Linear Programming Optimization Research Articles

Optimization of crop planting strategies: an integrated scheme of linear programming and intelligent optimization algorithms

To address the challenge of developing optimal planting strategies for multiple crops under the constraints of diverse greenhouse conditions and various types of cultivated land, a crop planting strategy based on intelligent optimization algorithms is proposed. First, assuming stable crop production and sales across years, a linear programming model is formulated to account for diversified planting risks. Uncertainty factors are incorporated into the decision-making process through interpolation techniques, with the dual objectives of maximizing net income and minimizing overproduction losses. Optimization and solution of the model are achieved using a combination of a greedy algorithm and a genetic algorithm, enhanced by the Pearson correlation coefficient. Sensitivity analysis is conducted to effectively evaluate the robustness and adaptability of the proposed planting strategy under different scenarios. Furthermore, the scope of the study is extended to scenarios involving year-on-year increases in crop sales, with additional considerations given to crop uncertainty and planting risks.

Progressive Linear Programming Optimality Method Based on Decomposing Nonlinear Functions for Short-Term Cascade Hydropower Scheduling

Short-term optimal scheduling of cascade hydropower stations enhances their flexible regulation and power generation capabilities. However, nonlinear function relationships and multistage and hydraulic interdependencies present significant challenges, resulting in considerable solution errors, premature convergence, and high computational demands. This study proposes a progressive linear programming method that decomposes nonlinear functions to address these challenges. First, to accurately represent nonlinear functions and mitigate computational complexity, the entire feasible domain is partitioned into multiple contiguous subdomains in which nonconvex nonlinear functions within each subdomain can be equivalently replaced by linear relationships. Second, a progressive linear programming optimization algorithm is devised to prevent premature convergence, utilizing continuous subdomains rather than discrete points as state variables and incorporating the progressive optimality principle. Finally, to increase the solution efficiency, a dimensionality reduction strategy via the feasible domain state dynamic acquisition method is presented and optimized after excluding the infeasible states in each stage. The simulation of three cascade hydropower stations in a river basin in southwest China shows that the proposed method can achieve a superior peak regulation effect compared to the conventional mixed integer linear programming and progressive optimality algorithm. During the dry and wet seasons, the residual load peak–valley differences at the three stations are reduced by 612 MW and 521 MW compared to the MILP and 1889 MW and 2439 MW compared to the POA, which underscores the effectiveness of the method in optimizing the short-term scheduling of cascade hydropower stations.

Optimal Planting Strategy Model for Crops in Mountainous Areas of North China Based on Robust Optimization

With the rural revitalization strategy's deepening, North China's mountainous rural economy needs to shift from traditional to modern efficient agriculture. This paper proposes a robust optimization-based optimal crop planting strategy model for the region's unique conditions. It first introduces the area's topography, climate, and arable land resources, then presents a combined linear programming and robust optimization model. Model performance is validated through data preprocessing and market analysis, and its effectiveness is shown by comparison with traditional strategies. The study also analyzes crop substitutability and complementarity, offering practical recommendations for North China's mountainous areas. Results indicate that robust optimization can handle market and climate uncertainties, ensuring planting scheme efficiency. This research provides scientific support for agricultural decision-making in these regions and offers theoretical and practical references for similar agricultural optimization issues.

Adaptive Control and Market Integration: Optimizing Distributed Power Resources for a Sustainable Grid

Distributed power resources (DPRs) offer a transformative opportunity to improve the efficiency, sustainability, and reliability of modern power infrastructures through their integration. This work presents a novel method based on a mix of renewable energy sources, energy storage technologies, and conventional generators for the optimization of DPR operations under dynamic market settings. Maximizing economic gains is the major objective while preserving system resilience and stability. To handle the complexity of DPR interactions, we offer a strong, hierarchical control architecture encompassing main, secondary, and tertiary levels. System performance is improved using advanced control strategies together with real-time market-responsive changes and predictive algorithms. The efficacy of the proposed methodology is validated through a detailed simulation of a small island grid using mixed-integer linear programming (MILP) and particle swarm optimization (PSO), which demonstrates significant operational improvements. Results indicate cost reductions of approximately 54.7%, which were achieved by effectively prioritizing renewable sources and optimizing energy storage usage. This research contributes both theoretically and practically to accelerating the transition toward sustainable, resilient, and economically viable power systems.

