BOUNDS Section (Optional) :: SAS/OR(R) 12.1 User's Guide: Mathematical Programming

BOUNDS Section (Optional)

The BOUNDS section specifies bounds for the columns.

Indicator record:

Field1	Field2	Field3	Field4	Field5	Field6
BOUNDS	Blank	Blank	.	Blank	.

Data record:

Field1	Field2	Field3	Field4	Field5	Field6
Bound type	Bound name	Column name	Bound for the column	Blank	Blank

Notes:

If you do not specify any bound for a column, then the upper bound is $+\infty$ for a continuous variable, and 1 for an integer variable, that is specified in the COLUMNS section. The lower bound is 0 by default.

General bound types include LO, UP, FX, FR, MI, and PL. Suppose the bound for a column identified in field3 is specified as in field4. Table 15.2 explains the effects of different bound types.

Table 15.2: Bound Type Rules

Bound Type	Ignore	Resultant Lower Bound	Resultant Upper Bound
LO	No		unspecified
UP	No	unspecified
FX	No
FR	Yes	$-\infty$	$+\infty$
MI	Yes	$-\infty$	unspecified
PL	Yes	unspecified	$+\infty$

If a bound (lower or upper) is not explicitly specified, then it takes the default values according to Note 1. There is one exception: if the upper bound is specified as a negative value () and the lower bound is unspecified, then the lower bound is set to $-\infty$ .

Mixed integer programming problems can specify integer variables in the BOUNDS section. Table 15.3 shows bound types defined for MIP.

Table 15.3: Bound Type Rules

Bound Type	Ignore	Variable Type	Value
BV	Yes	binary	0 or 1
LI	No	integer	$[b, \infty )$
UI	No	integer	$(-\infty , b]$

The columns that have bounds do not need to be specified in the same order in which the columns were specified in the COLUMNS section. However, all columns in the BOUNDS section should be defined in the COLUMNS section.
It is possible to specify multiple bound vectors, which are labeled by different bound names. Normally, the first bound vector encountered in the BOUNDS section is used, and all other bound vectors are discarded. All the elements of the selected bound vector must be specified before other bound vectors are introduced.
When data records in a sequence have an identical value in field2, you can specify the value in the first occurrence and omit the value by giving a missing value in the other records. If the value in field2 of the first data record in the section is missing, it means the name of the first vector is the missing value.
Within a particular BOUNDS vector, for a given column, if a bound (lower or upper) is explicitly specified by the bound type rules listed in Table 15.2, any other specification is considered to be an error.
If the value in field1 is LO, UP, FX, LI, or UI, then a data record with a missing value in field4 is ignored.