### 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:

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

2. 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 MI Yes unspecified PL Yes unspecified

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 .

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 UI No integer

3. 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.

4. 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.

5. 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.

6. 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.

7. If the value in field1 is LO, UP, FX, LI, or UI, then a data record with a missing value in field4 is ignored.