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Документ Optimization problems of power system economic dispatch(FOP Panov A. M., 2021) Lysenko, L. I.; Makhotilo, K. V.; Cherkashyna, H. I.The study guide considers mathematical modeling techniques for problems of linear and nonlinear programming in the field of power engineering. Control of power system operation requires specifying economic loading of power plants under various operating conditions as well as optimal electric grid dispatch with minimum active power loss. The first chapter describes linear programming problems of optimal fuel scheduling among power plants and economic electric grid loading. The second chapter deals with economic dispatch problems for thermal and hydropower plants taking into account power loss in the electric grid. The third chapter analyzes minimization of active power loss through optimal reactive power compensation in electric grids of various configurations. The study guide considers numerous examples of various-type optimization problems of power engineering focusing on building mathematical models and searching for optimal solutions with application of Microsoft Excel Solver. The manual contains information that may be helpful for students taking master’s and PhD programs in Electric Power Engineering.Документ Calculation of throughputs of intermediate centers in three-index transportation problems(Технологический Центр, 2017) Raskin, L.; Sira, O.; Karpenko, V.A transportation problem of linear programming with intermediate centers was considered. For cases where throughputs of intermediate centers are not specified, a problem of calculating rational distribution of the total throughput in order to minimize the average value of total transportation costs has been stated. Several options of constructing the method for solving the problem were proposed. The first option implements the iterative procedure of successive improvement of the initial distribution of throughputs of the centers by the Nelder-Mead method. Increase in speed of this method was achieved using the duality theory. The second option is based on a preliminary solution of the problem of finding optimal routes for all pairs "supplier-consumer" taking into account a possible intermediate center. In this case, the usual two-index transportation problem of delivering products from the system of suppliers to the system of consumers arises. The optimal plan of this task contains necessary data to calculate required throughput for each of the intermediate centers. Advantage of this method consists in the possibility of its effective propagation for solving problems with a multilayered structure of intermediate centers.Публікація Managing costs of an industrial enterprise when using secondary resources(Технологический центр, 2020) Raiko, Diana ; Podrez, O.; Cherepanova, V. O.; Melnikov, O.; Kharchenko, A.Cost price reduction is one of the ways to improve the competitiveness of products. It is possible by establishing the set of factors affecting the production costs at an industrial enterprise and building on this basis a mathematical model of in-house cost management. The study objective was to develop and substantiate an economic-and-mathematical model of management to minimize the enterprise costs taking into account the utilization of secondary resources obtained in the production of basic products. The model consists of two stages. At the first stage, full costs of production of basic and additional products are determined. The peculiarity of this production implies the generation of significant amounts of secondary resources that have both independent value and opportunities for their use in the main technological process. This leads to complex material flows within the production process, which were accounted for in the study with the help of an adapted “cost-output” balance model. A plant can function with the use of a variety of raw materials which differ in both prices and rates of the output of basic products and secondary resources. This brings about the problem of finding an optimal combination of input resources to minimize costs or maximize profits. The problem is solved in the second stage. It is formalized as a linear programming problem. It features the provision of the ability to establish indicative plans of production of both main products and by-products. The model was tested on the example of coke-chemical plants producing coke of KDM-2 grade with 6 % humidity content and KDM-1 grade coke of improved quality as the main products. Coke oven gas, coke fines, beans, and sludge are produced as by-products. After purifying the coke oven gas, it is further used in the production of heat and electricity, compressed air, and a fuel for coke ovens. Thus, the produced fuel and energy, utilizable material resources, and circulating water supply are secondary resources. A certain portion of by-products is sold to third parties. When applied, the model will make it possible to improve the efficiency of cost management at enterprises.Документ Метод решения задачи маршрутизации в реальном времени(НТУ "ХПИ", 2016) Карпенко, Вячеслав ВасильевичСформулирована задача обеспечения доставки продукта от производителя к случайному множеству потребителей. Рассмотрены методы отыскания кратчайших маршрутов. Установлено, что для задачи реальной размерности эти методы не обеспечивают возможности получения быстрого решения. Предложен метод отыскания кратчайшего маршрута, основанный на использовании специальной операции над числовыми матрицами, элементы которых – длины путей между соседними пунктами на маршруте. Метод позволяет получить быстрое приближенное решение задачи, близкое к оптимальному.Документ Транспортная задача линейного программирования с нечетким спросом(НТУ "ХПИ", 2015) Карпенко, Вячеслав Васильевич; Ахмадов, Рустам ХусейновичРассмотрена модель транспортной задачи линейного программирования, в которой спрос на транспортируемый продукт в пунктах его реализации задан нечетко. Предложен метод решения этой задачи, учитывающий потери, связанные с неопределённостью спроса, а также транспортные расходы. Метод реализует итерационную процедуру последовательного улучшения плана.Документ Анализ методов решения транспортных задач со стоимостями перевозок(Украинская государственная академия железнодорожного транспорта, 2013) Серая, Оксана ВладимировнаРассмотрена транспортная задача линейного программирования со случайными стоимостями перевозок. Введен критерии оптимальности плана перевозок - вероятность того, что случайная суммарная стоимость перевозок превысит пороговую. Задача сведена к максимизации дробно-линейного функционала с линейными ограничениями. Предложена процедура, преобразующая полученную нелинейную задачу к обычной задача линейного программирования.Документ Транспортная задача высокой размерности со стохастическим спросом(Украинская государственная академия железнодорожного транспорта, 2013) Серая, Оксана ВладимировнаПредложен метод решения транспортной задачи высокой размерности со случайным спросом. Решение основано на преобразовании исходной задачи к двойственной. Этот подход позволил радикально сократить продолжительность решения, существенно снижая вычислительные трудности, связанные с размерностью задачи.