, phenolic compounds, biogas, among others). An OPW flow rate of 140 kg/h was selected as the base case. From the stand-alone units, a biorefinery superstructure (second stage) was designed. Finally, the units with the best mass and energy results were selected in order to maximize the net present value (NPV) and obtain an optimal biorefinery configuration. The results evidenced that the production of essential oil and biogas presented the best yields (2.61 mL and 0.028 m3 per kg OPW, respectively). This biorefinery configuration obtained an NPV of −7.7 mUSD from the base case. Through the evaluation of the different superstructure configurations, the combined production of essential oil, biogas, and mucic acid and a scale-up of over 22 times the base case generated the minimum processing scale. Under a Colombian context, the implementation of the biorefineries analyzed are promising since the minimum processing scale contemplated only 8.8% of the OPW production. Efforts to increase yields and decrease capital and operating expenses while keeping environmental impacts low should be pursued.

The economic optimization of lactation and fertility in dairy cows

The economic optimization of lactation and fertility in dairy cows

Study on the Economic Operation of a 1000 MWe Coal-Fired Power Plant with CO2 Capture

The flexible operation of carbon capture units is crucial for the economic performance of coal-fired power plants equipped with CO2 capture systems. This paper aims to investigate the impact of electricity, CO2, and fuel prices on the economic operation of such plants. A novel economic optimization model is proposed, integrating a static model of the carbon capture system with a particle swarm optimization algorithm. A new concept, the CO2 boundary price, is introduced as a key metric for determining the operating conditions of CO2 capture units. The CO2 boundary price rises when the power load decreases due to the decline in power generation efficiency, and it also increases with rising fuel prices, as the cost of steam for CO2 capture increases. Additionally, when the objective is to meet power load demand, CO2 prices have a great influence on the operation of CO2 capture units, assuming fixed coal and electricity prices. However, when the primary goal is to maximize plant profitability, the system’s operational conditions are strongly influenced by the relative prices of electricity and CO2. The proposed optimization model and the uncovered price-effect mechanisms provide valuable insights into the economic operation of carbon capture power plants.

Efficient utilization of enriched oxygen gas in residential PEMFC-CHP system with hydrogen energy storage

The oxygen byproduct generated from water electrolysis can be utilized on-site in residential combined heat and power (CHP) systems to enhance economic efficiency. This study explores solutions for optimizing the use of enriched oxygen gas (EOG) and determining the ideal oxygen fraction to maximize economic viability. A novel EOG supply system is designed to regulate oxygen fraction, oxygen excess ratio (OER), and humidity. A dynamic model of a PEMFC integrated with the EOG supply system is developed using MATLAB/Simulink® software and partially validated. The dual effects of EOG on system efficiency and remaining useful lifetime (RUL) are analyzed using a comprehensive economic optimization algorithm, leading to the identification of optimal oxygen fractions for various hydrogen production modes. Additionally, a feedforward static decoupling controller is designed to independently control the OER and oxygen fraction. The results indicate that, under rated conditions (10 kW), system power increased by 15 %, along with a 10 % improvement in system efficiency, from 48 % to 58 %. In conclusion, the efficient use of enriched oxygen gas demonstrates significant economic feasibility and practical viability, making it highly suitable for distributed power generation applications.

Economic and technical optimization of a tri-generation setup integrating a partial evaporation Rankine cycle with an ejector-based refrigeration system using different solar collectors