Optimal Design of a PV/Hydrogen‐Based Storage System to Supply Heat and Power to a Direct Air Carbon Capture System

ABSTRACTDirect air capture (DAC) technology aims to curb the leading cause of global warming by reducing atmospheric carbon content. The DAC system uses thermal energy to desorb captured carbon, with its primary components powered by electrical energy. In this research, an approach integrates hybrid photovoltaic, with spectral splitting optical filtration (PV/SSOF), and hydrogen‐based energy storage to provide the required thermal and electrical energy for the DAC system, thereby minimizing environmental impact. To achieve this goal, a mixed‐integer linear programming (MILP) optimization model is formulated to minimize the project's lifecycle cost, and the problem is solved by the particle swarm optimization (PSO) algorithm. The model determines the optimal configuration of the system, including the number of PV panels, hydrogen tanks, electrolyzers, fuel cells, and heat buffer tanks. The study tracks the system's performance by assessing how much the PV system meets heat and power requirements. A real‐world case study from an industrial city located in the eastern region of Saudi Arabia is presented to showcase the practicality of the optimization model. Three configurations were considered to study the techno‐economic viability: standalone with and without a boiler and grid‐connected. A sensitivity analysis is conducted to examine techno‐economic viability and obtain managerial insights. It is found that the grid‐connected system is economically favorable and thermodynamically efficient due to its almost 19% cost reduction for electrical energy and 17% for exergy compared to a system without a boiler. Furthermore, a smaller electrical energy‐exergy cost gap shows the system's energy conversion efficiency with low losses.

<b>Improving Service Quality with the SERVQUAL Method and Linear Programming Optimization at a Transportation Provider Company</b>

The rapid growth of the technology industry poses significant challenges for transportation providers in maintaining service quality, particularly in addressing the gap between customer expectations and perceptions and ensuring efficient resource management. This study explores factors influencing service quality in Malaysian transportation provider companies using the SERVQUAL method, quality function deployment (QFD), and linear programming optimization. Key objectives include identifying issues in the TPM application service process, measuring gaps between customer perceptions and expectations, identifying critical service attributes using importance-performance analysis, and prioritizing technical responses to improve service quality using linear programming optimization. Based on root cause analysis, importance-performance mapping, and the house of quality framework, the study identified four key recommendations: updating standard operating procedures (SOPs) and monitoring service issues, providing driver training on methods and skills, implementing stricter driver selection criteria with a focus on code of conduct compliance, and developing an improved application interface for better customer location accuracy. These measures aim to enhance the efficiency and effectiveness of services, ensuring better alignment with customer needs and expectations while addressing critical operational challenges. By bridging the service quality gap, this research provides actionable insights to support continuous improvement in the Transportation Provider Company from Malaysia.

Integration optimization of factory production planning and joint replenishment in the supply chain considering uncertain lead time

This study introduces a mixed integer linear programming (MILP) optimization model for factory production planning and joint replenishment in a supply chain with dynamic demand variations, aiming to minimize transportation, inventory, and replenishment costs. The approach transforms the problem into a stochastic optimization model by combining the Monte Carlo Simulation (MCS) algorithm with the Sample Average Approximation (SAA) method, addressing the uncertainty of replenishment lead times at the distribution centers. Using the MCS and the Gurobi solver, the model is applied to real-world data from X Beverage Supply Company, demonstrating its effectiveness. Finally, the detailed production plans for each factory and refined replenishment strategies for distribution centers are obtained from the proposed optimization model. Additionally, a comparative analysis of scenarios with and without uncertain replenishment lead times is conducted, and out-of-sample experiments are performed to further validate the effectiveness and practicability of the proposed model and solution.

Process analysis-based industrial production modelling with uncertainty: A linear fractional programming for joint optimization of total caron emissions and emission intensity

Process analysis-based industrial production modelling with uncertainty: A linear fractional programming for joint optimization of total caron emissions and emission intensity

Optimal Allocation and Sizing of BESS in a Distribution Network with High PV Production Using NSGA-II and LP Optimization Methods

