Simplex Method Research Articles

Profit Optimization and Production of Maesa Cake and Bakery Shops with Linear Programming-Simplex Method

The need for cake as a complementary food at various events causes the demand to increase. This increase has an impact on the production level that will be produced with the aim of increasing profits. The production process is related to the allocation of the right raw materials to be efficient, so that maximum profits will be obtained. This study aims to analyze the maximum profit of the Maesa Cake and Bakery Shop, Permata Legenda Branch. There are two types of products sold in this shop, namely Banana Bolu (X1) and Banana Bolen (X2). The research method used is linear programming which is solved by the simplex method and the use of the POM For Windows application. The data obtained is observational data by meeting the shop owner directly to be interviewed. The process of calculating the simplex method is carried out using Ms. Excel with several completion steps, starting from creating a simplex table, entering the coefficients of the objective function and constraints, looking for key columns, key rows, and key numbers, until the last step is achieving positive coefficients generated in the objective function row. The final result obtained is the process of the iterations carried out. Apart from using Ms. Excel, researchers also use the POM for Windows application. Use both software to find the maximum profit to be achieved. So it is found that the maximum profit that can be obtained in one day by the Maesa Cake and Bakery Branch of Permata Legenda is IDR 270,000.00; by producing 5 units of Banana Bolu and 50 units of Banana Bolen.

Using Linear programming to find solution volterra Integral Equation.

Conclusion :This method is based on approximating the solution using a new technique based on the programming methodlinearity by using the Simplex method to find the solution to thisnumerically equations.

Addressing the urban-scale vehicle assignment and rebalancing problems in shared autonomous vehicle system while simultaneously considering immediate, reservation, shareable, and unshareable requests

Recently, the autonomous driving technology has developed rapidly with the shared autonomous vehicle system extensively investigated. However, little attention has been given to the diversity of the travel demands. In view of this, the paper proposes a dispatching strategy to solve the vehicle assignment and rebalancing problems with simultaneous consideration of immediate, reservation, shareable and unshareable requests. The centralised optimisation and the decentralised heuristic methods are combined to handle the different requests efficiently, which enables the dispatching strategy to address the urban scale problem. The centralised optimisation method assigns the short-term requests and plans the empty vehicle rebalance by the network simplex algorithm, while the decentralised heuristic method assigns the long-term requests and fully uses the previous step results in each solution step of the rolling horizon. The simulation of Manhattan, New York, with 4,000 vehicles and 1,823,152 requests, confirms the high operational performance and the efficiency of the proposed dispatching strategy compared to the existing approach and the benchmark strategy. It was also found that more reservation requests with the earlier reservation time did not generate significant improvement in operational performance, and the high sharable request ratio facilitated the reduction of the travel distance and empty distance.

Three-dimensional seismic stability of locally loaded slopes under a rotational velocity field

In practical engineering, slopes subjected to local loads, like footings of buildings, are common. This paper aims to give an insight into the effect of seismic force on the stability of locally loaded slopes. Numerical methods can be used to study this problem, but they require much computational time. Contrarily, limit analysis method is an approach to perform slope stability analysis with high computational efficiency. Thus, an accurate approach in mechanical points is proposed for this problem based on limit analysis method herein. In the framework of limit analysis, existing research about this problem used a kinematically translational velocity field. However, the velocity field of the locally loaded slope at failure is proved to be rotational possibly. Thus, to fill this gap, a 3D rotational velocity field is employed herein to obtain limit loads on the slope top, which improves the existing upper-bound solutions obtained by using the translational velocity field. The particle swarm optimization algorithm and the Nelder-Mead simplex algorithm are employed to search the global minimum of the upper-bound estimation of the limit load. Parametric analysis is performed and it shows that the limit load increases with the increase of a/H or the internal friction angle φ but decreases as the slope angle β or the length-to-width ratio (L/t) of the local load increases. Furthermore, the limit load is found to decrease with the increase of the seismic coefficient kh and it is proportional to the seismic coefficient.

Implementation of various-fidelity methods for viscous effects modeling on the design of a waverider

