The work is devoted to the problem of complex interaction with the surrounding social and business environment in the segment of long-term participants of various business activities. The study takes into account the periodicity of most economic processes, which has a complex characteristic. When selecting the optimization criterion, the negative consequences of the results of such activities are considered as externalities effects that are necessary when taking into account the environmental factor. It considers the assessment of economic or administrative measures aimed at reducing the negative effects of such activities. As a result, a mathematical model has been proposed that can be used as a basis for decision-making systems aimed at accounting for externalities of a wide range of nationwide, institutional, business and social activity
Keywords: ecology, engineering, mathematical model, digital city
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