Algorithm and software development to allocate locomotives for transportation of freight trains

We suggest a mathematical model to allocate locomotives for transportation of freight trains. The aim of the optimization in this model is to minimize the number of locomotives used for the transportation of the trains by choosing routes of the trains and locomotives. It is supposed that the trains can be transported only at defined time intervals (so-called train paths); every locomotive has possible routes called railway hauls. We take into account the necessity of periodic maintenance. We use graph theory and integer optimization to formulate the problem. We suggest mathematical definitions of a railway haul, a train path, a train route, and a locomotive route. An heuristic search algorithm to find an approximate solution of the problem is suggested. The main idea of the algorithm is maximal usage of locomotives that started earlier than other ones. The algorithm contains three stages. A solution of the previous stage is improved at each following stage. We use transfers of the locomotives to improve the current solution. We describe software development to optimize the model. We solve the problem using the historical data of Moscow railway.Russian Science Foundation, RSF: 16-11-00062The work has been supported by Russian Science Foundation (project No 16-11-00062)

ALGORITHM AND SOFTWARE DEVELOPMENT TO ALLOCATE LOCOMOTIVES FOR TRANSPORTATION OF FREIGHT TRAINS

We suggest a mathematical model to allocate locomotives for transportation of freight trains. The aim of the optimization in this model is to minimize the number of locomotives used for the transportation of the trains by choosing routes of the trains and locomotives. It is supposed that the trains can be transported only at defined time intervals (so-called train paths); every locomotive has possible routes called railway hauls. We take into account the necessity of periodic maintenance. We use graph theory and integer optimization to formulate the problem. We suggest mathematical definitions of a railway haul, a train path, a train route, and a locomotive route. An heuristic search algorithm to find an approximate solution of the problem is suggested. The main idea of the algorithm is maximal usage of locomotives that started earlier than other ones. The algorithm contains three stages. A solution of the previous stage is improved at each following stage. We use transfers of the locomotives to improve the current solution. We describe software development to optimize the model. We solve the problem using the historical data of Moscow railway.Russian Science Foundation, RSF: 16-11-00062The work has been supported by Russian Science Foundation (project No 16-11-00062)

Блокада грудных нервов как компонент мультимодальной анальгезии при операциях по поводу рака молочной железы

Objective: to evaluate the efficacy and safety of adding pectoral nerve block to anesthesia regimen in radical mastectomy.Subjects and methods. 65 female patients underwent unilateral radical mastectomy under general anesthesia. All patients enrolled into the study were divided into two groups. Group 1 included patients (the main one, n = 33) who had PEC block and general anesthesia; Group 2 (the control one, n = 32) had general anesthesia only.Results. The group of patients with PEC block versus the Control Group, demonstrated a lower score of the visual analogue scale at all stages of the study. The intra-operative fentanyl consumption was statistically significantly lower in Group 1 versus the Control Group (290.91 ± 67.84 and 393.75 ± 66.90 μg, respectively, p < 0.033). The consumption of opioid analgesics during the 1st day in the Main Group was 2-fold lower compared to the Control Group – 30.91 ± 12.34 and 63.75 ± 9.42 mg, respectively (p < 0.026). In Group 1, the time till the first analgesia with promedol made 309.55 ± 56.59 minutes.Conclusions. Pectoral nerves block combined with general anesthesia provides effective analgesia during breast surgery with axillary lymph node dissection.Цель исследования: оценить эффективность и безопасность включения блокады грудных нервов в схему обезболивания при радикальной мастэктомии.Материал и методы: 65 пациенткам выполнена односторонняя радикальная мастэктомия под общей анестезией. Все пациентки, включенные в исследование, разделены на две группы. В 1-ю группу включены пациентки (основная, n = 33), которым проведены PEC block и общая анестезия; во 2-й группе (контрольная, n = 32) проведена только общая анестезия.Результаты. В группе пациентов с PEC block в сравнении с контрольной группой выявлен более низкий показатель по визуально-аналоговой шкале на всех этапах исследования. Интраоперационная потребность в фентаниле статистически значимо была меньше в 1-й группе по сравнению с контрольной (290,91 ± 67,84 и 393,75 ± 66,90 мкг соответственно, p < 0,033). Потребность в опиоидных анальгетиках в 1-е сут в основной группе была в 2 раза меньше, чем в контрольной ‒ 30,91±12,34 и 63,75 ± 9,42 мг соответственно (p < 0,026). Время до первого обезболивания промедолом в 1-й группе составило 309,55 ± 56,59 мин.Выводы. Блокада грудных нервов в комбинации с общей анестезией обеспечивает эффективную анальгезию при операции на молочной железе с подмышечной лимфодиссекцией

