Algorithm for the set of similarity criteria formation for a physical process in the class of homogeneous functions

The efficiency of application of linear programming methods to problems of the theory of similarity and dimensions is shown. A general algorithm for formation of the set of similarity criteria for a physical process in the class of homogeneous functions is proposed. The set of systems of linear algebraic equations is created using the combinatorial method and chain diagrams. Basic and free variables and their corresponding variants of dimensionless sets of independent arguments, which are taken as the main similarity criteria, are distinguished. The set of derived similarity criteria is found using the basic criteria and the Cayley table.

Study of the soil stability theory problems by the simplex method

The questions of linear programming methods application to the main problems of stability theory - problems on slope stability, problems on ultimate pressure of soil on enclosures (case of landslide pressure), and problems on bearing capacity of horizontal base of a die are considered. The problems of stability theory are formulated as linear programming tasks. It is shown that the given systems of equations are linear with respect to the unknowns and may be solved by the Simplex method. The results of soil stability problems calculation by Simplex method are compared with the results of calculations according to the most known classical schemes. It is shown that a great scatter of final results is observed in calculating the stability of slopes by classical methods, and in this case, the results obtained by the Simplex method are the most trustworthy ones. The situation with landslide pressure definition is especially complicated in this sense where classical methods give a scatter of landslide pressure values by several times. It is established that with increasing discretization of the computational domain, the results tend to exact solutions of the limit equilibrium theory, obtained, for example, by the method of characteristics. The latter point is illustrated using the example of the problem of a die pushing into a ground massif with a Hill scheme bulge.

SIMULATION OF DESIGN COMPONENTS OF POWER SUPPLY SYSTEMS FOR PERSONAL COMPUTERS

Предложена разработка цифрового макета изделия, который представляет собой компонент ЭВМ - импульсный блок питания. Производится анализ предполагаемых компонентов персонального компьютера, которые будут установлены в систему. При необходимости есть возможность выбора с добавлением новых компонентов в системный блок ЭВМ. После определения заданных компонентов ПК производится расчет мощности, которая нужна для получения стабильной работы системы в целом. По произведенным расчетам выполняется 3D-моделирование блока питания с разъемами для подключения материнской платы, видеокарты, а также прочих устройств, в том числе и накопителей информации. В работе исследованы вопросы по применению методов линейного программирования для решения поставленных задач в соответствии с исходными данными, а также подходы по получению 3D-модели источника питания с построенными трассами до разъемов подключения устройств и компонентов персонального компьютера. Кроме того, подготовлено программное обеспечение, в котором визуально представлен процесс построения сборочной модели БП согласно произведенным расчетам We propose the development of a digital model of the product, which is a computer component - a pulsed power supply. We carried out the analysis of the expected components of the personal computer that will be installed in the system. If necessary, there is a choice with the addition of new components to the system unit of the computer. After determining the specified PC components, the power is calculated, which is needed to obtain stable operation of the system as a whole. According to the calculations made, 3D-modeling of the power supply unit with connectors for connecting the motherboard, video card, as well as other devices, including information storage devices, is performed. The paper investigates the issues of using linear programming methods for solving the assigned tasks in accordance with the initial data, as well as approaches to obtaining a 3D model of a power supply with constructed routes to the connectors for connecting devices and components of a personal computer. In addition, we prepared the software, in which the process of building an assembly model of a power supply unit is visually presented according to the calculations

Linear programming feedrate optimization - Adaptive path sampling and feedrate override

This paper focuses on two aspects of feedrate optimization via linear programming methods. Namely, the effect of curve sampling on time optimality of the resultant feedrate profile and a method of feedrate profile adaptation in response to a feedrate override command. A comparison of three distinct curve sampling approaches (uniform in parameter, uniform in arc length and curvature adaptive) is performed on a series of standard tool path curves. Results show that the curvature-adaptive sampling approach leads to substantial machining time reduction for tool path curves displaying high degree of curvature variation. Secondly, a method by which a new feedrate profile can be calculated in response to a feedrate override command is developed. The method formulates a new set of boundary conditions on the control point sequence of the feedrate curve in such a way that the resulting profile is guaranteed to coincide with the currently active profile up to the moment of override command, while minimizing the arc length necessary for transition to the newly commanded feedrate.

