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The NETFLOW Procedure |

The ARCOUT= data set contains a solution obtained when performing optimization that does not consider any constraints. The NODEOUT= data set contains nodal dual variable information for this type of solution. You can choose to have PROC NETFLOW create the ARCOUT= data set and the NODEOUT= data set and save the optimum of the network or the nodal dual variable values before any optimization that considers the side constraints is performed.

If there are side constraints, the CONOUT= data set can be produced and contains a solution obtained after performing optimization that considers constraints. The DUALOUT= data set contains dual variable information for nodes and side constraints from the solution obtained after optimization that considers the constraints. The CONOUT= data set and DUALOUT= data set can be used to save the constrained optimal solution.

- _FROM_
- a tail node of an arc. This is a missing value if an observation has information about a nonarc variable
- _TO_
- a head node of an arc. This is a missing value if an observation has information about a nonarc variable
- _COST_
- the cost of an arc or the objective function coefficient of a nonarc variable
- _CAPAC_
- the capacity of an arc or upper value bound of a nonarc variable
- _LO_
- the lower flow bound of an arc or lower value bound of a nonarc variable
- _NAME_
- a name of an arc or nonarc variable
- _SUPPLY_
- the supply of the tail node of the arc in the observation. This is a missing value if an observation has information about a nonarc variable
- _DEMAND_
- the demand of the head node of the arc in the observation. This is a missing value if an observation has information about a nonarc variable
- _FLOW_
- the flow through the arc or value of the nonarc variable
- _FCOST_
- flow cost, the product of _COST_ and _FLOW_
- _RCOST_
- the reduced cost of the arc or nonarc variable
- _ANUMB_
- the number of the arc (positive) or nonarc variable (nonpositive). Used for warm starting PROC NETFLOW
- _TNUMB_
- the number of the tail node in the network basis spanning tree. Used for warm starting PROC NETFLOW
- _STATUS_
- the status of the arc or nonarc variable

The variables present in the ARCDATA= data set are present in an ARCOUT= data set or a CONOUT= data set. For example, if there is a variable called tail in the ARCDATA= data set and you specified the SAS variable list

from tail;then tail is a variable in the ARCOUT= and CONOUT= data sets instead of _FROM_. Any ID list variables also appear in the ARCOUT= and CONOUT= data sets.

The other type of observation contains information about constraints. These are called the

Many of the variables in the NODEOUT= and DUALOUT= data sets contain information used to warm start PROC NETFLOW. The variables _NODE_, _SD_, _DUAL_, _VALUE_, _RHS_, _TYPE_, and _CON_ contain information that might be of interest to you.

The NODEOUT= and DUALOUT= data sets look similar, as the same variables are in both. These variables and their values in an observation of each type are

- _NODE_
- Type N: the node name.

Type C: a missing value. - _SD_
- Type N: the supply (positive) or demand (negative) of the node.

Type C: a missing value. - _DUAL_
- Type N: the dual variable value of the node in _NODE_.

Type C: the dual variable value of the constraint named in _CON_. - _NNUMB_
- Type N: the number of the node named in _NODE_.

Type C: the number of the constraint named in _CON_. - _PRED_
- Type N: the predecessor in the network basis spanning tree
of the node named in _NODE_.

Type C: the number of the node toward which the arc with number in _ARCID_ is directed, or the constraint number associated with the slack, surplus, or artificial variable basic in this row. - _TRAV_
- Type N: the traversal thread label of the node named in _NODE_.

Type C: a missing value. - _SCESS_
- Type N: the number of successors (including itself) in the
network basis spanning tree of the node named in _NODE_.

Type C: a missing value. - _ARCID_
- Type N: if _ARCID_ is nonnegative, _ARCID_ is the number of
the network basis spanning tree arc directed from the node with
number _PRED_ to the node named in _NODE_. If _ARCID_ is negative,
minus _ARCID_
is the number of the network basis spanning tree arc directed
from the node named in _NODE_ to the node with number _PRED_.

Type C: if _ARCID_ is positive, _ARCID_ is the number of the arc basic in a constraint row. If nonpositive, minus _ARCID_ is the number of the nonarc variable basic in a constraint row. - _FLOW_
- Type N: the flow minus the
lower flow bound of the arc _ARCID_.

Type C: the flow minus lower flow bound of the arc _ARCID_ or value lower bound of the nonarc variable value minus _ARCID_. - _FBQ_
- Type N:
if _FBQ_ is positive, then _FBQ_ is the subscript in arc length arrays
of the first arc directed toward the node named in _NODE_.
PROC NETFLOW's arc length arrays are sorted so that data of arcs
directed toward the same head node are together.
If _FBQ_ is
negative, no arcs are directed toward the node
named in _NODE_.
Arcs directed toward node
*i*have subscripts in the arc length arrays between observations FBQ(*i*) abd (FBQ(*i*+1))- 1, inclusive.

Type C: missing value. - _VALUE_
- Type N: missing value.

Type C: the lhs value (the sum of the products of coefficient and flows or values) of the constraint named in _CON_. - _RHS_
- Type N: missing value.

Type C: the rhs value of the constraint named in _CON_. - _TYPE_
- Type N: missing value.

Type C: the type of the constraint named in _CON_. - _CON_
- Type N: missing value.

Type C: the name of the constraint.

If specified in variable lists, the variables in the input data sets are used instead of some of the previous variables. These variables are specified in the NODE, SUPDEM, RHS, TYPE, and ROW (if there is only one variable in the ROW list) lists and are used instead of _NODE_, _SD_, _RHS_, _TYPE_, and _CON_, respectively.

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