Flow Conservation Constraints

The constraints $ F x = b$ are referred to as the nodal flow conservation constraints. These constraints algebraically state that the sum of the flow through arcs directed toward a node plus that node’s supply, if any, equals the sum of the flow through arcs directed away from that node plus that node’s demand, if any. The flow conservation constraints are implicit in the network model and should not be specified explicitly in side constraint data when using PROC NETFLOW. The constrained problems most amenable to being solved by the NETFLOW procedure are those that, after the removal of the flow conservation constraints, have very few constraints. PROC NETFLOW is superior to linear programming optimizers when the network part of the problem is significantly larger than the nonnetwork part.

The NETFLOW procedure can also be used to solve an unconstrained network problem, that is, one in which $H$, $Q$, $d$, $r$, and $z$ do not exist.