Geometric Interpretation of the Simplex Method

1983 ◽  
pp. 124-141
Author(s):  
Michel Sakarovitch
Keyword(s):  
Simplex Method ◽  
Geometric Interpretation

A Geometric Interpretation of the Simplex Method of Linear Programming

1973 ◽  
Vol 66 (3) ◽  
pp. 257-264
Author(s):  
Maurice Nadler
Keyword(s):  
Linear Programming ◽  
Simplex Method ◽  
Mathematical Knowledge ◽  
Matrix Algebra ◽  
Elementary Mathematics ◽  
Geometric Interpretation ◽  
Analytic Geometry ◽  
Mathematical Basis ◽  
Straight Line ◽  
Linear Programming Problems

Concepts and techniques of matrix algebra, sometimes relatively sophisticated ones, are the mathematical basis of the simplex method of solving linear programming problems. The procedures, however, can be learned without advanced mathematical knowledge and can to an extent be explained on the basis of elementary mathematics. Simple analytic geometry of the straight line will be used for an explanation of the strategy of the simplex method.

Mathematical simulation of error functions of decision-making at tolerance control of measuring techniques availability

Metrologiya ◽  
2020 ◽  
pp. 3-15
Author(s):  
Rustam Z. Khayrullin ◽  
Alexey S. Kornev ◽  
Andrew A. Kostoglotov ◽  
Sergey V. Lazarenko
Keyword(s):  
Measurement Error ◽  
Geometric Interpretation ◽  
Measuring Instruments ◽  
Measured Quantity ◽  
Metrological Examination ◽  
Technical Documentation ◽  
Error Functions ◽  
Measuring Techniques ◽  
Tolerance Control ◽  
Laws Of Distribution

Analytical and computer models of false failure and undetected failure (error functions) were developed with tolerance control of the parameters of the components of the measuring technique. A geometric interpretation of the error functions as two-dimensional surfaces is given, which depend on the tolerance on the controlled parameter and the measurement error. The developed models are applicable both to theoretical laws of distribution, and to arbitrary laws of distribution of the measured quantity and measurement error. The results can be used in the development of metrological support of measuring equipment, the verification of measuring instruments, the metrological examination of technical documentation and the certification of measurement methods.

Maksimalisasi Keuntungan Dengan Pendekatan Metode Simpleks Kasus Pada Pabrik Sosis SM

Liquidity ◽  
2018 ◽  
Vol 2 (1) ◽  
pp. 59-65 ◽  
Author(s):  
Yanti Budiasih
Keyword(s):  
Linear Programming ◽  
Simplex Method ◽  
Optimal Combination ◽  
Optimal Input ◽  
Maximum Profit ◽  
Input Combination

The purpose of this study are to (1) determine the combination of inputs used in producing products such as beef sausages and veal sausage meatball; and (2) determine the optimal combination whether the product can provide the maximum profit. In order to determine the combination of inputs and maximum benefits can be used linear programming with graphical and simplex method. The valuation result shows that the optimal input combination would give a profit of Rp. 1.115 million per day.

Digital Multiple Notch Filter Design with Nelder-Mead Simplex Method

2017 ◽  
Vol E100.A (1) ◽  
pp. 259-265
Author(s):  
Qiusheng WANG ◽  
Xiaolan GU ◽  
Yingyi LIU ◽  
Haiwen YUAN
Keyword(s):  
Simplex Method ◽  
Filter Design ◽  
Notch Filter

GEOMETRIC THEORY OF MULTIDIMENSIONAL INTERPOLATION

2020 ◽  
Vol 2020 (1) ◽  
pp. 9-16
Author(s):  
Evgeniy Konopatskiy
Keyword(s):  
Response Function ◽  
Algebraic Curves ◽  
Geometric Theory ◽  
Analytical Description ◽  
Geometric Interpretation ◽  
Affine Geometry ◽  
Mathematical Apparatus ◽  
Multidimensional Interpolation ◽  
Pass Through

The paper presents a geometric theory of multidimensional interpolation based on invariants of affine geometry. The analytical description of geometric interpolants is performed within the framework of the mathematical apparatus BN-calculation using algebraic curves that pass through preset points. A geometric interpretation of the interaction of parameters, factors, and the response function is presented, which makes it possible to generalize the geometric theory of multidimensional interpolation in the direction of increasing the dimension of space. The conceptual principles of forming the tree of the geometric interpolant model as a geometric basis for modeling multi-factor processes and phenomena are described.

Optimizing Costs of Customer Attraction as a Competitiveness Factor

2019 ◽  
pp. 172-182
Author(s):  
A. V. Katernyuk
Keyword(s):  
Simplex Method ◽  
Investment Analysis ◽  
Economic Indicators ◽  
The Internet ◽  
Internet Services ◽  
Induction Method ◽  
Matrix Methods ◽  
Fast Growing ◽  
Analysis Methods ◽  
Available Resources

In all spheres business experts try to raise competitiveness of the company by different ways, for instance at the expense of more efficient redistribution of available resources (costs). Objectives connected with modeling and optimizing resources used in advertising are becoming the most topical. Deeper knowledge in planning and conducting any marketing and advertising campaigns are in demand today among many specialists. The process of searching for and finding optimum costs of advertising in the Internet as a factor of the rise in the company sustainability can be successfully shaped through universal matrix methods of solution (e.g. simplex-method). Objectives which cannot be resolved by this method can be supplemented by such economic indicators, as profitability of investment and return on one ruble. The article summarizes the instrumental base dealing with estimating the efficiency of events connected with customer attraction to such a fast growing industry as internet-services. The author proposes besides traditional ways of expense optimization to take into account economic indicators connected with profitability of each sale channel. The following tools were used in the research: modeling, induction method, investment analysis, methods of statistics and formal logics, multi-criteria optimization, specific software meant for solving similar tasks, in particular special macros for excel table.  

Error correction technique for numerical control machine tools based on the simplex method

2021 ◽  
pp. 095440542110281
Author(s):  
Hongwei Liu ◽  
Rui Yang ◽  
Pingjiang Wang ◽  
Jihong Chen ◽  
Hua Xiang
Keyword(s):  
Machine Tool ◽  
Error Compensation ◽  
Simplex Method ◽  
Tool Path ◽  
Repeated Measurements ◽  
Numerical Control ◽  
Machining Accuracy ◽  
Correction Technique ◽  
Fluctuation Range ◽  
Nc Machine

The objective of this research is to develop a novel correction mechanism to reduce the fluctuation range of tools in numerical control (NC) machining. Error compensation is an effective method to improve the machining accuracy of a machine tool. If the difference between two adjacent compensation data is too large, the fluctuation range of the tool will increase, which will seriously affect the surface quality of the machined parts in mechanical machining. The methodology used in compensation data processing is a simplex method of linear programming. This method reduces the fluctuation range of the tool and optimizes the tool path. The important aspect of software error compensation is to modify the initial compensation data by using an iterative method, and then the corrected tool path data are converted into actual compensated NC codes by using a postprocessor, which is implemented on the compensation module to ensure a smooth running path of the tool. The generated, calibrated, and amended NC codes were immediately fed to the machine tool controller. This technique was verified by using repeated measurements. The results of the experiments demonstrate efficient compensation and significant improvement in the machining accuracy of the NC machine tool.

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