On the structure of an extremal problem of rout optimization with constraints in the form of precedence conditions

A discrete-continuous extremal problem of route optimization with constraints in the form of precedence conditions is considered. A version of the dynamic programming method is constructed which includes a procedure for determining the Bellman function and the realization of the quasioptimal solution in the form of a route-path couple. The first component of this couple (i.e. the route) consists in indices commutation for a given set of multifunctions, and the second one (the path) is a cortege of points in the sections of multivalued maps indexed according to the route.