Three collector types, namely parabolic trough solar collector (PTSC), linear Fresnel collector (LFC), and dish collector, are employed to drive a tri-generation configuration composed of a partial evaporation Rankine cycle (PERC), a hot water production unit (HWPU), and a cascade ejector-based compression refrigeration system (ECRS) for electricity, cooling, and heating production. The ECRS is integrated with the topping PERC through an absorption refrigeration system (ARS). Moreover, the collector is indirectly connected to the system by a storage tank to increase the operating hours of the system. The performance of the system is evaluated by thermodynamic and economic analysis. The three-objective optimization result is a testament to the fact that utilizing PTSC brings about the best performance of the system. The system exergy efficiency (ηex) in the case of PTSC is 8.1 % and 24.9 % higher than in the case of LFC and dish collector, respectively. The economic performance of the system in the case of PTSC is superior to that of the dish collector. Furthermore, the PTSC case results in a relatively similar economic performance to the LFC case. The system produces power, cooling, and heating at rates of 200.8 kW, 564.9 kW, and 795.7 kW in the optimum case of utilizing PTSC, respectively. Moreover, ηex, total cost rate (C˙tot), and specific cost of tri-generation (ctri) are obtained as 11.48 %, 204.7 $h−1, and 44.91 $GJ−1, correspondingly. The results indicate that ηex of the proposed layout in the case of PTSC is superior to a comparable tri-generation configuration introduced in the field by 2.78 % points.

The Profound Nature of Derivatives and Integration: A Comprehensive Examination

This article delves into the fundamental concepts of derivatives and integration, two core principles of calculus that govern a wide range of mathematical and real-world applications. Derivatives, which measure the rate of change of a function, and integration, which calculates accumulation and areas under curves, are essential tools in fields such as physics, economics, engineering, and finance. The article offers a detailed exploration of their mathematical definitions, key properties—including linearity, the product and chain rules, and the Fundamental Theorem of Calculus—and the diverse techniques used in integration. The practical applications of these concepts are also examined, with special emphasis on their role in modeling dynamic systems, optimizing processes, and solving real-world problems such as motion analysis, financial modeling, and economic optimization. Through in-depth discussion and examples, this comprehensive article bridges the theoretical underpinnings of derivatives and integration with their vast and critical uses in various scientific and economic disciplines.

A practical approach to promoting sustainable development in the construction industry through the use of the LOTUS-Vietnamese green-building assessment tool

In the context of global climate change mitigation, building design optimization is crucial for effective and efficient resource management throughout a project’s life cycle. This study addresses the challenge of assessing green building levels using a Vietnamese perspective. A survey of over 220 participants, including investors, consultants, contractors, and other stakeholders, was conducted to identify factors influencing green building assessments. Data analysis, employing SPSS software, explored 57 factors encompassing life-cycle economic optimization, energy and water conservation, material selection, project management, and strategic market benefits. The findings highlight effective energy management as a key determinant shaping sustainable building approaches and assessments. These results offer valuable insights for life cycle cost assessments and environmental impact evaluations during project implementation. Furthermore, the study emphasizes the importance of project developers prioritizing factors that influence the achievement of green building goals based on LOTUS green building rating standards in Vietnam. The predicted results demonstrate that governments should enforce legislation and establish clear green construction regulations to promote environmentally friendly growth, and that construction companies should use environmentally friendly materials and practices in their projects. This research contributes to the knowledge base for scholars, designers, and sustainability experts by systematically identifying factors that influence green building assessments under LOTUS standards.

Rigorous design and economic optimization of reactive distillation column considering real liquid hold-up and hydraulic conditions of industrial device

The liquid hold-up in a reactive distillation (RD) column not only has a significant impact on the extent of reactions, but also affects the pressure drop and hydraulic conditions in the column. Therefore, the liquid hold-up would be a critical design factor for RD columns. However, the existing design methods for RD columns typically neglect the influence of considerable amount of liquid hold-up in downcomers owing to the difficulties of solving a large-scale nonlinear model system by considering downcomer hydraulics, resulting in significant deviations from actual situation and even operation infeasibility of the designed column. In this paper, a pseudo-transient (PT) RD model based on equilibrium model considering tray hydraulics was established for rigorous simulation and optimization of RD plate columns considering the liquid hold-up both in downcomers and column trays, and a steady-state optimization algorithm assisted by the PT model was adopted to robustly solve the optimization problem. The optimization results of either ethylene glycol RD or methyl acetate RD demonstrated that assuming all the liquid hold-up of a stage belonged to the tray will cause significant deviations in the column diameter, weir height, and the number of stages, which leads to not meeting the separation requirements and even operation hydraulic infeasibility. The rigorous model proposed in this study which considers the liquid hold-up both on trays and in downcomers as well as hydraulic constraints can be applied to systematically design industrial RD plate columns to simultaneously obtain optimal operating variables and equipment structure variables.

