Simplex Method Research Articles

Application of The Simplex Method and Digital Literacy in Profit Optimization Problems Taufik Tempe

Resource allocation in the production process are important things that need to be considered to achieve optimal production levels. Production optimization problems are still an obstacle for most businesses operating in the food sector. One of them is the “Taufik Tempe” business which produces tempeh in three different sizes, namely large, medium, and small. The business owner finds it difficult to determine the amount of production according to market demand and minimize production costs for maximum profits. This research aims to solve the profit optimization problem of “Taufik Tempe” with appropriate production allocation to achieve maximum profits. The method used is the method of data collection and data analysis. Data collection methods include field studies (observations and interviews) and literature review. Meanwhile, data analysis uses the simplex method and uses MATLAB software. Data analysis techniques using observation and interviews. Meanwhile, the research results show that the maximum profit per month obtained is Rp 750.000,00 by focusing on producing only large-sized tempeh. Furthermore, by using MATLAB software the same results are obtained as using the simplex method but with a simple, effective and efficient algorithm, ofcourse with precise results and the use of this software aims to avoid calculation errors.

Penerapan Program Linear untuk Mengoptimalkan Jumlah Produksi dalam Memperoleh Keuntungan Maksimal pada Rumah UMKM Produk Wedang Sehat

Linear programming is a mathematical method used to solve problems related to linear optimization (maximum value and minimum value). Quoted from Mathematics 3 competency by Johanes, linear programming is a part of mathematics in the form of models, which consist of linear inequalities as a method for solving various problems in everyday life. This linear program can help solve problems ranging from basic to complex. This article aims to apply the use of linear programming in determining the maximum profit that can be obtained for managers of healthy wedang products. In this case, traders of ginger wedang products can use linear programming using the simplex method to find maximum profits manually and analyze using POM-QM for Windows software. The results of the analysis using the linear program of the simplex method with calculations on POM-QM have the same results, namely the maximum profit of MSME houses wedang sehat buk Sumiati in one day reaches Rp. 180,000 by producing healthy wedang ginger powder (X1) as much as 1 piece and wedang sehat suetajarah (X2) as much as 1 piece.

Optimasi Keuntungan Bisnis Toko Kue Menggunakan Program Linear Metode Simpleks (Studi Kasus: Toko Kue Bread Islamy Bakery and Cake Shop)

A bakery business, or bakery in Indonesian, is a shop that produces and sells flour-based foods baked in the oven such as bread, pastry, cakes, donuts, pastries, cookies, pies, and many more. It is a problem if one of these ingredients is not fulfilled, production in the bakery business will be hampered. Therefore, to find out what variables hinder the optimum value in the bakery business, mathematical modeling can be made using the linear program of the simplex method. The method used is a qualitative descriptive method. Data collection techniques in this study include the use of primary data obtained through observation, interviews, or distribution of questionnaires to relevant sources. And secondary data are obtained through literature search from books and magazines relevant to the research topic. The analysis technique used is linear programming using the simplex method. The results and discussion of research show that the function has reached optimal conditions. Therefore, the calculation is stopped after all values in the goal function become positive. The result of the settlement shows that the maximum profit (Zmaks) is Rp. 69,626.

Extraction of charge transfer states dissociation probability and localised states parameters for PTB7-Th:PC71BM photovoltaic cells: using experimental J-V curves

The efficient separation of bounded electron–hole pairs (excitons) through charge transfer states (CTS) is a fundamental process in organic photovoltaic cells (OPVs). Introduction of CTS dissociation probability CTSdis factor in the generation rate equations is a simple and effective method to estimate the number of dissociated CTS. In the present study, for a specified recombination coefficient (k), first we obtained the values of CTSdis and subsequently determined the localized states parameters, i.e., electron/hole trap densities, tail slopes, and trap cross sections within the active layer (PTB7-Th:PC71BM). In order to extract these values, the experimental data of dark/light J-V curves and the density of charge carriers at the electrodes are fitted using the downhill simplex algorithm. An iterative approach is used to obtain the converged values. Furthermore, we explored the effect of compositional variation on CTSdis and obtained values are 80%, 89%, 71%, and 57% for weight ratios of 1:1, 1:1.5, 1:2, and 1:2.5 respectively. All calculations and simulations are performed using OghmaNano.