In the present study, the implementation of three viscous effects modeling methods at hypersonic flow conditions is investigated. The design of a hypersonic passenger transport waverider configuration is employed as a case study. The methods, each of which has a different fidelity level, are evaluated in terms of their capability to predict aerodynamic performance, as well as their effect on the final geometric design of the waverider. More specifically, for the same mission profile and design constraints, three different waverider configurations (Cases A, B and C) are designed with the osculating cone methodology, and each employing a different viscous effect modeling method. These three configurations are designed (a) assuming a purely inviscid flowfield, (b) using Eckert's Reference Temperature and (c) Van Driest's viscous effects modeling semi-empirical methods respectively, each subsequent one of higher complexity and fidelity than the previous. An optimization loop, employing the Nelder-Mead simplex algorithm, is also incorporated into the overall design process. Each configuration is evaluated with all three viscous effects modeling methods and the analytical results are compared against those of CFD modeling. The CFD analyses are performed by solving the steady-state three-dimensional Euler and Reynolds Averaged Navier Stokes (RANS) equations. Overall, the three configurations are evaluated in terms of aerodynamic performance, design/optimization computational cost, and accuracy between the analytical and CFD results. All inviscid analytical calculations demonstrate very good agreement with the Euler CFD results. Indicatively, the lift-to-drag predictions deviate by as much as 2% between the two approached. The Van Driest's method predictions result to 5%-6.5% lower lift-to-drag ratios compared to the RANS CFD, and to higher wall shear stress values. Contrarily, the Ref. Temperature method predictions are in a much closer agreement to the RANS CFD results, leading to a slight overprediction (0%-2.4%) of lift-to-drag ratios. The incorporation of viscous effects in the design process reduces the waverider's aerodynamic efficiency by about 8.5%-11% and results in a 46%-98% increase in computational time, compared to the inviscid analysis.

Optimization of the Cultivation Conditions of the Green Algae Dunaliella salina by Using Simplex Method

The green algae Dunaliella salina offers great potential for the food industry due to its high β-carotene content. To guarantee the economic profitability of cultivation, growth conditions must be improved. Therefore, the effects of pH and salinity on the cultivation of the green alga D. salina were investigated and optimized. The simplex method was applied to find the optimum of these two parameters to maximize the biomass and the cell number of D. salina. The optimum pH was found at 7 and 8 at a salt content of 50 g/L, with a biomass content of 1.09 and 1.11 g/L, respectively. The highest biomass was found at a salinity of 50 g/L, with a final biomass of 1.11 g/L. However, by using the simplex method, an optimum product yield was found at a salinity of 64 g/L and an initial pH value of 7.2. Thus, a biomass of 1.23 mg/mL was achieved. In the single observation of both parameters, 14 experiments were conducted to obtain a satisfactory result, whereas eight runs only were required with the simplex method. This leads to the conclusion that using the simplex method is a useful way to drastically reduce the number of required experiments.

Weighted distances in the Cairo pattern

The Cairo Pattern is an interesting tiling of the plane. It consists of pentagons which completely cover the plane without overlapping. The Cairo Pattern is the dual of a semi-regular grid. It is assumed that one can walk on the pentagons such that it is possible to step only two neighboring pentagons. Different types of steps have different weights. The distance of two pentagons is the length of the minimal path between them. All distances are based on a linear programming model. The main tool of the analysis is the simplex method of linear programming. The analysis also uses the special properties of the model of minimal path. All minimal paths are given explicitly. Therefore, the complexity of our final result is O(1) inspite of the fact that the general simplex method is thought to be exponential.

Non-local polarization alignment and control in fibers using feedback from correlated measurements of entangled photons.

Quantum measurements that use the entangled photons' polarization to encode quantum information require calibration and alignment of the measurement bases between spatially separate observers. Because of the changing birefringence in optical fibers arising from temperature fluctuations or external mechanical vibrations, the polarization state at the end of a fiber channel is unpredictable and time-varying. Polarization tracking and stabilization methods originally developed for classical optical communications cannot be applied to polarization-entangled photons, where the separately detected photons are statistically unpolarized, yet quantum mechanically correlated. We report here a fast method for automatic alignment and dynamic tracking of the polarization measurement bases between spatially separated detectors. The system uses the Nelder-Mead simplex method to minimize the observed coincidence rate between non-locally measured entangled photon pairs, without relying on classical wavelength-multiplexed pilot tones or temporally interleaved polarized photons. Alignment and control is demonstrated in a 7.1 km deployed fiber loop as well as in a controlled drifting scenario.

A dynamic gear load distribution model for epicyclic gear sets with a structurally compliant planet carrier

Structural deformations in a planet carrier under operating conditions results in misalignment of planet gears, which can significantly effect the gear mesh load distribution and load sharing of a planetary gear set. Therefore, to capture the influence of structural compliance associated with planet carrier, planet pin, and input/output shaft, a hybrid planetary dynamic load distribution model is developed in this paper. Finite element sub-structuring techniques are employed to ensure that the model is computational efficiency. The proposed model employs a 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 without the need for an empirical mesh stiffness formulation or transmission error excitation of the system. The developed formulation is used to study the effects of planet carrier flexibility on both the quasi-static and dynamic response of planetary gearsets. The discussed results not only illustrate the influence of carrier flexibility on the system response but also highlight the need for such computationally efficient models which could be used as design tools.

