Linear Programming Techniques Research Articles

Implementing 4D seismic inversion based on Linear Programming techniques for CO2 monitoring at the Sleipner field CCS site in the North Sea, Norway

Implementing 4D seismic inversion based on Linear Programming techniques for CO2 monitoring at the Sleipner field CCS site in the North Sea, Norway

Improving Estimation of Specific Differential Phase and Assessing Differential Backscattering Phase

Abstract Polarimetric variables such as differential phase (фDP) and its range derivative, specific differential phase (KDP), contain useful information for improving quantitative precipitation estimation (QPE) and microphysics retrieval. However, the usefulness of the current operationally utilized estimation method of KDP is limited by measurement error and artifacts resulting from the differential backscattering phase (δ). The contribution of δ can significantly influence the фDP measurements and therefore negatively affect the KDP estimates. Neglecting the presence of δ within non-Rayleigh scattering regimes has also led to the adoption of incorrect terminology regarding signatures seen within current operational KDP estimates implying associated regions of unrealistic liquid water content. A new processing method is proposed and developed to estimate both KDP and δ using classification and Linear Programming (LP) to reduce bias in KDP estimates caused by the δ component. It is shown that by applying the LP technique specifically to the rain regions of Rayleigh scattering along a radial profile, accurate estimates of differential propagation phase, specific differential phase and differential backscattering phase can be retrieved within regions of both Rayleigh and non-Rayleigh scattering. This new estimation method is applied to cases of reported hail and tornado debris and the LP results are compared to the operationally utilized least-square-fit (LSF) estimates. The results show the potential use of the differential backscattering phase signature in the detection of hail and tornado debris.

Smart home energy management and active power loss analysis of a residential community

As the demand for energy continues its upward trajectory, judiciously managing the global energy resources has become increasingly imperative. One effective strategy to accomplish this efficiency is by strategically scheduling intelligent household appliances, a process that considers dynamic pricing schemes and the availability of renewable energy sources. This paper presents a comprehensive study that delves into optimizing smart home appliance utilization, considering electric vehicles and a modest rooftop photovoltaic installation. The study seeks to ascertain their potential impact on both energy consumption and cost mitigation. The proposed scheduling approach is centered on the optimal scheduling of smart appliances, harnessing the power of real-time pricing schemes to curtail the overall energy expenditure. The scheduling conundrum is meticulously modelled using General Algebraic Modeling System software and subsequently tackled by the CPLEX solver, leveraging mixed-integer linear programming techniques. Results reveal a remarkable achievement, with the potential for up to an 80.6 % reduction in the overall cost compared to the base case under various scenarios considering different approaches. To validate the integrity of the study, outcomes are juxtaposed with those of the base paper, and the superiority of the proposed method is evident from the results. Furthermore, the paper considers the ramifications of optimized scheduling on the voltage profile and overall system losses nearly 7 % less compared to the base case within the context of the IEEE 33-bus system. Thus, the presented work successfully analyzes the effect of household energy scheduling on the community level and scales up to a microgrid level.

Optimization of a syngas-fueled SOFC-based multigeneration system: Enhanced performance with biomass and gasification agent selection

In light of abundant sources of biomass feedstocks and regarding the higher performance in syngas-fueled-based SOFC systems, this work proposes a novel multigeneration system based on the combination of syngas-fuel SOFC, Kalina cycle, humidification-dehumidification desalination unit, and proton exchange membrane electrolyzer. This system is designed for simultaneous production of power, heating, freshwater, and hydrogen. Comprehensive energy, exergy, exergoeconomic, environmental, and economic analyses have been conducted to evaluate its performance. The optimum input biomasses, gasification agents, and operating conditions were determined using a coupled approach of an artificial neural network, multi-objective Particle Swarm Optimization algorithm, and the Linear Programming Technique for Multidimensional Analysis of Preference decision-making method. Under base input conditions, the energy and exergy efficiencies of the proposed system were found to be 53.66 % and 38.2 %, respectively. The system also demonstrated the capability to produce 0.1633 kg/s of freshwater and generate a net power output of 377.6 kW. The results indicate that using oxygen-enriched air in the gasification process notably enhances efficiency while reducing emissions. Straw and CO₂ were identified as the optimal feedstock and gasification agent, yielding an exergy efficiency of 42.71 % and a total product cost of 6.29 $/GJ at the optimum point. Moreover, with a selling price of $0.20/kWh for electricity and a fuel cost of $6/GJ, the system can achieve total revenue of approximately $1.65 million with a payback period of 4.01 years. These findings underscore the proposed plant's profitability under specific pricing conditions, making it an attractive investment opportunity.

