A dynamic problem for synthesis of a production-transport system with a tree-like configuration of connecting network components

A dynamic problem is studied for the allocation of productive capacities in the presence of additional constraints on a connectivity graph. An approac h to the solution is proved that rests on the combination of both the princ iple of the decomposition of NP-hard problems and the implicit exhaustive m ethod, which carries out the search for admissible subvectors of variables on the finite set. For each subvector, the initial problem is broken, up in to a number of readily solvable polynomial problems.