Maximum Dynamic Flow Finding Task with the Given Vitality Degree

This paper is devoted to the task of the maximum flow finding with nonzero lower flow bounds taking into account given vitality degree. Transportation network with the flow is considered in fuzzy conditions due to the fuzzy character of the network’s parameters. Arcs of the network are assigned by the fuzzy arc capacities and nonzero lower flow bounds, vitality parameters and crisp transit times. All network’s parameters can vary over time, therefore, it allows to consider network as dynamic one. The vitality parameter assigned to the arcs means ability of its objects to be resistant to weather conditions, traffic accidents and save and restore objects themselves, arc capacities of the network’s sections in case of damage. The nonzero lower flow bounds are used to assess economic reliability of the transportation. Such methods can be applied in the real railways, roads and air roads solving the task of the optimal cargo transportation.