Battery energy storage systems (BESSs) can play a significant role in overcoming the challenges in Distribution Systems (DSs) with a high level of penetration from renewable energy sources (RESs). In this paper, the goal is to determine the optimal location, size, and charging/discharging dispatches of BESSs in DSs with a high level of photovoltaic (PV) installations. The problem of the location and size of BESSs is solved with multi-criteria optimization using Non-dominated Sorting Genetic Algorithm-II (NSGA-II). The criteria of the multi-criteria optimization are minimal investment costs for BESS and improvement of the network performance index. The network performance index includes the reduction in annual losses of active energy in DSs and the minimization of voltage deviations. The dispatch of a BESS is determined using auxiliary optimization. Linear Programming (LP) is used for auxiliary optimization, with the aim of dispatching the BESS to smooth the load profile in DS. The proposed optimization method differs from previous studies because it takes in its calculations all days of the year. This was performed using the K-means clustering technique. The days of one year are classified by the level of consumption and PV production. The optimization was performed for five different levels of PV penetration (60%, 70%, 80%, 90%, and 100%) and for two scenarios: the first with one BESS and the second with two BESSs. The proposed methodology is applied to the IEEE 33 bus balanced radial distribution system. The results demonstrate that with an optimal choice of location and parameters of the BESS, significant improvement in network performance is achieved. This refers to a reduction in losses of active power, improvement of voltage profile, smoothing the load diagram, and reducing the peak load. For the scenario with one BESS and PV penetration of 100%, the reduction in daily energy losses reaches a value of up to 10% compared to the base case (case without a BESS). The reduction in peak load goes to 20%. Further, the highest voltage during the day is significantly lower in all buses compared to the base case. Similarly, the lowest voltage during the day is considerably higher. The methodology from this paper can be applied to any radial distribution network with a variable number of BESSs. The testing results confirm the effectiveness of the proposed method.

Optimal Scheduling of Integrated Energy System Based on Carbon Capture–Power to Gas Combined Low-Carbon Operation

In this paper, an IES optimal cooperative scheduling method based on a master–slave game is proposed considering a carbon emission trading (CET) and carbon capture system (CCS) combined operation with power to gas (P2G). We analysed the behaviour of integrated energy system operators (IESO) and energy suppliers (ES) when the system is operating in different states. This paper first introduces the structure of IES and the mathematical model of the game frame. Secondly, mixed integer linear programming and particle swarm optimization (MILP–PSO) are used. The final simulation results show that in the main scenario, IESO and ES have an income of CNY 181,900 and CNY 279,400, respectively, and the actual carbon emission is 106.75 tons. The overall income is balanced, and the carbon emission is in the middle. The results provide a reference value for operators and users to make decisions.

Hybridization of wind farms with co-located PV and storage installations

Hybridization of wind farms with co-located PV and storage installations

Mitigating Water Shortages and Enhancing Food Security through Crop Optimization: Insights from the Eastern Nile Delta

Aim of the studyThis provides insight into the current and future water situation in the East Nile Delta in Egypt. Additionally, the study aimed to identify gaps in knowledge that require further research and to illustrate the different types of models used to optimize water resources management and maintain food security.Material and methodsThe study analyzed the status of water resources availability, water demand, and other influencing factors in the East Nile Delta. To address water scarcity, the study employed optimization models, specifically using linear optimization programming. This model was applied to the Eastern Delta area, focusing on the region supplied by the Ismailia Canal. The model aimed to balance the limited supply of freshwater with the increasing demand by proposing changes in cropping patterns.Results and conclusionsThe study found that the best way to secure water supply and minimize water scarcity is by using optimization models. In the Eastern Delta, the area supplied by the Ismailia Canal had a water deficit of about 789.81 MCM. By changing the cropping patterns, the water deficit could be reduced. The results indicated a decrease in the cultivation of non-strategic crops such as onions, garlic, fruit trees, peanuts, sesame, and soybeans. Conversely, there was an increase in the cultivation of strategic crops such as wheat, cotton, maize, and corn, as well as crops with high net yields like tomatoes and potatoes. These changes would help balance water demand and supply, ensuring a more sustainable water management strategy for the future.

Linear Programming Optimization of Local Food-Based Recommendations for Undernourished Urban Poor Malaysian Children Aged 2 to 5 Years.

BackgroundPoor diet quality may contribute to undernutrition, particularly affecting young children from low-income households. Therefore, affordable and healthy local food-based recommendations (FBRs) are needed.ObjectivesThis study aimed to (1) identify problem nutrient(s), (2) identify locally available nutrient-dense food sources that can provide adequate nutrients to meet the recommended dietary intakes of undernourished urban poor children aged 2-5 years, and (3) use linear programming to recommend a daily diet based on the current food patterns that achieves dietary adequacy and meets average food costs for these children.MethodsA cross-sectional study was conducted in Seremban, Malaysia. Three-day 24-hour dietary recalls were collected from the mothers (n = 168). Food costs were estimated using market surveys. The FBRs were formulated by linear programming analysis using Optifood software.ResultsFolate was an "absolute problem nutrient" (such a nutrient does not achieve the 100% recommended nutrient intake even upon diet optimization). Full-cream milk, chocolate malted milk, fortified cornflakes, and chicken egg were the common locally available nutrient-dense foods that would provide adequate nutrients to meet the recommended dietary intakes of undernourished urban poor children. The final FBR set would ensure dietary adequacy for 8 to 9 of 11 nutrients at a cost of ringgit Malaysia (RM) 4.80/day (US $1.05/day) and RM6.20/day (US $1.34/day), depending on the age group.ConclusionsInterventions are required to ensure dietary adequacy for undernourished urban poor children under 5 years old. Dietary adequacy could be improved via realistic changes in habitual food consumption practices.