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Algorithm of Effective Transportation Work for Cargo Traffic

We suggest a mathematical model that describes railway network. This model is applied to the problem of allocation locomotive for transportation of freight trains. The aim of the optimization is to minimize the size of active locomotive eet by choosing trains and locomotives routes. An alternative formulation of the optimization problem is proposed with the usage of a heuristic objective function, which makes it possible to construct an eective decision algorithm. A new deterministic algorithm for suboptimal control is described. This algorithm is a modication of the previously proposed, based on the construction of routes tree for each locomotive and, subsequently, the choice of such a route, in which the maximum value of the given objective function is reached. Numerical experiments were carried out on the example of the historical data of the Moscow Railway. The analysis and comparison of the results are given.Рассматривается известная математическая модель управления грузовыми перевозками. Ставится задача оптимизации управления с критерием в форме объема эксплуатируемого парка магистральных локомотивов. Предлагается альтернативная постановка задачи оптимизации с использованием эвристической целевой функции, позволяющая построить эффективный алгоритм решения. Описывается новый детерминированный алгоритм субоптимального управления. Указанный алгоритм является модификацией ранее предложенного, основанного на построении дерева маршрутов для каждого локомотива и, в последствии, выбора такого маршрута, при котором достигается максимальное значение заданной целевой функции. Проведены численные эксперименты на примере исторических данных Московской железной дороги. Приводится анализ и сравнение полученных результатов

On solving the geometrically nonlinear and linear problems of transverse bending of a hinged fixing sandwich plate with transversally soft core

© 2019 IOP Publishing Ltd. The study of the problem of finding the stress-strain state of a sandwich plate with a transversally soft core under the action of a transverse load in a one-dimensional geometrically nonlinear formulation was carried out. A generalized formulation of the problem in the form of an operator equation is proposed. The properties of the operator of the equation are established, which make it possible to use the general results of the theory of monotone operators in the study of correctness. To find the stress-strain state of the plate, a two-layer iterative method is proposed with lowering the nonlinearity on the lower layer. A finite-dimensional approximation of the problem and the iterative method was carried out. The convergence of finite-dimensional approximations and the iterative method has been studied. For the numerical implementation of the proposed approximate methods, a software package has been developed in the Matlab environment. Based on it, numerical experiments were carried out

On solving the geometrically nonlinear and linear problems of transverse bending of a hinged fixing sandwich plate with transversally soft core

© 2019 IOP Publishing Ltd. The study of the problem of finding the stress-strain state of a sandwich plate with a transversally soft core under the action of a transverse load in a one-dimensional geometrically nonlinear formulation was carried out. A generalized formulation of the problem in the form of an operator equation is proposed. The properties of the operator of the equation are established, which make it possible to use the general results of the theory of monotone operators in the study of correctness. To find the stress-strain state of the plate, a two-layer iterative method is proposed with lowering the nonlinearity on the lower layer. A finite-dimensional approximation of the problem and the iterative method was carried out. The convergence of finite-dimensional approximations and the iterative method has been studied. For the numerical implementation of the proposed approximate methods, a software package has been developed in the Matlab environment. Based on it, numerical experiments were carried out