SIMULATION AND OPTIMIZATION OF INTERACTION PROCESS PARAMETERS THREE ENTERPRISES IN A SINGLE PRODUCTION SYSTEM

The article presents a method of designing the process of interaction of three enterprises in a single production system. The matrix method of dynamic programming establishes calculation formulas for design parameters: the share of the flow of gross output, which is sent by enterprises for the development of their own production. The quadratic functional is accepted as a criterion of optimality, the physical meaning of which is the expenditure of funds to support the stable functioning of the process. In this case, the final product of the production system, sent to external consumption should be maximum. The software product is created and the optimum decision is received. Modeling in the modeling system of MVTP 3.7 of the process of interaction of three enterprises for three variants is performed. The option with optimal design parameters provides an increase in the production capacity of enterprises and corresponds to the area of rational values of the shares of intermediate products of enterprises, which is established by modeling.

Simulation and optimization of interaction process parameters three enterprises in a single production system

The article presents a method of designing the process of interaction of three enterprises in a single production system. The matrix method of dynamic programming establishes calculation formulas for design parameters: the share of the flow of gross output, which is sent by enterprises for the development of their own production. The quadratic functional is accepted as a criterion of optimality, the physical meaning of which is the expenditure of funds to support the stable functioning of the process. In this case, the final product of the production system, sent to external consumption should be maximum. The software product is created and the optimum decision is received. Modeling in the modeling system of MVTP 3.7 of the process of interaction of three enterprises for three variants is performed. The option with optimal design parameters provides an increase in the production capacity of enterprises and corresponds to the area of rational values of the shares of intermediate products of enterprises, which is established by modeling.

Neural network method for search of the active site of a wind power plant

The article presents the results of the study of the possibilities of using neural networks to solve the problem of determining the active set of a wind farm (WF), taking into account the efficiency of each wind turbines (WT). The comparative analysis of the obtained results with the known methods of determining the active composition of WF, such as: the method of dynamic programming; the method of dynamic programming with increasing the load on the experimentally set percentage; modified method of dynamic programming. The advantages and disadvantages of using each of the studied methods in terms of the possibility of achieving a given generation power at the maximum efficiency of the selected WT are determined. It is established that when using recurrent neural networks to solve the problem of determining the active composition of WF, the minimum direct linear variation of the difference between the power to be generated and the actual power of the determined active set of WF is 2.7%. Under the same conditions, the use of other known methods, in particular, the modified method of dynamic programming ensures the achievement of this parameter at the level of 0.05%. This significantly increases the time to solve the problem. By computer simulation, it was found that under equal conditions, the time to solve the problem using neural networks - 0.04 s, and using a modified method of dynamic programming 3.4 s. The obtained results provide an opportunity to implement effective decision support systems in energy flow management.

Multistage Dynamic Optimization with Different Forms of Neural-State Constraints to Avoid Many Object Collisions Based on Radar Remote Sensing

This article presents the possibility of helping navigators direct the movement of an object, while safely passing through other objects, using an artificial neural network and optimization methods. It has been shown that the best trajectory of an object in terms of optimality and security, from among many possible options, can be determined by the method of dynamic programming with the simultaneous use of an artificial neural network, by depicting the encountered objects as moving in forbidden domains. Analytical considerations are illustrated with examples of simulation studies of the developed calculation program on real navigational situations at sea. This research took into account both the number of objects encountered and the different shapes of domains assigned to the objects encountered. Finally, the optimal value of the safe object trajectory time was compared on the setpoint value of the safe passing distance of objects in given visibility conditions at sea, and the degree of discretization of calculations was determined by the density of the location of nodes along the route of objects.

Application of Criteria Aggregation Techniques for the Selection of Innovative Products

The peculiarity of innovative products requires taking into account a large number of criteria that should be aggregated into generalized ones and building a convolution tree with qualitative, quantitative and fuzzy rules. The paper proposes a methodology for the optimal partitioning of criteria scales into generalized gradations for using combined methods of multicriteria analysis of alternatives. The transition to fewer criteria leads to a signifi cant increase in the dimension of the scales of generalized criteria. Scales have to be converted to new scales with fewer gradations. To solve the problem of minimizing the information loss occurring when converting the scales picked Bellman function and applied method of dynamic programming. Computational experiments have shown the effectiveness of the proposed approach.

Elaboration of Balance-Optimization in Economic and Mathematical Model of Development of a Large Municipal Unit: Real Experience

The objective of the study is to develop a balance-optimizing economic and mathematical model which enables predicting steady and sustainable development of a large municipal unit. Using the method of dynamic programming introduced by Richard Bellman, the authors worked out the economic and mathematical model for optimizing the key indicators of soсial and economic development of a municipal unit. The model used and predicted indicators included in the list of the key performance indicators of municipal unit authorities. There is an analysis of the results of applying the model for a large municipal unit — Novosibirsk. The calculations made by the authors indicate that the model may work with actual economic information and may be used for predicting and making managerial decisions at a municipal level

THE OPTIMAL PRINCIPLE OF BELLMAN IN THE PROBLEM OF OPTIMAL MEANS DISTRIBUTION BETWEEN ENTERPRISES FOR THE EXPANSION OF PRODUCTION

The method of dynamic programming has been considered, which is used in solving multiple problems in economics, on the example of using Bellman’s optimality principle for solving nonlinear programming problems. On a specific numerical example, the features of the solution have been shown in detail with all the calculations. The problem of optimal distribution of funds among enterprises for the expansion of production has been formulated, which would give the maximum total increase in output. The solution of the task has been presented in the case, when the number of enterprises is 3. It has been shown, that the Bellman optimality principle allows you solve applied problems of cost forecasting with obtaining the optimal solution-maximum profit at minimum costs.

МЕТОД ДИНАМІЧНОГО ПРОГРАМУВАННЯ ЩОДО СИНТЕЗУ ВХІДНОГО ВИМІРЮВАЛЬНОГО СИГНАЛУ ДЛЯ КОНТРОЛЮ ТЕХНІЧНОГО СТАНУ РАДІОНАВІГАЦІЙНИХ КОМПЛЕКСІВ

The article shows that the use of modern navigation systems and complexes for controlling the movement of means of water transport makes it possible to ensure safe navigation. It is substantiated that the proper functioning of the means of navigation support – radio navigation complexes – depends on their technical condition. The work substantiates and investigates mathematical expressions for calculating the parameters of input measuring signals for controlling the technical state of radio navigation complexes. The results of the analysis of methods for determining the technical state of radio electronic devices are presented, based on studies of their dynamic characteristics. It has been shown that inertial units (elements) are used to increase the noise immunity coefficient of radio navigation complexes, which increases the time to control the harmonic signal of a sinus or cosine type. It is possible to avoid this disadvantage by using test signals with a normalized spectrum, representing the sum of a certain number of useful harmonics – test signals of complex form. The purpose of the article is to develop a method of dynamic programming for the synthesis of the input measurement signal for monitoring the state of the radio navigation complexes of the means of water transport. The obtained recurrence ratio can be used to determine the characteristics of a measuring signal in the case of continuous monitoring of the output signal. To do this, you need to replace the integral in the expression for the synthesis criterion with the corresponding integral sum. The method of dynamic programming when using personal computers in comparison with other methods has the advantage since it allows you to use a cyclic program in calculations. However, although in the dynamic programming method at each stage it is necessary to calculate and memorize only one function, with a considerable amount of coordinates (with a significant amount of control parameters and rather complex systems and complexes of navigation and traffic control of sea vessels), the volume of calculations can be very large.