Set Cover Model with Path-Segment Concept to Determine the Optimum Rest Areas on Toll Road as the Location of Electric Vehicle Battery Charging Stations

The rapid adoption of electric vehicles (EVs), especially battery-based electric vehicles (BEVs), requires battery recharging facilities. Battery charging station (BCS) is an important component in EVs ecosystem. EVs requires BCS infrastructure for battery recharging. Limited battery range in one full charge is a concern for EVs users which is often called range anxiety so the number and placement of BCS must be adequate to prevent EVs from running out of battery in the middle of the trip. This study uses the real data of Trans Java toll road network, specifically the Semarang-Ngawi section for running numerical experiment to test the performance of the proposed model. Rest areas on toll roads are considered as candidate points for BCS locations. The proposed model is a set cover model formulated into binary integer programming. The Simplex algorithm in Microsoft Excel Solver is used to find the optimum solution on numerical experiment. Four locations are found as the optimum locations of BCS, i.e rest area r3, r6, r9, and rest area r12. The novelty of this study is combining the path-based approach with node-based approach to get a more compact set cover model.

Optimal occlusal force field of masticatory system under clenching by simplex method and principal component analysis

In the present paper, a method to evaluate the occlusal state and occlusal morphology that can integrate an optimal occlusal force field under clenching is proposed using simplex optimization and principal component analysis (PCA). The objective function of the optimization is taken as a sum of the weighted occlusal forces and reaction on temporomandibular joint (TMJ) to maximize the former and to minimize the latter. The optimized solutions in the region defined by the combination among three kinds of muscle forces were obtained by two-step simplex method, and the subregion with no reaction of TMJ was summarized as a ratio to the whole region, newly defined here as a good balance ratio. As a result of PCA of total 528 samples of the good balance ratios for 13 different muscle force combinations, two principal components (PCs) are enough to represent the optimized masticatory system. The first PC suggests the ideal state of occlusion and the second one implies the characterization of combination among muscles. From the consideration of PCA, with the wider equalizer angle, the easier it is to support the force of the temporalis muscle in an ideal occlusal position, and the more the occlusal contact point is shifted backward, the harder it is to support the force of the temporalis muscle. Comprehensively, the proposed good balance ratio becomes the effective quantity to evaluate the ideal masticatory system with the optimized occlusal force field for the statistically reduced indexes showing the combination of muscles.

Hybrid Strategy Improved Sparrow Search Algorithm in the Field of Intrusion Detection

Aiming at the problem that sparrow search algorithm(SSA) may fall into local optima and has slow convergence speed, a hybrid strategy improved Sparrow Search Algorithm(HSISSA) is proposed in this paper, and it is applied to feature selection and model optimization of intrusion detection. Firstly, the hybrid circle-piecewise map is proposed to initialize the population and improve the uniformity of the initial population distribution; Secondly, merging the spiral search method in the vulture search algorithm and Levy’s flight formula to update the positions of the discoverer and the scouter respectively, to expand the population search range and enhance the search capability; Finally, simplex method and pinhole imaging method are used to optimize the position of sparrows with poor fitness and optimal fitness, to avoid stagnation in the population search and falling into local optima. The performance of the algorithm is optimized through the above methods. The algorithm is tested on 10 classical benchmark functions and combined with Wilcoxon rank sum test analysis to verify the effectiveness of the algorithm, which showed improvements in convergence speed and accuracy. Finally, it is applied to feature selection and model optimization of intrusion detection. On average, 7.6 features and 10.1 features are retained on the CIC-IDS2017 dataset and UNSW-NB15 dataset, respectively, and 99.5% and 96.01% accuracy are achieved. The number and accuracy of the optimized features are better than the original algorithm. For DenseNet and random forest models, HSISSA can achieve 99.34% and 97.22% accuracy after optimization, which improves the performance of the model, thus, the algorithm shows better performance than other algorithms.

Neutrosophic Treatment of the Modified Simplex Algorithm to find the Optimal Solution for Linear Models

Neutrosophic Treatment of the Modified Simplex Algorithm to find the Optimal Solution for Linear Models

Neutrosophic Treatment of Duality Linear Models and the Binary Simplex Algorithm

Neutrosophic Treatment of Duality Linear Models and the Binary Simplex Algorithm

Neutrosophic Treatment of Duality Linear Models and the Binary Simplex Algorithm

One of the most important theories in linear programming is the dualistic theory and its basic idea is that for every linear model has dual linear model, so that solving the original linear model gives a solution to the dual model. Therefore, when we solving the linear programming model, we actually obtain solutions for two linear models. In this research, we present a study of the models. The neutrosophic dual and the binary simplex algorithm, which works to find the optimal solution for the original and dual models at the same time. The importance of this algorithm is evident in that it is relied upon in several operations research topics, such as integer programming algorithms, some nonlinear programming algorithms, and sensitivity analysis in linear programming...