DEVELOPMENT OF A METHOD FOR ASSIGNING PRIVATE LOCOMOTIVES TO TRAINS

Purpose. Ukraine is currently in the process of reforming the railway transportations market, which is related to the implementation of European Union Directives to its legislation. As a result of these reforms, the opening of the railway transportation market for carriers independent of Ukrzaliznytsia is envisaged. In such conditions, the problem of ensuring access of rolling stock to the receiving and departure tracks and the elimination of conflict situations with train and shunting movements of rolling stock of Ukrzaliznytsia can be solved by passing trains of independent carriers according to a tight schedule. One of the use areas of private locomotives is servicing of points of mass loading or unloading of goods. One of the tasks that arises in this case is to improve the methods of assigning private locomotives to the threads of the train schedule. Methodology. The research is performed based on the methods of organization of operational work of railways and methods of linear programming. Findings. The paper considers the problem of improving the methods of calculating the size of the working fleet of locomotives. Based on the analysis of possible conditions of interaction between Ukrzaliznytsia JSC and private carriers, it is determined that one of the possible options for using private transport companies at the stage of implementation of their services will be the service of points of mass loading or unloading of goods. In the course of the research a method of determining the number of locomotives by reducing this problem to an optimization problem of purpose was developed. An example of solving the problem of determining the required working fleet of locomotives to service the transportation of grain cargo sent to the port by shipping routes and developing schedules of their turnover is given. The number of locomotives needed to service transportations was set and the procedure for their connection to trains developed. Originality. The research improves the methods of assignment locomotives to the threads of the train schedule based on the use of linear programming methods. Practical value. The results of the work allow us to assess the needs of the working fleet of locomotives in the open market of railway transportations for independent carriers.

Research of the College Enrollment Plan Based on Fuzzy Linear Programming Model

This paper aims at the problems of professional structure and hierarchical structure in college admission plans, uses linear programming methods to establish mathematical models, maximizes the use of resources on the basis of completing the national enrollment plan, determines the reasonable enrollment structure and enrollment scale, and makes the enrollment plan more scientific and reasonable. In actual situations, the number of students enrolled in the school, the consumption of students, and the number of teachers are constantly changing. Therefore, the concept of fuzzy linear programming is introduced, and the constraints of the linear programming model are fuzzy optimized to obtain more reasonable results, which inspires some reasonable suggestions for colleges in formulating enrollment plans.

Network programming theory application to project portfolio formation

The paper deals with an application of the network (dichotomous) programming method for solving multi-extremal problems and discrete optimization problems. The concept of a generalized dual problem is introduced and a theorem on its convexity is proved. Network programming method is used to build a business-forming project portfolio as well as an algorithm for solving completely dependent related projects is developed. Also, this method is used to solve the problem of building a business-supporting project portfolio for which the lower cost estimate is obtained. A computational experiment is carried out to evaluate the suggested algorithm, which showed that for large dimensions of the problem it is more effective than for solving the problem by linear programming methods.

RESEARCH AND OPTIMISATION OF THE QUANTITATIVE AND QUALITATIVE CHARACTERISTICS OF GRAIN SHIPLOAD LOTS IN GRAIN TERMINALS

The structure of loading different crops onto vessels at the company Ukrelevatorprom’s grain terminal has been considered. The total grain shipped in 2012–2015 was comprised of 33.7–41.5% of maize, 19.7– 32.2% of wheat, 14.4–26.0% of rapeseed, 6.7–14.2% of barley, and 5.4– 11.0% of soya beans. When forming a 35,000-tonne grain shipload, grain lots stored in silos are sometimes of lower quality than contracts require: the protein and gluten contents can be inappropriate, or there can be smut grains or those damaged by sunn pests. The accepted technology of grain shipload formation does not guarantee that the grain quality will be uniform throughout the whole period of loading a vessel, especially in the beginning. In the first 1,000 tonnes of a grain shipload formed, the weight content of wet gluten was found to be 22.6% instead of 23%, the Falling Number was 145–180 s instead of 230s, and the content of smut grains was not the tolerable 5%, but 6.95–7.8%. The subsequent 2,000–3,000 tonnes of wheat, too, had the Falling Number lower than the contract prescribed (142–215 s), and only further on, its value achieved the required range 295–356 s. In the wheat sample formed from 5,000 tonnes, only the test values of the Falling Number (176s) and the content of smut grains (5.1%) were different from what the contract required. The calculated arithmetic means of the quality parameters of the 5,000-tonne wheat samples formed were practically the same as those determined experimentally, except for the values of the Falling Number and the smut grain content. The values of the coefficient of variation obtained showed that the grain lot was of non-uniform quality: it varied in such parameters as the foreign material (20.82–50.93%), sunn pest-damaged grains (7.41–25.76%), Falling Number (8.76–36.36%), and smut grain content (35.88–78.34%). Application of linear programming methods to optimise the shipload composition has allowed all the quality parameters to meet the contract requirements. Loading grain from all silos simultaneously, with the optimum flow ratio, will result in its even distribution in a shipload, and the grain lot will be of higher quality by all the parameters the contract specifies.

Density Estimates of 1-Avoiding Sets via Higher Order Correlations

We improve the best known upper bound on the density of a planar measurable set A containing no two points at unit distance to 0.25442. We use a combination of Fourier analytic and linear programming methods to obtain the result. The estimate is achieved by means of obtaining new linear constraints on the autocorrelation function of A utilizing triple-order correlations in A, a concept that has not been previously studied.