Optimizing Agricultural Planting Strategies with Linear Programming and MOPSO

The deep implementation of rural revitalization strategy has put forward higher requirements for our agricultural economy and production. However, in reality, the unreasonable allocation of resources and the impact of natural disasters pose challenges to agricultural output. In this paper, a new agricultural planting optimization model combining linear programming and multi-objective particle swarm optimization algorithm is proposed, and the resource allocation and production conditions in the northern mountainous areas are systematically studied from 2024 to 2030. By integrating economic benefits and ecological constraints, the model realizes the maximization of agricultural benefits and the sustainability of resource utilization. Linear programming effectively optimizes planting area and resource allocation, while MOPSO improves the adaptability and robustness of the model through global search. The model introduces dynamic constraints, such as crop rotation and land use restrictions, and innovatively incorporates the soil restoration benefits of legume crops into the optimization framework. Case studies under different market scenarios (slow sales and low sales) show that the model can provide efficient planting strategies, and its practicability and effectiveness are verified. The research results provide theoretical support and practical guidance for precision agriculture and rural revitalization, and suggest that dynamic variables and data-driven technologies should be combined in the future to further enhance the optimization potential and application value of the model.

A Deep Q-Learning Based UAV Detouring Algorithm in a Constrained Wireless Sensor Network Environment

Unmanned aerial vehicles (UAVs) play a crucial role in various applications, including environmental monitoring, disaster management, and surveillance, where timely data collection is vital. However, their effectiveness is often hindered by the limitations of wireless sensor networks (WSNs), which can restrict communications due to bandwidth constraints and limited energy resources. Thus, the operational context of the UAV is intertwined with the constraints on WSNs, influencing how they are deployed and the strategies used to optimize their performance in these environments. Considering the issues, this paper addresses the challenge of efficient UAV navigation in constrained environments while reliably collecting data from WSN nodes, recharging the sensor nodes’ power supplies, and ensuring the UAV detours around obstacles in the flight path. First, an integer linear programming (ILP) optimization problem named deadline and obstacle-constrained energy minimization (DOCEM) is defined and formulated to minimize the total energy consumption of the UAV. Then, a deep reinforcement learning-based algorithm, named the DQN-based UAV detouring algorithm, is proposed to enable the UAV to make intelligent detour decisions in the constrained environment. The UAV must finish its tour (data collection and recharging sensors) without exceeding its battery capacity, ensuring each sensor has the minimum residual energy and consuming energy for transmitting and generating data, after being recharged by the UAV at the end of the tour. Finally, simulation results demonstrate the effectiveness of the proposed DQN-based UAV detouring algorithm in data collection and recharging the sensors while minimizing the total energy consumption of the UAV. Compared to other baseline algorithm variants, the proposed algorithm outperforms all of them.

Integrated optimization for sizing, placement, and energy management of hybrid energy storage systems in renewable power systems

Integrated optimization for sizing, placement, and energy management of hybrid energy storage systems in renewable power systems

A Computationally Efficient Rule-Based Scheduling Algorithm for Battery Energy Storage Systems

This paper presents a rule-based control strategy for the Battery Management System (BMS) of a prosumer connected to a low-voltage distribution network. The main objective of this work is to propose a computationally efficient algorithm capable of managing energy flows between the distribution network and a prosumer equipped with a photovoltaic (PV) energy production system. The goal of the BMS is to maximize the prosumer’s economic revenue by optimizing the use, storage, sale, and purchase of PV energy based on electricity market information and daily production/consumption curves. To achieve this goal, the method proposed in this paper consists of developing a rule-based algorithm that manages the prosumer’s Battery Energy Storage System (BESS). The rule-based approach in this type of problem allows for the reduction of computational costs, which is of fundamental importance in contexts where many users will be coordinated simultaneously. This means that the BMS presented in this work could play a vital role in emerging Renewable Energy Communities (RECs). From a general point of view, the method requires an algorithm to process the load and generation profiles of the prosumer for the following three days, together with the hourly price curve. The output is a battery scheduling plan for the timeframe, which is updated every hour. In this paper, the algorithm is validated in terms of economic performance achieved and computational times on two experimental datasets with different scenarios characterized by real productions and loads of prosumers for over a year. The annual economic results are presented in this work, and the proposed rule-based approach is compared with a linear programming optimization algorithm. The comparison highlights similar performance in terms of economic revenue, but the rule-based approach guarantees 30 times lower processing time.

