The optimization of energy supply system becomes especially important problem in those cases where there are several different energy sources, including, e.g., renewable energy sources, and several energy sinks of different power. This problems can be solved with the use of a graph of exergy and economic expenditures for the pairwise interaction of flows. The purpose of the study is to specify the concept of exergy schedule and economic costs applied to energy supply systems (ESS). We shall interpret a graph of the exergy and economic expenditures of an ESS, having an arbitrary structure, as a bipartite graph Z such that the set of its nodes C corresponds to the heating H and heated C flows, and the set of its arcs D to a possible distribution of the exergy and economic expenditures in the corresponding elements of this ESS in the course of interaction between the heating and heated flows. A symmetric graph represents an oriented graph, whose arcs can be grouped into pairs of parallel but oppositely directed arcs. Such graphs, having no isolated nodes, are convenient for studying complex interrelated systems. If we have determined the optimal pair of elements (аі, aj), corresponding to the sequence of nodes, beginning from the root of the foretree and finishing by a suspended node, giving a matrix of unit dimension, then the obtained sequence of elements forms a single-contour system with the minimum level of exergy and economic expenditure. For finding the optimal solution it is advisable to use the method of branches and boundaries, which enables one to improve the solution simpler than with the application of different methods of exergy analysis.

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