Optimizing Bio-energy Supply Chain to Achieve Alternative Energy Targets

In response to global warming and the dwindling reservoirs of fossil fuels, Thailand has increasingly embraced alternative energy sources. Central to its energy development strategy is the Alternative Energy Development Plan (AEDP), which aims to reduce energy intensity, capitalize on residual resources, and mitigate greenhouse gas emissions. While significant strides have been made in meeting various consumption targets set forth by the AEDP, notable challenges persist, particularly in the realms of bio-mass-derived electricity generation, bio-gas utilization, and bio-ethanol production from bio-mass. Therefore, this study delves into the factors contributing to the shortfall in achieving AEDP targets and proposes strategies to enhance the efficiency of the bio-energy supply chain. Leveraging mathematical and linear programming techniques, our research optimizes the supply chain dynamics, accounting for monthly supplier profiles spanning 77 provinces, 17 distinct biomasses, and 427 bio-energy plants equipped with diverse energy conversion technologies. Our findings indicate that Thailand currently boasts adequate bio-mass resources to fulfill the electricity and bio-ethanol targets outlined in the AEDP—provided enhancements are made to supply chain efficiency. To fully realize the objectives of the AEDP, we recommend augmenting bio-mass cultivation efforts and implementing new power plant installations. Additionally, we advocate for the consideration of high-methane content fuels, such as solid waste, as a means to alleviate bio-mass demand. This study underscores the paramount importance of strategic planning and optimization in propelling Thailand towards its alternative energy ambitions while surmounting supply chain impediments.

Optimizing Concrete Paver Block Production: A Linear Programming Approach for Enhanced Profitability in the Construction Industry

As an operational optimization (maximization or minimization) methodology, linear programming (L.P.) in operation research has proven successful in several areas by offering logical outcomes to challenging issues, including resource constraints. The study aimed to bridge the gap between theoretical applications of L.P. and the practical needs of the construction industry, specifically focusing on determining the optimal production quantities of 60 mm and 40 mm concrete paver blocks for Janta Udhog Pvt. Ltd. as a case study to achieve maximum profitability, offering essential new insights into how L.P. may successfully handle the complex problems encountered by businesses in this industry. An interview with the owner of Janta Udhog Pvt. Ltd. was conducted to obtain the primary data for the study. Secondary data such as sale records, monthly demand of each product, and inventory records were also obtained to formulate a linear programming model. The model was then solved using the LINGO software. This research underscores the optimal production recommendations for Janta Udhog Pvt. Ltd., advising the manufacture of 566.67 units of the 60 mm block and 350 units of the 40 mm block, leading to a maximum daily profit of NPR 2966.67. By applying linear programming techniques, these findings contribute to a more informed and strategic decision-making approach in the construction sector. The study illuminates the benefits of utilizing linear programming in challenging situations, providing valuable insights for academics, business owners, and decision-makers.

INTEGER LINEAR PROGRAMMING MODEL FOR AGGREGATE PRODUCTION PLANNING, APPLICATION OF LEARNING CURVES, AND HYPOTHESIS TESTING

ABSTRACT: Efficient production management and business administration are essential to maintain competitiveness in a business environment in constant change and complexity; the optimization of production systems becomes imperative to minimize costs and maximize operational efficiency. In this context, the implementation of advanced integer linear programming techniques emerges as a solution for aggregate production planning, based on the establishment of a uniform flow of processes to contribute to improving the efficiency of the system and reducing associated cost overruns. This article presents the analysis of the use of integer linear programming for aggregate production planning, applied to the production process of concrete blocks and concrete for structural masonry in the company Blocks del Sinú SAS in the department of Córdoba - Colombia. An optimization model is proposed that satisfies the forecasted demand through adjustments to the levels of production, labor, inventories, contracting and raw materials. The results show that with the standardization of the production process and work methods to minimize the costs of the production plan and meet the demand requirements in accordance with the company's capacity, demand will strictly occur within the planning horizon. , which implies that there will be no shortage of raw materials. Keywords: Aggregate planning, integer linear programming, production.

