There are several model-based applications which contain networks and flows. Typical examples are applications for the distribution of electricity, water, materials, etc. AIMMS offers two special constructs, Arcs and Nodes, to formulate flows and flow balances as an alternative to the usual algebraic constructs. Specialized algorithms exist for pure network problems.

Mixed formulations

It is possible to intermingle network constructs with ordinary variables and constraints. As a result, the choice between Arcs and Variables on the one hand, and Nodes and Constraints on the other, becomes a matter of convenience. For instance, in the formulation of a flow balance at a node in the network you can refer to flows along arcs as well as to variables that represent import from outside the network. Similarly, you can formulate an ordinary capacity constraint involving both network flows and ordinary variables.

Flow keywords

It is assumed here that you know the basics of network flow formulations. Following are three flow-related keywords which can be used to specify a network flow model:

  • NetInflow-the total flow into a node minus the total flow out of that node,

  • NetOutflow-the total flow out of a node minus the total flow into that node, and

  • FlowCost-the cost function representing the total flow cost built up from individual cost components specified for each arc.

The first two are always used in the context of a node declaration, while the third may be used for the network model declaration.