In this paper, an analytical formulation of the minimum-cut theorem is proposed for Max-Flow determination in networks modeled as weighted and directed acyclic s-t graphs with both parametric arc and node capacities. Such organizations are commonly found in manufacturing and logistics. A parametric Max-Flow approach avoiding redundant cuts is presented, then a recursive aggregation mechanism is provided to allow multi-level Max-Flow assessment in the case of complex networks.
Graph theory, networks flows, maximum flow, minimum cut, manufacturing.
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