Elliptic curves with a rational 2-torsion point ordered by conductor and the boundedness of average rank

In this paper we refine recent work due to A. Shankar, A. N. Shankar, and X. Wang on counting elliptic curves by conductor to the case of elliptic curves with a rational 2-torsion point. This family is a small family, as opposed to the large families considered by the aforementioned authors. We prove the analogous counting theorem for elliptic curves with so-called square-free index as well as for curves with suitably bounded Szpiro ratios. We note that the assumptions we impose on the size of the Szpiro ratios are less stringent than would be expected by the naive generalization of their approach; this requires an application of a theorem of Browning and Heath-Brown. Our proof also relies on linear programming techniques.

Marginal abatement cost of CO2: A convex quantile non-radial directional distance function regression method considering noise and inefficiency

By purchasing emission reduction equipment or reducing production scale, it is possible to effectively decrease CO2. Therefore, understanding the marginal abatement cost (MAC) associated with these methods is crucial for making decisions. However, previous studies using the directional distance function (DDF) approach often mis-specified production functions and neglected data noise. They also assumed decision-making units (DMUs) to be on the production frontier and used proportional changes in inputs and outputs as abatement paths. This paper addresses these limitations by developing the convex quantile non-radial directional distance function (CQR-NDDF) method, which estimates the MAC of CO2 and determines optimal abatement paths for DMUs without assuming a specific production function, employing linear programming techniques. Applying this method to 30 provinces in mainland China from 2011 to 2019, the study finds that China's CO2 MAC increased from 182 to 247 yuan/ton. The lowest-cost abatement path varies by province and time. The club convergence and ordered probit model are employed to conclude that the second industry and urbanization increase the MAC of CO2, while factors such as foreign direct investment, openness level, and human capital decrease the MAC. Moreover, the CQR-NDDF method yields significantly lower MAC estimates than the NDDF method. In conclusion, this paper provides new insights into China's CO2 MAC, emphasizing the importance of considering inefficiency and data noise in MAC estimation. We anticipate that utilizing CO2 MAC as a benchmark for carbon trading market prices could lead to an increase in prices within China's carbon trading market.

Multi-objective optimization of twisted tri-lobed tube geometry for enhanced heat transfer and reduced resistance in turbulent flow

This study presents a detailed multi-objective optimization analysis of turbulent flow and heat transfer within a twisted tri-lobed tube, employing an integrated approach that combines Central Composite Design (CCD), Response Surface Methodology (RSM), Non-dominated Sorting Genetic Algorithm II (NSGA-II), Pareto frontier analysis, Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP), and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). The investigation focuses on optimizing key design parameters: Reynolds number (Re), twist pitch (P), and minor circle radius (r), targeting Nusselt number (Nu), Poiseuille number (fRe), and Performance Evaluation Criterion (PEC) as optimization objectives. Our major findings reveal that the developed second-order regression model precisely predicts the influences of these parameters on Nu, fRe, and PEC, with sensitivity analysis showing Re's strong positive impact on Nu and fRe, P's negative effect on fRe, and r's minimal impact. The study notably highlights the significant Nu enhancement with Re increase. Utilizing multi-objective optimization, we identified a Pareto optimal set, and through LINMAP and TOPSIS methods, derived compromise solutions that optimally balance heat transfer efficiency, flow resistance, and overall performance. These outcomes underscore the critical importance of parameter selection to meet specific engineering needs, offering a strategic framework for enhancing twisted tri-lobed tube designs.

