In this paper we consider an approximation-interpolation approach based on the combination of interpolation method and approximation method. An approximation method for single-machine scheduling theory problem with an unknown objective function that depends on the completion times of jobs is studied. The idea of approximating an unknown function by a linear function with some weight coefficients is considered. An approximation-interpolation algorithm has been developed, which allows to determine the values of weight coefficients of the objective function of single-machine problem of the scheduling theory. In this algorithm the minimization of the total weighted completion times according to the given set of values of the problem parameters and the corresponding known optimal schedules was carried out. Experiments with Lagrange polynomials interpolation and cubic splines have been conducted. The hypothesis of the necessity to take into account long-range bounds when calculating weighting coefficients has been confirmed.

В работе исследуется переходное поведение многоканальной системы массового обслуживания. Для анализа используется аналитический метод решения системы уравнений Колмогорова, основанный на использовании так называемой трансляционной матрицы. Рассмотрены случаи, когда скорости прихода и обслуживания являются постоянными и кусочно-постоянными функциями. Приведены аналитические выражения для нестационарных вероятностей состояний, среднего числа пакетов в системе, среднего числа занятых каналов и средней задержки обслуживания в переходном режиме. Проанализированы переходное время и пропускная способность системы массового обслуживания в переходном режиме. Проведено численное моделирование многоканальной системы массового обслуживания на примере системы М/М/2/3. Получены зависимости вероятностей состояний, пропускной способности и среднего количества пакетов в системе для различных начальных условий в переходном режиме. Рассмотрен случай периодического изменения скоростей прихода, соответствующий периодической передаче управляющих сигналов в составе полезной нагрузки.

As of February 07, 2022, more than 395 million cases of COVID-19 had been identified in the world, with 5.74 million deaths. The paper considers methodology for predicting the number of cases in the short term using a preliminary assessment of countries based on three indicators: expert assessments of the law-abiding population, the level of education and restrictive measures taken in the country. The description and composition of the groups obtained are given. An assessment of the accuracy of the forecast results is made. A comparison of the considered models of 2020 with 2022 is given.

The paper presents an algorithm of assigning a sequence of tasks in the collaborative robotic system (CRS). These tasks are represented both as a directed graph, and a timeline with the operations’ start events. The algorithm focuses on assigning the operations based on the availability of CRS members and their effectiveness. After the assignment, the execution time of the operation is recalculated according to the efficiency of the assigned humans and cobots, modifying the weight of the corresponding graph edge and rebuilding the time sequence after the current time event. If these conditions are not met, the assignment for the operation is postponed until the next event. The algorithm makes the transition from the current time event to the nearest one and traverses the graph from the first vertex to the last one. The analysis of modeling results shows that the use of the algorithm for a sequence of interdependent operations that requires human–robot collaboration allows reducing the time of execution of both the technological process and its individual operations. The algorithm can be used to test various hypotheses for the optimal number of participants to perform the operations by the CRS as a team of heterogeneous participants.

When producing perishable products or using perishable raw materials, large producers face the problem of organizing supplies and forming stocks, taking into account this specificity of resources. Product shelf life is key in optimizing and synchronizing supply and manufacturing processes. An approach to optimization of delivery not based on VMI-technology of joint inventory management with an extended module for monitoring stocks of perishable goods is proposed. It is noted that monitoring should be carried out according to a specific algorithm based on an economic and mathematical model for managing stocks of perishable goods. The developed model provides the calculation of the optimal proportions for the purchase, storage and sale of perishable products. It is shown that this approach is applicable to the dairy cluster of the Voronezh Oblast, the structure of which includes the logistic subsystem of interaction between the producer and the consumer of the product.