Optimal load management of autonomous power systems in conditions of water shortage

The issues of optimizing the operation of micro hydropower plants in conditions of water scarcity, performed by additional connection to the grid of an energy storage system and wind power turbine, as well as optimal load management, are considered. It is assumed that the load of the system is a concentrated autonomous power facility that consumes only active power. The paper presents a rigorous mathematical formulation of the problem, the solution of which corresponds to the minimum cost of an energy storage system and a wind turbine, which allows for uninterrupted supply of electricity to power facilities in conditions of water shortage necessary for the operation of micro hydropower plants (under unfavorable hydrological conditions). The problem is formulated as a nonlinear multi-objective optimization problem to apply metaheuristic stochastic algorithms. At the same time, a significant part of the problem is taken out and framed as a subproblem of linear programming which will make it possible to solve it by a deterministic simplex method that guarantees to find the exact global optimum. This approach will significantly increase the efficiency of solving the entire problem by combining metaheuristic algorithms and taking into account expert knowledge about the problem being solved.

Assessment and optimization of a single flash geothermal system recovered by a trans‐critical CO2 cycle using different scenarios

AbstractIn the evolving landscape of sustainable energy, optimizing geothermal power systems presents a critical challenge. This study explores the energy and exergy efficiencies of a power production system utilizing a single‐flash geothermal cycle integrated with a trans‐critical CO2 cycle. The study's methodology involves a detailed examination of key performance parameters—separator pressure, CO2 turbine intake pressure, and steam turbine output pressure. Utilizing the EES software environment, the study innovatively employs a combination of Genetic Algorithm (GA), Nelder–Mead Simplex (NMS) method, and Direct algorithm (DA). When using GA, NMS and DA, the system's exergy efficiency increases from 32.46% in the default operating mode to 39.21%, 36.16%, and 38.82%, respectively. One of the notable outcomes is the identification of optimal separator pressure for maximum energy efficiency. Furthermore, the study reveals that increasing the CO2 turbine's inlet pressure adversely impacts the system's efficiency. The study's results contribute significantly to the field of renewable energy, offering practical guidelines for enhancing the performance of geothermal power systems.

Implementasi Metode Simpleks dalam Penentuan Jumlah Keuntungan pada Jus Buah

The problem that is often felt by small MSMEs, such as sellers of fresh fruit juice drinks, is the shortage of ingredients which results in a lack of production. This is an obstacle in terms of linear programming models. To maximize production and production yields, there needs to be a method that can be used to increase production yields and reduce the number of raw material constraints on Mauza Jus. This study aims to determine the implementation of the simplkes method in determining the amount of profit in the fruit jur, in order to increase efficiency and optimal results in a system by applying the simplex method in solving optimization problems. By using the simplex method Mauza Jus can increase profits by up to 60%, this happens because Mauza Jus can determine the amount of production per day and does not experience any losses at all. The processing results are done in QM For Windows. In conclusion, Mauza Jus is getting a considerable increase in profits

OPTIMIZATION OF DICLOFENAC POTASSIUM TRANSDERMAL PATCH FORMULA USING A COMBINATION OF POLYVYNIL PYRROLIDONE K 30, ETHYL CELLULOSE AND MENTHOL WITH SIMPLEX LATTICE DESIGN METHOD