Mismatch between provincial grain production and consumption increased cropland soil erosion in China

Cropland soil erosion is primarily caused by agricultural production and indirectly altered by consumption patterns. A well-developed grain trade system transfers grain products to distant locations, away from their place of origin where soil erosion may have occurred. Evidence-based policies to control soil erosion can be developed by holding consumers responsible for the soil erosion caused by their consumption. However, there have been few systematic studies on cropland soil erosion that is embodied in grain trade. In this study, we estimated the soil erosion intensity (SEI) of grain production in each province of China from 1990 to 2020 by combining the Revised Universal Soil Loss Equation and socio-economic statistics. We also constructed an interprovincial grain trade network using linear programming techniques and analyzed the cropland soil erosion associated with the interprovincial grain trade. The results showed a rise in national cropland soil erosion attributed to grain production from 5.36×108 t in 1990 to 7.56×108 t in 2020. In particular, those embodied in interprovincial grain trade increased from 0.94×108 t in 1990 to 3.52×108 t in 2020. Nationally, about 10.72% of soil erosion exports in 2020 was from provinces with lower-than-average SEI, compared to 18.42% in 1990, indicating that current patterns of grain production and consumption are unfavorable for erosion control. Accordingly, measures have been proposed to build a soil erosion control system that includes consumers, such as changing farming practices, optimizing agricultural layout, promoting technology export and establishing a provincial compensation mechanism.

Integrated design of a sustainable waste management system with co-modal transportation network: A robust bi-level decision support system

Efficient waste management practices play a critical role in addressing the acute challenges of environmental protection, public health and resource conservation. A well-designed system guarantees that waste is efficiently collected, treated and disposed while minimizing negative impacts on ecosystems and human well-being. This work presents a robust bi-level decision support system to establish a sustainable waste management system using a co-modal transportation network to treat municipal solid waste timely and efficiently. Consequently, two integrated multi-objective mathematical models are developed to formulate the problem. Configuring the municipal solid waste network in the first level of the suggested decision support system, the transportation network is designed in the second level taking into account non-identical modes. The objectives are to minimize total cost and total emission in both levels, while maximization of total job creation is also addressed in the first level. Robust optimization method and weighted goal programming method are then utilized to accommodate the developed decision support system against uncertainty and multi-objectiveness, respectively. To validate the efficiency of these methods, they are assessed against possibilistic linear programming technique and Lp-metric approach with the help of simple additive weighting (SAW) method, respectively. Eventually, several numerical examples are generated based on the benchmarks given in the literature, which are then tackled using CPLEX solve to appraise the applicability and complexity of the developed methodology. The findings reveal the efficacy of the decision support system in terms of finding solutions in less than 448 s on average. Finally, sensitivity analyses are performed to draw out useful practical implications and decision aids.

Lattice layout and optimizer effect analysis for generating optimal transcranial electrical stimulation (tES) montages through the metaheuristic L1L1 method.

This study focuses on broadening the applicability of the metaheuristic L1-norm fitted and penalized (L1L1) optimization method in finding a current pattern for multichannel transcranial electrical stimulation (tES). The metaheuristic L1L1 optimization framework defines the tES montage via linear programming by maximizing or minimizing an objective function with respect to a pair of hyperparameters. In this study, we explore the computational performance and reliability of different optimization packages, algorithms, and search methods in combination with the L1L1 method. The solvers from Matlab R2020b, MOSEK 9.0, Gurobi Optimizer, CVX's SeDuMi 1.3.5, and SDPT3 4.0 were employed to produce feasible results through different linear programming techniques, including Interior-Point (IP), Primal-Simplex (PS), and Dual-Simplex (DS) methods. To solve the metaheuristic optimization task of L1L1, we implement an exhaustive and recursive search along with a well-known heuristic direct search as a reference algorithm. Based on our results, and the given optimization task, Gurobi's IP was, overall, the preferable choice among Interior-Point while MOSEK's PS and DS packages were in the case of Simplex methods. These methods provided substantial computational time efficiency for solving the L1L1 method regardless of the applied search method. While the best-performing solvers show that the L1L1 method is suitable for maximizing either focality and intensity, a few of these solvers could not find a bipolar configuration. Part of the discrepancies between these methods can be explained by a different sensitivity with respect to parameter variation or the resolution of the lattice provided.