Economic optimization of sustainable soil management: a Dutch case study

Soil quality is pivotal for crop productivity and the environmental quality of agricultural ecosystems. Achieving sufficient yearly income and long-term farm continuity are key goals for farmers, making sustainable soil management an economic challenge. Existing bio-economic models often inadequately address soil quality. In this study, we apply the novel FARManalytics model, which integrates chemical, physical, and biological indicators of soil quality indicator, quantitative rules on how these indicators respond to farmers’ production management over time, and an economic calculation framework that accurately calculates the contribution of production management decisions towards farm income. This is the first study applying this model on existing arable farms. FARManalytics optimizes crop rotation design, cover crops, manure and fertilizer application and crop residue management. Nine Dutch arable farms were analyzed with a high variation in farm size, soil type, and cultivated crops. First, we assessed farm differences in soil quality and farm economics. Second, we optimized production management to maximize farm income while meeting soil quality targets using farm-specific scenarios. Third, we explored the impact of recent policy measures to preserve water quality and to increase the contribution of local protein production. The results show that the case farms already perform well regarding soil quality, with 75% of the soil quality indicators above critical levels. The main soil quality bottlenecks are subsoil compaction and soil organic matter input. We show that even in front-runner farms, bio-economic modeling with FARManalytics substantially improves economic performance while increasing soil quality. We found that farm income could be increased by up to €704 ha−1 year−1 while meeting soil quality targets. Additionally, we show that to anticipate on stricter water quality regulation and market shift for protein crops, FARManalytics is able to provide alternative production management strategies that ensure the highest farm income while preserving soil quality for a set of heterogenous farms.

Experimental Study on Plugging Behavior of Multitype Temporary Plugging Agents in Hydraulic Fractures

Summary Various types of temporary plugging agents are used in hydraulic fracturing to promote the uniform propagation of multicluster hydraulic fractures and increase the complexity of hydraulic fractures. However, the plugging behavior of these agents in hydraulic fractures has not yet been fully clarified, making the optimization of temporary plugging formulas challenging. In this study, dozens of plugging experiments were carried out to reveal the plugging behavior of pure fiber, pure particle, and fiber-particle combination materials in hydraulic fractures. The results indicate that the high fiber concentration and long fibers are beneficial to obtaining high maximum plugging pressures. However, the low tensile strength of fibers makes it difficult to form stable plugging layers under high pressure, especially for wide fractures. For particle plugging agents, the high rigidity of the particles prevents them from compacting tightly within the plugging layer, resulting in high permeability and low temporary plugging pressure. Excessive particle diameter and concentration tend to cause rapid blockage at the fracture entrance, leading to poor plugging performance. In contrast, the fiber-particle composite plugging scheme can form a stable and tight plugging layer at lower concentrations of both fibers and particles. Moreover, replacing single-size particles in composite with multisize particles can further enhance the plugging effect, allowing for a higher plugging pressure with a lower dosage of temporary plugging agents. Comprehensively considering the effects of material concentration and size on the plugging effect, the critical plugging quantitative characterization equations for pure fiber, pure particle, and fiber-particle combination plugging schemes are established respectively, with fracture width as the independent variable and the product of material concentration and size as the dependent variable. The temporary plugging schemes for various hydraulic fracture widths can be preliminarily determined using these equations. Based on the principle of economic optimization, the optimal temporary plugging schemes with consideration of the plugging pressure requirements were selected, which have shown good field application performance.