Diclofenac potassium is one of the NSAID drugs which can cause gastrointestinal irritation and damage to the small intestinal mucosa including erosion and ulceration. The purpose of this study was to determine the effect of the combination of PVP K 30, ethyl cellulose and menthol on organoleptic, thickness, weight uniformity, moisture and folding resistance of diclofenac potassium transdermal patch.This research is an experimental study that includes an experiment to optimize the formulation of a transdermal patch preparation with the active ingredient potassium diclofenac and a combination of PVP K 30, ethyl cellulose and menthol. The optimization method uses the simplex lattice design method. There are 13 formula designs consisting of a combination of PVP K 30, ethyl cellulose and menthol. Each formula was tested for organoleptic, thickness, weight uniformity, moisture and folding resistance. Then the optimum formula was determined and analyzed using the simplex lattice design method. The combination of PVP K 30, ethyl cellulose and menthol with a simplex lattice design has an effect on the transdermal patch of diclofenac potassium which increases the consistency of the patch surface, reduces the thickness directly proportional to the weight of the patch and increases folding resistance. The proportion of PVP K 30, ethyl cellulose and menthol that can produce the optimum formula for diclofenac potassium transdermal patches with the simplex lattice design on the critical parameters of thickness, moisture, folding resistance and penetration tests, namely PVP K 30 of 14.87%, ethyl cellulose of 10.00% and 5.13% menthol.

A novel opposition-based hybrid cooperation search algorithm with Nelder–Mead for tuning of FOPID-controlled buck converter

This paper introduces a novel metaheuristic algorithm named the opposition-based cooperation search algorithm with Nelder–Mead (OCSANM). This enhanced algorithm builds upon the cooperation search algorithm (CSA) by incorporating opposition-based learning (OBL) and the Nelder–Mead simplex search method. The primary application of this algorithm is the design of a fractional-order proportional–integral–derivative (FOPID) controller for a buck converter system. A comprehensive evaluation is conducted using statistical boxplot analysis, nonparametric statistical tests and convergence response comparisons to assess the algorithm’s performance and confirm its superiority over CSA. Furthermore, the FOPID-controlled buck converter system based on OCSANM is compared with two top-performing algorithms: one using a hybridized approach of Lévy flight distribution with simulated annealing (LFDSA) and the other employing the improved hunger games search (IHGS) algorithm. This comparison encompasses transient and frequency responses, performance indices and robustness analysis. The results reveal the notable advantages of the proposed OCSANM-based system, including 25.8% and 8.7% faster rise times, 26% and 8.8% faster settling times compared with the best-performing approaches, namely LFDSA and IHGS, respectively. In addition, the OCSANM-based system exhibits a 34.7% and 9.6% wider bandwidth than the existing approaches-based systems. Incorporating voltage and current responses of the buck converter’s switched circuit with the OCSANM-based FOPID controller further underscores the algorithm’s effectiveness. To provide a comprehensive assessment, the paper also compares the proposed approach’s time and frequency domain responses with those of 17 other state-of-the-art approaches attempting to control buck converter systems similarly. These findings affirm the effectiveness of the OCSANM in designing FOPID controllers for buck converter systems.

Theoretical solutions for the anchoring force of 3‐D anchored slope and optimization strategy for anchoring force distribution

AbstractBased on the three‐dimensional limit equilibrium method with modifying normal stress over the slip surface, this study presents a theoretical solution for the anchoring force of three‐dimensional slopes and proposes a new optimization strategy for anchor force distribution. The method employed the Boussinesq solution from the field of elasticity. It led to the derivation of an equilibrium equation set, which incorporated the anchoring force increment. As a result, the approach yielded a more accurate theoretical value for a three‐dimensional anchoring force. In practical engineering applications, the prestress of anchor cables is often uniformly set, which may lead to discrepancies in the anchoring force requirements at different locations on the slope, potentially resulting in resource waste. The research introduces a linear programming approach to optimize resource allocation, aiming to minimize the total anchoring force under fixed anchor cable quantities, installation angles, and locations. Nevertheless, the results from the Simplex Method could lead to an overly concentrated distribution of anchoring force. Therefore, the study further employs the normal distribution theory to reallocate anchoring forces, thus achieving a more reasonable distribution. The proposed method has been validated through three example studies and a practical engineering case study, resulting in significant reductions in the total anchoring force following optimization. Moreover, such an approach allows for optimized handling of the anchoring force for each anchor cable. The work provides a new perspective and tool for practical engineering applications.