Uniform negative immersions and the coherence of one-relator groups

Previously, the authors proved that the presentation complex of a one-relator group G\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$G$\\end{document} satisfies a geometric condition called negative immersions if every two-generator, one-relator subgroup of G\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$G$\\end{document} is free. Here, we prove that one-relator groups with negative immersions are coherent, answering a question of Baumslag in this case. Other strong constraints on the finitely generated subgroups also follow such as, for example, the co-Hopf property. The main new theorem strengthens negative immersions to uniform negative immersions, using a rationality theorem proved with linear-programming techniques.

Understanding energy performance in drinking water treatment plants using the efficiency analysis tree approach

Water treatment processes are known to consume substantial amounts of energy, making it crucial to understand their efficiency, drivers, and potential energy savings. In this study, we apply Efficiency Analysis Tree (EAT), which combines machine learning and linear programming techniques to assess the energy performance of 146 Chilean drinking water treatment plants (DWTPs) for 2020. Additionally, we utilize bootstrap regression techniques to examine the influence of operating characteristics on energy efficiency. The results indicate that the evaluated DWTPs exhibited poor energy performance, with an average energy efficiency score of 0.197. The estimated potential energy savings were found to be 0.005 kWh/m3. Several factors, such as the age of the facility, source of raw water, and treatment technology, were identified as significant drivers of energy efficiency in DWTPs. The insights gained from our study can be valuable for policymakers in making informed decisions regarding the adoption of practices that promote efficient and sustainable energy use within the water cycle.

A big data quality evaluation method based on group heterogeneity rationality perception information fusion

Big data is complex, and it is difficult to evaluate big data quality with only a few evaluation subjects. This paper designs a universal evaluation method for big data quality based on the idea of group heterogeneity rationality perception information fusion. Group evaluation information is usually large-scale and heterogeneous. The linear programming technique for multidimensional analysis of preference (LINMAP) model has the performance of large-scale evaluation information processing. Because the existing LINMAP models cannot effectively process group evaluation information with heterogeneous rationality, the LINMAP model of heterogeneous rationality (HR-LINMAP) based on group evaluation information is proposed. The research results show: under certain conditions, the LINMAP model of bounded rationality (BR-LINMAP) can be transformed into the LINMAP model of perfect rationality (PR-LINMAP), and the HR-LINMAP is the general form of PR-LINMAP and BR-LINMAP. The scientific research big data resources with mature trading markets are selected as the evaluation objects, and HR-LINMAP is used to analyze the big data quality evaluation cases. The empirical analysis shows that the HR-LINMAP model is feasible and effective, which provides a new idea for big data quality evaluation.

Application Of Linear Programming in the Minimization of Transportation Cost in Dangote Cement, Port Harcourt

This study delved into the optimization of transportation expenses for Dangote Cement in Port Harcourt, Rivers State. It aligned the quantities of products required by national distributors with the supply available from their depots, employing linear programming techniques to achieve cost minimization. Three sources (depots) - Onne, Rumuodumaya and Trans Amadi as well as six destinations (national distributors) - Aluu, Bori, Elelewon, Omagwa, Oyibo and Rumuola were examined. The secondary data was obtained from a field survey and it contained the unit cost (in Naira) of transporting the products per bag from their various sources to various destinations as at October, 2023. Also, the data obtained from Dangote Cement National Consumer Promotion 2020 (Redemption Centres Detail) contained the list of eleven national distributors in Port Harcourt; however, only six of the national distributors were used in this research. Initial feasible solutions for the secondary data collected were determined through the application of the North-West Corner Method, the Least Cost Method, and the Vogel Approximation Method resulting in values of ₦452,000, ₦380,750, and ₦370,500, respectively. Upon analyzing the outcomes, it was established that the allocation strategy proposed by the Vogel Approximation Method is the most advantageous for optimizing the company's transportation costs. As such, it is recommended to the company as it offers the potential to reduce transportation expenses to a minimum of ₦370,500.

