# Allocation of resources in distribution systems with optimal redistribution of load of the product suppliers

## Abstract

Mathematical models of flow distribution of scarce resources in energy systems are constructed and investigated. Methods for solving problems of flow distribution, based on a combination of extreme approach to the calculation of nets and joint solution of the two main systems of Kirchhoff are developed. An efficient network link algorithm to find an initial approximation to the solution of complex nonlinear transportation problem is proposed. The problem of optimal redistribution of load of product suppliers is analyzed. As an example the problem of delivery to consumers the mixture of substance in certain proportions or with certain quantitative restrictions is considered. Thanks to the general formulation of the problem the proposed models, methods and algorithms can be used to calculate the different types of distribution of the networks and pipelines.

## References

Merenkov А.P., KHasilev V.YA. Teoriya gidravlicheskikh tsepey. — M.: Nauka, 1985. — 235 s.

Sistemnyye issledovaniya v energetike / pod red. chl.-kor. RАN N.I. Voropaya. — Novosibirsk.: "NАUKА", 2010. — 686 c.

Pshenichnyy B.N., Kirik E.E. Аlgoritmy optimal’nogo raspredeleniya potokov v setyakh // Kibernetika i sistemnyy analiz. — 1993. — № 4. — S. 29–39.

Pshenichnyy B.N., Kirik E.E. Metody nelineynogo programmirovaniya i potoki v setyakh // Kibernetika i sistemnyy analiz. — 1994. — № 6. — S. 67–77.

Kirik E.E., Pshenichnyy B.N. Teoriya i metody rascheta setey. // Obozreniye prikladnoy i promyshlennoy matematiki. — 1995. — t. 2, vyp.1. — S. 49–69.

Pshenichnyy B.N. Vypuklyy analiz i ekstremal’nyye zadachi. — M.: Nauka, 1980. — 320 s.

Kirik O.Ye. Rozpodil potokiv v merezhakh skladnoyi kil'tsevoyi topolohiyi // Naukovi visti NTUU "KPI". — 2009. — # 2. — S. 18–26.

SHor N.Z. Metody minimizatsii nedifferentsiruyemykh funktsiy i ikh prilozheniya. — Kiyev: Nauk. dumka, 1979. — 199 s.