Sparse Data Input Format
The sparse format to PROC LP is designed to enable
you to specify
only the nonzero coefficients in the description of linear programs,
integer programs, and mixed-integer programs.
The SAS data set that
describes the sparse model must contain at least four
Each observation in the data set associates a type with a row or a column,
and defines a coefficient or a numerical value in the model.
In addition to the keywords in the dense format, PROC LP
also recognizes the keywords RHS, RHSSEN, and RANGE
as values of the type variable.
The values of the row and column variables are the names of
the rows and columns in the model.
The values of the coefficient variables specify the coefficients or other
The SAS data set can contain multiple pairs of row and coefficient
variables. In this way, more information about the model can be
specified in each observation in the data set.
See Example 3.2 for details.
Table 3.4 shows
the keywords that are recognized by
PROC LP and in which variables can appear in the problem
The SAS data set that
describes the sparse model must contain at least four SAS variables: a
type variable, a column variable, a row variable, and
a coefficient variable.
Each observation in the data set defines one or more rows
or coefficients in the model. The value of the type variable
is a keyword that tells PROC LP how to interpret the observation.
The values of the row and column variables name the rows and columns in the
The values of the coefficient variables define coefficients and lower and
upper bounds and identify model variables with type BASIC, FIXED, BINARY,
All character values in the sparse data input format are case insensitive.
Table 3.4: Variable Keywords Used in the Problem Data Set
Follow these rules for sparse data input:
- The order of the observations is unimportant.
- Each unique column name appearing in the COL variable
defines a unique column in the model.
- Each unique row name appearing in the ROW variable
defines a unique row in the model.
- The type of the row is identified
when an observation in which the row name appears (in a ROW
variable) has type MIN, MAX, LE, GE, EQ, SOSLE, SOSEQ,
LOWERBD, UPPERBD,UNRSTRCT, FIXED,
BINARY, INTEGER, BASIC, FREE, or PRICESEN.
- The type of each row must be identified at least once.
If a row is given a type more than once, the multiple definitions
must be identical.
- When there are multiple rows named in an observation (that is,
when there are multiple ROW variables), the TYPE variable
applies to each row named in the observation.
- The type of a column is identified when an observation in which
the column name but no row name appears has the type LOWERBD, UPPERBD,
UNRSTRCT, FIXED, BINARY, INTEGER, BASIC, RHS, RHSSEN, or RANGE. A
column type can also be identified in an observation in which
both column and row names appear and the row name has one of the
- Each column is assumed to be a structural column in the model
unless the column is identified as a right-hand-side vector,
a right-hand-side change vector, or a range vector.
A column can be identified as one of these types using either the
keywords RHS, RHSSEN, or RANGE in the TYPE variable;
the special column names _RHS_, _RHSSEN_, or _RANGE_; or
the RHS, RHSSEN, or RANGE statements following the PROC LP statement.
- A TYPE variable beginning with the character *
causes the observation to be interpreted as a comment.
When the column names appear in the
Variable Summary in the PROC LP output,
they are listed in alphabetical order.
The row names appear in the order in which they appear
in the problem data set.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.