### Balancing Total Supply and Total Demand

#### When Total Supply Exceeds Total Demand

When total supply of a network problem exceeds total demand, PROC NETFLOW can add an extra node (called the excess node) to the problem and set the demand at that node equal to the difference between total supply and total demand. There are three ways that this excess node can be joined to the network. All three ways entail PROC NETFLOW generating a set of arcs (henceforth referred to as the generated arcs) that are directed toward the excess node. The total amount of flow in generated arcs equals the demand of the excess node. The generated arcs originate from one of three sets of nodes.

When you specify the THRUNET option, the set of nodes that generated arcs originate from are all demand nodes, even those demand nodes with unspecified demand capability. You indicate that a node has unspecified demand capability by using a missing D value instead of an actual value for demand data (discussed in the section Missing S Supply and Missing D Demand Values). The value specified as the demand of a demand node is in effect a lower bound of the number of flow units that node can actually demand. For missing D demand nodes, this lower bound is zero.

If you do not specify the THRUNET option, the way in which the excess node is joined to the network depends on whether there are demand nodes with unspecified demand capability (nodes with missing D demand).

If there are missing D demand nodes, these nodes are the set of nodes that generated arcs originate from. The value specified as the demand of a demand node, if not missing D, is the number of flow units that node actually demands. For a missing D demand node, the actual demand of that node may be zero or greater.

If there are no missing D demand nodes, the set of nodes that generated arcs originate from are the set of supply nodes. The value specified as the supply of a supply node is in effect an upper bound of the number of flow units that node can actually supply. For missing S supply nodes (discussed in the section Missing S Supply and Missing D Demand Values), this upper bound is zero, so missing S nodes when total supply exceeds total demand are transshipment nodes, nodes that neither supply nor demand flow.

#### When Total Supply Is Less Than Total Demand

When total supply of a network problem is less than total demand, PROC NETFLOW can add an extra node (called the excess node) to the problem and set the supply at that node equal to the difference between total demand and total supply. There are three ways that this excess node can be joined to the network. All three ways entail PROC NETFLOW generating a set of arcs (henceforth referred to as the generated arcs) that originate from the excess node. The total amount of flow in generated arcs equals the supply of the excess node. The generated arcs are directed toward one of three sets of nodes.

When you specify the THRUNET option, the set of nodes that generated arcs are directed toward are all supply nodes, even those supply nodes with unspecified supply capability. You indicate that a node has unspecified supply capability by using a missing S value instead of an actual value for supply data (discussed in the section Missing S Supply and Missing D Demand Values). The value specified as the supply of a supply node is in effect a lower bound of the number of flow units that node can actually supply. For missing S supply nodes, this lower bound is zero.

If you do not specify the THRUNET option, the way in which the excess node is joined to the network depends on whether there are supply nodes with unspecified supply capability (nodes with missing S supply).

If there are missing S supply nodes, these nodes are the set of nodes that generated arcs are directed toward. The value specified as the supply of a supply node, if not missing S, is the number of flow units that node actually supplies. For a missing S supply node, the actual supply of that node may be zero or greater.

If there are no missing S supply nodes, the set of nodes that generated arcs are directed toward are the set of demand nodes. The value specified as the demand of a demand node is in effect an upper bound of the number of flow units that node can actually demand. For missing D demand nodes, (discussed in the section Missing S Supply and Missing D Demand Values), this upper bound is zero, so missing D nodes when total supply is less than total demand are transshipment nodes, nodes that neither supply nor demand flow.