A novel balanced Aquila optimizer using random learning and Nelder–Mead simplex search mechanisms for air–fuel ratio system control

A novel balanced Aquila optimizer using random learning and Nelder–Mead simplex search mechanisms for air–fuel ratio system control

An electromembrane microextraction-based green method for the determination of trace copper in natural waters.

Driven by the search for an environmentally-friendly methodology, electromembrane extraction (EME) has recently emerged as a green and versatile tool for the analysis of trace pollutants in water samples, being mainly applied to the preconcentration and determination of organic compounds. Recently, EME has also shown its applicability to the analysis of inorganic species, allowing a considerable reduction in both reagent consumption and extraction times, and without loss of efficacy, in comparison with other liquid phase microextraction techniques. In this study, an EME system for trace copper analysis in natural waters has been optimised by the modified simplex method. A chemical modifier, di-2-pyridyl ketone benzoylhydrazone (dPKBH) was synthesized and dissolved in 1-nonanol, to be used as an organic phase impregnated into the pores of a polymeric hollow fibre. With only 15 min of extraction, an enrichment factor of 77.1 ± 10.8 was obtained for a wide salinity range (0-35), allowing its application in a variety of different waters, including seawater. Optimum operating conditions were a sample pH of 6.26, an electric potential of 95 V, 0.08 M nitric acid as the acceptor phase, 4.01 mM dPKBH in 1-nonanol as the organic phase and a stirring rate of 1500 rpm. A LOD of 0.004 μg L-1 was obtained, and the system was successfully applied to the analysis of several water samples containing copper at low ppb levels (tap water and river water) or even at sub-ppb levels (seawater).

Solving Multi-Objective Linear Programming Problem by Statistical Averaging Method with the Help of Fuzzy Programming Method

A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming problem can be converted into the single objective function by various methods as Chandra Sen’s method, weighted sum method, ranking function method, statistical averaging method. In this paper, Chandra Sen’s method and statistical averaging method both are used here for making single objective function from multi-objective function. Two multi-objective programming problems are solved to verify the result. One is numerical example and the other is real life example. Then the problems are solved by ordinary simplex method and fuzzy programming method. It can be seen that fuzzy programming method gives better optimal values than the ordinary simplex method.

Sensitivity analysis of large body of control parameters in machine learning control of a square-back Ahmed body

Active drag reduction (DR) of a square-back Ahmed body is experimentally studied based on machine learning or artificial intelligence (AI) control. The control system consists of four independently operated arrays of pulsed microjets, 25 pressure taps and an explorative downhill simplex method controller. Two strategies, i.e. asymmetric and symmetric actuations, are investigated, with 12 and 9 control parameters, respectively. Both achieve a DR by 13%, though with distinct flow physics and control mechanisms behind. A model linking the control parameters with the cost is developed based on Taylor expansion around the K-nearest neighbours of the smallest cost obtained from the AI control, resulting in a substantially reduced deviation between measured and predicted costs, especially when involving a large number of control parameters, compared with that based on Taylor expansion around the optimum cost. Sensitivity analysis, conducted based on the model, indicates that the control efficiency, i.e. the ratio of the power saving from DR to the total power consumption, may reach 55 and 78 for the symmetric and asymmetric strategies, respectively, given a 1–2% sacrifice on DR. This efficiency greatly exceeds that (26.5) obtained by Fan et al. (Fan et al. 2020 Phys. Fluids 32 , 125117. ( doi:10.1063/5.0033156 )), whose independent control parameters are only three.

Optimal Production in Vacuum Food Packaging Thermoforming with Linear Programming

This article presents an optimization model to determine the ideal production distribution in the thermoforming lines of a sausage factory. A linear programming model subject to the simplex method is used to find the production coefficient, determining the ideal workload for three machines involved in the packaging process. The methodology considers common characteristics of the sausage industry, where production programming, thermoforming machines, and their capacities are the ones that directly influence the execution of the experiment. Using the model allows for analyzing the variations of the actual production plan and its effectiveness against the optimized production results. The experiments compared and evaluated the fulfillment of the optimization objective. The modeling was executed with the free software language programming R. A mathematical model was generated that allows evaluating and programming the optimal production in the thermoforming lines to maximize packaging and optimize resources, considering the restrictions of the process. The purpose is to avoid overproduction and misuse of available resources. The results show that the model makes it possible to optimize daily production in the thermoforming lines by 11% for October and 8% for March, equivalent to 5,500 and 3,500 units per day, respectively.