Optimization of the structure of the system with «cold» reservation
Purpose – to give designers of highly technical systems, do not know the modern methods of optimization and programming skills, a simple mathematical tool for choosing the optimal structure of a redundant system. Methodology. In the design of highly reliable systems using the method of structural redundancy is always a question of rational choice of one of several options for the composition of the system. On the one hand, it is desirable to provide each of the elements of the system a greater number of redundant elements, and, on the other hand, can not be designed with too large system cost values mass or size. Therefore, the actual problem is, how to reserve the system so as to provide the required level of system reliability at acceptable cost. Usually, the problem of optimal structural redundancy of technical systems are formulated as a nonlinear integer programming problems and to solve them, depending on the complexity and required precision, using special algorithms based primarily on dynamic programming method. This article proposes an approach to solving these problems based on the representation of the original optimization model in terms of the problem of nonlinear integer programming with binary variables and its subsequent implementation in numerical workbench MS Excel spreadsheet processor. Conclusions. The resulting article of specific examples demonstrate the efficacy and sufficient generality of this approach to solving problems of optimal reservation. The proposed optimization models belong to the class of non-linear integer programming problems with binary variables for the numerical implementation of which is well suited spreadsheet MS Excel. These models may be useful for analyzing the reliability of technical systems in the early stages of their design.
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