Output Data Sets
The procedure determines the flow that should pass through
each arc as well as
the value assigned to each nonarc variable. The goal is that
the minimum flow bounds, capacities, lower and upper
value bounds, and side constraints are not violated.
This goal is reached when
total cost incurred by such a flow pattern and value
assignment is feasible and optimal.
The solution found must also
conserve flow at each node.
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.
The ARCOUT= and CONOUT= data sets
contain the same variables.
These variables and their possible
values in an observation are
- _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.
There are two types of observations in the NODEOUT=
and DUALOUT= data sets.
One type of observation contains information about a node.
These are called type N observations.
There is one such observation of this type for each node.
The _NODE_ variable has a name of a node, and the _CON_ variable
values in these observations are missing values.
The other type of observation contains information about constraints.
These are called the type C observations.
There is one such observation for each constraint.
The _CON_ variable has a name of a constraint, and the _NODE_
variable values in these observations are missing values.
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.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.