A bottleneck routing problem with a system of priority tasks

We consider a minimax routing problem related to visiting megacities under precedence conditions and cost functions with task list dependence. It is supposed that some megacity system requiring visiting above all is selected. For solving, an approach with decomposition into a set of two minimax routing problems is proposed. A two-step widely understood dynamic programming procedure realizing an optimal composition solution is constructed. The above-mentioned optimality is established by theoretical methods. Application of the results obtained is possible under investigation of multi-stage processes connected with regular allocation of resources. Another variant of application concerns the particular case of one-element megacities (i.e., cities) and may be related to the issues of aviation logistics under organization of flights using one tool (airplane or helicopter) under system of tasks on the realization of passing cargo transportation with prioritization of visits realized above all.