A maximum flow problem with intermediate node requirements (Q801796)

A modified version of the maximum flow problem is considered. Instead of flow conservation constraints at any node, the restriction is that the outflow at a node be equal to the excess of the inflow over the node requirement (and 0 if the requirement exceeds the inflow). In other words, a node absorbs up to its requirement and lets the excess go through. The authors propose a modification of Ford and Fulkerson's algorithm to solve this problem. They introduce pseudo-arcs called priority arcs in the network between the various nodes and the sink and impose on these arcs capacities which are the requirements at the nodes. An example is treated in detail.