Optimal economic operation of smart home devices based on home microgrids and time-of-use tariffs

Abstract In this paper, a two-layer model is proposed for smart devices in a home energy management system in order to optimize residential energy use under time-of-use tariffs and home microgrids. Home smart devices are modelled based on their power consumption attributes and building thermal resistance. An HVAC-transferable device cooperative operation strategy is introduced to construct the economic optimization of the upper-level HVAC operation and the lower-level transferable device operation. This strategy reduces home power costs while maintaining user comfort. By iteratively solving the two-layer model, the optimal power consumption scheme for home smart devices is determined.

Timber Harvest Planning Using Reinforcement Learning: A Feasibility Study

This study developed a forest management plan model using reinforcement learning (Q-learning) to optimize both the economic and ecological functions of forests. Management objectives for national forests were established, and forest conditions were analyzed using GIS spatial data and administrative records. A 60-year forest management plan was formulated to predict timber production and management performance across different regions and time periods. Our analysis revealed that Scenario 3 (Carbon Storage Priority) demonstrated the highest economic value, starting at approximately KRW 576.2 billion in the initial period and escalating to KRW 775.7 billion over six 10-year periods, totaling 60 years. In addition to its economic performance, Scenario 3 effectively improved forest age class structure and ensured a stable timber supply, making it the most balanced approach for sustainable forest management. By focusing on carbon storage as a key management goal, this approach highlights the potential for achieving both economic and environmental benefits concurrently. These results suggest that reinforcement learning is a powerful tool for developing long-term forest management strategies that address multiple objectives, including economic viability, ecological sustainability, and resource optimization.

Optimal low-carbon scheduling of integrated energy systems considering stepped carbon trading and source-load side resources

Under the dual-carbon goal of achieving carbon peaking and carbon neutrality, the Integrated Energy System (IES) enhances the power sector's environmental sustainability by integrating multiple energy sources. To enhance the low-carbon utilization of IES energy, this paper introduces an economic optimization model that incorporates stepwise carbon trading and both source and load-side resources. Initially, the model integrates a Concentrated Solar Power Plant (CSPP) with a Combined Heating and Power (CHP) unit for bidirectional electricity-heat conversion, and incorporates Power to Gas (P2G) and Carbon Capture System (CCS) for carbon recycling within the IES. On the demand side, demand response optimizes the electricity-heat load curve. Subsequently, a stepped carbon trading mechanism guides the system in controlling carbon emissions and constructing a carbon emission model. Finally, the model minimizes the sum of energy purchase costs, carbon transaction costs, demand response compensation costs, wind curtailment penalties, and equipment maintenance costs to optimize the IES economically. By establishing five scenarios for comparative analysis, incorporating CSPP, P2G-CCS, demand response, and a stepped carbon trading mechanism reduces system costs, carbon emissions, and abandonment rates by 21.1 %, 30.87 %, and 23.78 %, respectively, validating the model's effectiveness in promoting a low-carbon economy.

Research on origin-based cold storage location and routing optimization of fresh agricultural products based on hybrid whale algorithm

With the focus on the insufficient origin-based cold storage in China, this study investigates the location and routing problem (LRP) of origin-based cold storage for fresh agricultural products. This study considers the loss of fresh agricultural products in different environments during transportation and presents a cold storage LRP model. To address this issue, a hybrid whale algorithm with heuristic rules is designed, and the effectiveness of the algorithm is verified by standard instances. Finally, taking Chenggu County as a practical case, the influence of cold storage capacity and farmers’ demand for refrigeration are analysed. Experimental results show that the proposed algorithm has a good effect in solving medium-scale LRP. As the storage capacity increases, the total cost of the system can be increased by 0.086%. As farmers’ demand for refrigeration increases, the total cost of the system can be increased by 34.034%. Farmers’ demand has a greater impact on the system’s total costs than the cold storage capacity. When optimizing the cold storage layout, changes in fresh agricultural product output in the next few years can be roughly predicted, and the most economical optimization scheme can be obtained.

