Problem of successive megalopolis traversal with the precedence conditions

Consideration was given to the problem of constrained routing including visits to a finite system of megalopolises and at that execution of one or another internal job. The costs of displacements and executed jobs may depend on the list of the not yet completed tasks. A variant of the method of dynamic programming doing without construction of the entire array of values of the Bellman function was proposed. Some variants of the heuristic algorithms were discussed. Possible applications may be related, in particular, with the problems of reducing irradiance of the personnel of the nuclear power plants and sheet article cutting on the numerically controlled machine tools.