Enhancing understanding of moisture diffusion in wood: numerical approach and diffusion parameter optimization

Wood, an environmentally friendly construction material, is characterized by a critical attribute that significantly influences its mechanical properties and durability: its moisture absorption behavior. This study expands upon an existing one-dimensional model to develop an innovative two-dimensional numerical framework for simulating moisture propagation within wood. Utilizing the finite difference method, this approach offers a more detailed analysis of moisture behavior in wood structures. The research adopts an inverse modeling technique, integrating a simplex optimization algorithm programmed in VBA software. This algorithm is employed to deduce diffusion parameters from the evolution of moisture content over time. Focusing on the analysis of moisture diffusion parameters, the study examines both longitudinal and transverse directions in two temperate species (Beech and Fir) and two tropical species (Moabi and Ozigo). The findings provide insightful data on the hygroscopic behavior of these woods, revealing significant distinctions between temperate and tropical species. This research offers valuable information for the application of these wood species in construction and other fields, enhancing the understanding of their moisture-related properties.

Analisis Optimalisasi Produksi Dengan Linear Programming Melalui Metode Simpleks (Studi Kasus UMKM Aqisa Rumah Rosella Surabaya)

The simplex method is a method used to solve linear programming problems with repeated (repeated) calculations done many times to reach an optimal solution. To solve linear programming problems, it is necessary to determine the constraints and inequalities contained in the linear program. The simplex method can solve linear programming problems involving many inequalities and many variables. This study aims to optimize the production of rosella flower tea drinks and rosella flower syrup at UMKM Aqisa Rumah Rosella Surabaya. This study is a literature study, namely a literature study by examining books, journals and reports that are relevant to the field under study. The steps for optimizing production results include: (1) observation, (2) data collection, (3) mathematical modeling, (4) optimizing production results using the simplex method, (5) optimizing production results using POM-QM. The results of simplex linear program calculations using the POM-QM application, in order to get maximum profit, UMKM Aqisa Rumah Rosella needs to increase production of rosella tea drinks to 35 bottles per day and for rosella syrup it is necessary to reduce production to 5 bottles per day. With a total profit of IDR 142,500. Profits earned increased by 5%

A novel fast and efficient adaptive shuffled complex evolution algorithm for model parameter calibration

The research and optimization of hydrological forecasting models are among the most crucial components in the scope of water management and flood protection. Optimizing the calibration of hydrological forecasting models is crucial for forecasting performance. A rapid adaptive Shuffled Complex Evolution (SCE) method called Fast Adaptive SCE (FASCE) is proposed for calibrating model parameters. It builds upon the previously established SCE-UA, known for its effectiveness and robustness in the same calibration context. The robustness of the original SCE-UA is expanded upon, introducing a revised adaptive simplex search to bolster efficiency. Additionally, a new strategy for setting up the initial population base enhances explorative capacities. FASCE’s performance has been assessed alongside numerous methods from prior studies, demonstrating its effectiveness. Initial tests were conducted on a set of functions to assess FASCE’s efficacy. Findings revealed that FASCE could curtail the failure rate by a minimum of 80%, whereas the requirement for function evaluations fell between 30% and 60%. Two hydrological models - Support Vector Machine (SVM) and Xinanjiang rainfall-runoff model were employed to estimate the new algorithm’s performance. No failures were reported, and there was a reduction of at least 30% in function evaluations using FASCE. The outcomes from these studies affirm that FASCE can considerably reduce both the number of failures and the count of function evaluations required to reach the global maximum. Hence, FASCE emerges as a viable substitute for model parameter calibration.