Incorporating a Load-Shifting Algorithm for Optimal Energy Storage Capacity Design in Smart Homes

In today’s power system landscape, renewable energy (RE) resources play a pivotal role, particularly within the residential sector. Despite the significance of these resources, the intermittent nature of RE resources, influenced by variable weather conditions, poses challenges to their reliability as energy resources. Addressing this challenge, the integration of an energy storage system (ESS) emerges as a viable solution, enabling the storage of surplus energy during peak-generation periods and subsequent release during shortages. One of the great challenges of ESSs is how to design ESSs efficiently. This paper focuses on a distributed power-flow system within a smart home environment, comprising uncontrollable power generators, uncontrollable loads, and multiple energy storage units. To address the challenge of minimizing energy loss in ESSs, this paper proposes a novel approach, called energy-efficient storage capacity with loss reduction (SCALE) scheme, that combines multiple-load power-flow assignment with a load-shifting algorithm to minimize energy loss and determine the optimal energy storage capacity. The optimization problem for optimal energy storage capacity is formalized using linear programming techniques. To validate the proposed scheme, real experimental data from a smart home environment during winter and summer seasons are employed. The results demonstrate the efficacy of the proposed algorithm in significantly reducing energy loss, particularly under winter conditions, and determining optimal energy storage capacity, with reductions of up to 11.4% in energy loss and up to 62.1% in optimal energy storage capacity.

Nutrient density of Bangladeshi foods and its application in planning diet for pregnant women.

Nutrient profiling is a method that classifies foods based on their nutrient content and identifies foods that are high in micronutrients both across and within food groups. This study aimed to identify foods that are rich sources of the seven micronutrients (iron, zinc, calcium, thiamine, riboflavin, vitamin A, and vitamin B12) of public health concern for the Bangladeshi population.. This study developed a metric termed "naturally nutrient-rich score 7 (NNR7)" specifically for third-trimester pregnant women to identify nutrient-dense foods. Further, it computed the nutrient adequacy score (NAS) of the top NNR7-scored foods for seven micronutrients to assess the extent (percent) to which foods can meet pregnant women's recommended dietary allowances (RDA). A linear programming technique was then used to construct a nutrient-adequate model diet for third-trimester pregnant women using the top ten NNR7-scored foods. According to the NNR7, food groups such as leafy vegetables, fish, meat, poultry and eggs, and vegetables are the richest sources of the problem micronutrients. Mutton liver (916.7%), soybean (39.3%), lamb liver (2160%) and duck liver (50.0%) were found to fulfill the highest percentage of the RDA of vitamin A, zinc, vitamin B12, and iron, respectively. In the formulated nutrient-adequate diets for pregnant women, rice, potato, brown wheat flour, and soya oil were universal to all three diets and Bengal gram, orange, Ganges River sprat, and duck liver were the most common ones. The study findings highlight the need for the consumption of foods such as leafy vegetables, fish, meat, poultry, eggs, pulses and vegetables to increase the intake of problematic micronutrients. Planning a nutrient-adequate diet for pregnant women using linear programming can be an alternative approach to optimize and shape food choices to meet their nutritional requirements.

MILP/MIQCP-Based Fully Automatic Method of Searching for Differential-Linear Distinguishers for SIMON-Like Ciphers

Differential-linear (DL) cryptanalysis is an important cryptanalytic method in cryptography and has received extensive attention from the cryptography community since its proposal by Langford and Hellman in 1994. At CT-RSA 2023, Bellini et al. introduced continuous difference propagations of XOR, rotation, and modulo-addition operations and proposed a fully automatic method using Mixed-Integer Linear Programing (MILP) and Mixed-Integer Quadratic Constraint Programing (MIQCP) techniques to search for DL distinguishers of Addition-Rotation-XOR (ARX) ciphers. In this paper, we propose continuous difference propagation of AND operation and construct an MILP/MIQCP-based fully automatic model of searching for DL distinguishers of SIMON-like ciphers. We apply the fully automatic model to all versions of SIMON and SIMECK. As a result, for SIMON, we find 13 and 14-round DL distinguishers of SIMON32, 15, 16, and 17-round DL distinguishers of SIMON48, 20-round DL distinguishers of SIMON64, 25 and 26-round DL distinguishers of SIMON96, 31 and 32-round DL distinguishers of SIMON128. For SIMECK, we find 14-round DL distinguishers of SIMECK32, 17 and 18-round DL distinguishers of SIMECK48, 22, 23, 24, and 25-round DL distinguishers of SIMECK64. As far as we know, our results are currently the best.