Sustainable Valorization of Oil and Gas Industry Biosolids: Optimal Reuse Pathways

This study investigates the potential of converting waste biosolids from industrial sources, focusing on economic viability and heavy metal removal efficiency. Traditional management methods like landfilling and incineration are increasingly impractical due to land constraints and environmental concerns, prompting a shift towards thermal and biological conversion technologies including anaerobic digestion, pyrolysis, gasification, and hydrothermal liquefaction. Incorporating a pretreatment for heavy metal removal is essential, as industrial wastes are highly subjected to metal contamination. The study screens a range of metal removal processes, including precipitation, adsorption, ion exchange, and microwave induction. Although a techno-economic analysis can help give a perspective on the economic viability and environmental impact of each technology, it does not account for technical limitations and variations in the treated waste stream. A mixed integer linear programming (MILP) optimization model is developed to fill in this gap and assist in waste stream allocation to the most appropriate technology, taking into account both technology capacities and feed characteristics. This study looked into the optimal treatment route at different feed moisture contents and varying flow rates. The results demonstrate that the model distributes the feed across the different technologies on the basis of maximizing the capacity of the optimal technology while ensuring the moisture and heavy metal content limits are satisfied. Thus, it maximizes profitability and ensures heavy metal removal efficiency. By optimizing industrial biosolids treatment pathways, this study promotes sustainable resource recovery aligning with circular economy principles in waste management. The developed model facilitates informed decision-making in biosolids management and industrial waste treatment practices.

Theoretical foundations and practical implementation of supply chain optimization a metal fabrication business model

In the dynamic landscape of modern business, effective management of supply chains stands as a cornerstone of organizational success and competitive edge. This study investigates the theoretical principles and practical implementations of optimization models aimed at refining supply chain operations in the metal fabrication business, giving the maximum profit. It begins with a comprehensive survey of optimization theory, encompassing linear programming, integer programming, and stochastic optimization. It proceeds to their application in addressing diverse challenges encountered in supply chain management. The discussion includes deterministic models, such as those optimizing facility location under capacity constraints and transportation logistics, alongside stochastic models designed to manage uncertainties inherent in demand forecasting and inventory control. Advanced methodologies like metaheuristic algorithms and multi-objective optimization techniques are examined for their capacity to navigate the intricate and often conflicting objectives within supply chain networks. Through comprehensive theoretical analysis and a study of the supply chain model developed for the metal fabrication business, this paper contributes to advancing knowledge in mechanical engineering and supply chain management, offering insights pertinent to practitioners and researchers alike. Ultimately, it emphasizes the critical role of optimization models in optimizing efficiency, reducing costs, improving profit margin, reducing CO2 emission, and enhancing competitiveness in modern supply chain operations.

Mitigation and Optimization of Induced Seismicity Using Physics‐Based Forecasting

AbstractFluid injection can induce seismicity by altering stresses on pre‐existing faults. Here, we investigate minimizing induced earthquake potential by optimizing injection operations in a physics‐based forecasting framework. We built a 3D finite element model of the poroelastic crust for the Raton Basin, Central US, and used it to estimate time dependent Coulomb stress changes due to 25 years of wastewater injection in the region. Our finite element model is complemented by a statistical analysis of the seismogenic index (SI), a proxy for critically stressed faults affected by variations in the pore pressure. Forecasts of seismicity rate from our hybrid physics‐based statistical model suggest that induced seismicity in the Raton Basin, from 2001 to 2022, is still driven by wastewater injection despite declining injection rates since 2011. Our model suggests that pore pressure diffusion is the dominant cause of Coulomb stress changes at seismogenic depth, with poroelastic stress changes contributing about 5% to the driving force. Linear programming optimization for the Raton Basin reveals that it is feasible to reduce earthquake potential for a given amount of injected fluid (safety objective) or maximize fluid injection for a prescribed earthquake potential (economic objective). The optimization tends to spread out high‐rate injectors and shift them to regions of lower SI. The framework has practical importance as a tool to manage injection rate per unit field area to reduce induced earthquake potential. Our optimization framework is both flexible and adaptable to mitigate induced earthquake potential in other regions and for other types of subsurface fluid injection.