New Approach to Solving Fuzzy Multiobjective Linear Fractional Optimization Problems

In this paper, an iterative approach based on the use of fuzzy parametric functions is proposed to find the best preferred optimal solution to a fuzzy multiobjective linear fractional optimization problem. From this approach, the decision-maker imposes tolerance values or termination conditions for each parametric objective function. Indeed, the fuzzy parametric values are computed iteratively, and each fuzzy fractional objective is transformed into a fuzzy non-fractional parametric function using these values of parameters. The core value of fuzzy numbers is used to transform the fuzzy multiobjective non-fractional problem into a deterministic multiobjective non-fractional problem, and the ε-constraint approach is employed to obtain a linear single objective optimization problem. Finally, by setting the value of parameter ε, the Dangtzig simplex method is used to obtain an optimal solution. Therefore, the number of solutions is equal to the number of used values, and the optimal solution is chosen according to the preference of the decision-maker. We have provided a didactic example to highlight the step of our approach and its numerical performances.

Finding a Basic Feasible Solution for Neutrosophic Linear Programming Models: Case Studies, Analysis, and Improvements


 Since the inception of operations research, linear programming has received the attention of researchers in this field due to the many areas of its use. The focus was on the methods used to find the optimal solution for linear models. The direct simplex method, with its three basic stages, begins by writing the linear model in standard form and then finding a basic solution that is improved according to the simplex steps until We get the optimal solution, but we encounter many linear models that do not give us a basic solution after we put it in a standard form, and here we need to solve a rule through which we reach the optimal solution. For these models, researchers and scholars in the field of operations research introduced the simplex method with an artificial basis, which helped to Find the optimal solution for linear models, given the importance of this method and as a complement to the previous research we presented using the concepts of neutrosophic science. In this research, we will reformulate the simplex algorithm with an artificial basis using concepts of neutrosophic science.

Digital Impedance Bridge for Four-Terminal-Pair AC Resistor Calibration up to 20 kHz

For this study, a substitution principle-based impedance bridge has been developed to calibrate AC resistors in a four-terminal-pair (4TP) configuration. The calibration is performed in the full complex plane for resistances ranging from 100 mΩ to 400 Ω and frequencies of between 50 Hz and 20 kHz. The automated bridge is based on four resistors associated with two high-impedance stages. The balancing of the bridge is achieved by means of PXI modules. The bridge is automatically balanced via a simplex top-down algorithm. The new bridge is primarily used for the measurement chain of AC standard resistors defined in a 4TP configuration at LNE, which are used for routine customer calibrations. The traceability of LNE’s standard resistors when defined in a 4TP configuration is ensured by a measurement chain from a 1 kΩ reference resistor using the new bridge. The reference resistor was calibrated previously via comparison with a calculable resistor up to 20 kHz. The bridge was validated via comparison with calibration results obtained in 1983 and 2009. For a resistor of 1 Ω at 1 kHz, the uncertainty of the series resistance variation and the phase shift are less than 6 µΩ/Ω (k = 1) and 6 µrad (k = 1), respectively.

Influence of Fixed Ring Gear Structural Compliance on the Quasi-Static and Dynamic Response of Epicyclic Gear Sets

Abstract The structural compliance of annular ring gear can significantly influence the quasi-static and dynamic performance of an epicyclic gear set. As powertrain components are continually being optimized to their design limits, this influence becomes prominent and can no longer be ignored. The current paper will study the impact of ring gear compliance on the dynamic response of epicyclic gear sets, in fixed ring kinematic configuration. To achieve this objective the current study will incorporate a finite element based ring gear formulation into the three-dimensional planetary load distribution model of Ryali and Talbot [1]. The proposed model employs a modified simplex algorithm to iteratively solve for the elastic gear mesh contacts in conjunction with a numerical integration scheme, which enables it to inherently capture the influence of several component and system level design variations. The developed formulation is used to conduct parametric studies involving different planetary gear designs, ring gear fixtures (bolted vs. splined), and operating conditions (quasi-static, dynamic). In the case of a splined ring gear fixture, an external splined tooth contact model is developed, which will be used to validate the model against the quasi-static experiments of Ligata et al. [2]. The discussed results demonstrate the fidelity of the developed model, thus making it an excellent tool for the design and analysis of planetary gears with thin annular ring gears.