MILP and PSO approaches for solving a hydropower reservoirs intraday economic optimization problem

AbstractShort-term hydropower generation with several water reservoirs requires deciding, for each moment in time, the volume of water (outflow) that is released from every reservoir to be turbined and generate energy. Knowing the price of energy at every time period, the objective is to maximize the income earned from the generated energy. In this paper, we present (1) a Hydropower Reservoirs Operation Optimization problem with a higher level of detail than those found in the literature, encompassing temporal delays, water hammer effects, and increased temporal discretization, among others features, and (2) two distinct approaches for addressing this problem: MILP and PSO. These methods are compared across instances of varying nature to evaluate their performance. We make our code available on GitHub: https://github.com/baobabsoluciones/flowing-basin.

Energy, exergy, exergy‐economic, and environmental evaluation of an optimized hybrid photovoltaic heat pump system with solar collector and PCM

AbstractNowadays, the use of hybrid systems has become very common all over the world. In this study, the aim is to minimize the use of grid energy to provide heating and cooling energy with the help of a hybrid heat pump equipped with a flat solar collector, phase change material (PCM), and photovoltaic (PV) panels. To achieve the best results, a numerical dynamic model consisting of different solar PV panels in three models, batteries, inverters, and hybrid heat pump along with collector and PCM has been modeled by solving Engineering Equation Solver (EES) and TRNSYS software. According to the proposed scenarios, multi‐objective optimization has been done to simultaneously improve the study answers in several sections by multi‐objective particle swarm optimization algorithm with MATLAB software. Also, economic and environmental optimization is also presented separately for comparing and reviewing solutions. The results of multi‐objective optimization show that the amount of lifecycle cost (LCC) when using polycrystalline panel is 21.26% lower than monocrystalline panel and 38.71% higher than thin film panel. As a result, according to the specific conditions and attitude, you can choose the desired system. Also, in the economic optimization, it was found that the best system is related to the polycrystalline panel, the volume of PCM used in the system is equal to 1 , the number of panels used is 18, and the minimum amount of LCC is $3929.08.

Low-Carbon Economic Operation Optimization of Mine Integrated Energy System Considering Energy Supply Uncertainty

Low-Carbon Economic Operation Optimization of Mine Integrated Energy System Considering Energy Supply Uncertainty

Plant-wide modeling and techno-economic optimization of a low-pressure microwave-assisted ammonia synthesis process with adsorption separation

Ammonia production has traditionally been done by using the Haber-Bosch process, that operates at extremely high pressure (200–300 bar), has a large carbon footprint, and requires significant energy. For ammonia to be used as a hydrogen carrier, it is desired that it is produced by using modular technologies under benign conditions, yet the economics remain commercially viable. This paper investigates a novel technology for ammonia synthesis by using a microwave-assisted low-pressure reactor. Microwave reactors are compact and can be readily modularized and started/shutdown thus making them ideal to be integrated with the electric grid or with regional/local renewable-based electric generation facilities. For separation of unreacted reactants from the product ammonia, if the traditional condensation separation technology used in the high-pressure Haber-Bosch process is used, then the separation process needs to be operated under cryogenic condition thus adversely affecting the economics. A solid sorbent based separation technology is investigated in this paper. A kinetic model for the microwave-catalytic synthesis process is used. An isotherm model is developed for MgCl2–Si adsorbent and used for modeling the dynamic adsorption-desorption cycle. A plant-wide model with heat and mass integration is developed. An economic model is developed and used for economic optimization by using an equation-oriented approach. Since the adsorption-desorption process is dynamic, for techno-economic optimization, a reduced order model for the key performance measures of the adsorption-desorption process as a function of its input and decision variable is developed under cyclic steady-state conditions. For the optimized MW-assisted process, the levelized cost of ammonia is $772/mt as opposed to $808/mt for the conventional Haber-Bosch process for a hydrogen price of $2.07/kg. The MW-assisted process is found to be economically viable in the US market if the hydrogen price is below $4/kg.