Influence of the radius of Monson’s sphere and excursive occlusal contacts on masticatory function of dentate subjects

ObjectiveTo determine the influence of the radius of Monson’s sphere, the number of posterior laterotrusive, mediotrusive, and protrusive contacts, and the chewing rate on food comminution. DesignSixty healthy dentate subjects, aged 21.22 ± 2.30 years, were selected. The three-dimensional coordinates of the cusp tips of the lower canine, premolar, and molar teeth were identified from the subjects’ digital models. Monson’s sphere was designed using the simplex method for function minimisation by adjusting the coordinates on its surface. The contacts were verified using 12 µm metal strips in jaw excursions at 0.5, 1.0, 2.0, and 3.0 mm. The masticatory performance and efficiency, swallowing threshold, and chewing rate were assessed through particle size fractionation. Data were analysed with multiple linear regression (α = 0.05). ResultsThe sphere’s radius, laterotrusive and protrusive contacts at 0.5 mm, and chewing rate were found to be negative predictor variables for masticatory performance until 20 chewing cycles (R2 = 0.429). For 40 cycles, the radius and total contacts (0.5 mm) were also explanatory factors (R2 = 0.223). Only the radius (R2 = 0.176) and the chewing rate (R2 = 0.082) were found to be significant for 60 cycles and swallowing threshold, respectively. Masticatory efficiency was influenced by masticatory performance until 40 and 60 cycles, as well as the radius and total contacts at 2.0 and 3.0 mm (R2 = 0.958). ConclusionA larger radius of Monson’s sphere and a greater number of posterior excursive contacts were found to be related to better masticatory function.

Hybrid beluga whale optimization algorithm with multi-strategy for functions and engineering optimization problems

Beluga Whale Optimization (BWO) is a new metaheuristic algorithm that simulates the social behaviors of beluga whales swimming, foraging, and whale falling. Compared with other optimization algorithms, BWO shows certain advantages in solving unimodal and multimodal optimization problems. However, the convergence speed and optimization performance of BWO still have some performance deficiencies when solving complex multidimensional problems. Therefore, this paper proposes a hybrid BWO method called HBWO combining Quasi-oppositional based learning (QOBL), adaptive and spiral predation strategy, and Nelder-Mead simplex search method (NM). Firstly, in the initialization phase, the QOBL strategy is introduced. This strategy reconstructs the initial spatial position of the population by pairwise comparisons to obtain a more prosperous and higher quality initial population. Subsequently, an adaptive and spiral predation strategy is designed in the exploration and exploitation phases. The strategy first learns the optimal individual positions in some dimensions through adaptive learning to avoid the loss of local optimality. At the same time, a spiral movement method motivated by a cosine factor is introduced to maintain some balance between exploration and exploitation. Finally, the NM simplex search method is added. It corrects individual positions through multiple scaling methods to improve the optimal search speed more accurately and efficiently. The performance of HBWO is verified utilizing the CEC2017 and CEC2019 test functions. Meanwhile, the superiority of HBWO is verified by utilizing six engineering design examples. The experimental results show that HBWO has higher feasibility and effectiveness in solving practical problems than BWO and other optimization methods.

СРАВНЕНИЕ МЕТОДОВ РЕШЕНИЯ ТРАНСПОРТНОЙ ЗАДАЧИ

Mathematical programming is a mathematical discipline that studies various extremal problems and develops algorithms for solving them. Among the problems are those of mathematical integer programming. Integer programming is indispensable for solving mathematical programming problems in which some or all of the variables take on integer values. The problems include the transport problem. The paper considers the transport problem and three linear programming methods for solving it: the method of potentials, the method of differential rents and the simplex method. The paper analyzes and assesses the effectiveness of the three algorithms for optimizing transport problems. Several linear optimization algorithms have been studied and presented. The paper contains the basic concepts, formulas, and algorithms of the methods used. The method of potentials, the method of differential rents and the simplex method are considered. The results of solving the problem using these methods are presented and compared. All calculations were performed using Excel.