MPS data files are analogous to a deck of computer input cards: each line of the MPS file represents a single card record. Records in an MPS data file consist of two types: indicator records and data records. The records contain fields delimited by blank spaces.

Indicator Records

Each section of the MPS file except the RANGES and BOUNDS sections is mandatory. If no BOUNDS section is present, all variables have their bounds set from 0 (zero) to + (positive infinity). Failure to include an RHS section causes ILOG CPLEX to generate a warning message and set all righthand side values to 0 (zero). Variables and constraints must be declared in the ROWS and COLUMNS sections before they are referenced in the RHS, RANGES, and BOUNDS sections.

Data Records

Any ASCII character (32 through 126) is legal, but names must contain no embedded blanks. In addition, names over 255 characters are truncated. CPLEX issues an error message if truncation causes the names to lose their uniqueness. Numeric fields can be at most 25 characters long.

If the first character in Field 3 or 5 is a dollar sign ($), the remaining characters in the record are treated as a comment. Another method for inserting comments is to place an asterisk (*) in column 1. Everything on such a line is treated as a comment.

Values may be defined with decimal or exponential notation and may utilize 25 characters. In exponential notation, plus (+) and minus (-) signs must precede the exponent value. If an exponent value is missing where one is expected, it is assigned a value of 0 (zero).

ROWS Section

In the ROWS section, each row of the problem is specified with its name and sense, one row per record.

If more than one free row is specified, the first one is used as the objective function and the others are discarded.

The ROWS section of our example looks like this:

ROWS
 N  obj
 L  c1
 L  c2

COLUMNS Section

In the COLUMNS section, all the columns of the constraint matrix are specified with their name and all of the nonzero elements. Multiple records may be required to completely specify a given column.

After a matrix element is specified for a column, all other nonzero elements in that same column should be specified.

The COLUMNS section of our example looks like this:

COLUMNS
    x1        obj                 -1   c1                  -1
    x1        c2                   1
    x2        obj                 -2   c1                   1
    x2        c2                  -3
    x3        obj                 -3   c1                   1
    x3        c2                   1

RHS Section

In the RHS section, the nonzero righthand-side values of the constraints are specified.

Several RHS vectors can exist. The name of each RHS vector appears in Field 2. However, only the first RHS vector is selected when a problem is read. Additional RHS vectors are discarded.

The RHS section of our example looks like this:

RHS
    rhs       c1                  20   c2                  30

RANGES Section

In the RANGES section, RHS range values to be applied to constraints may be specified.

The name of each range vector appears in Field 2. More than one range vector can be specified within an MPS file. However, only the first range vector is selected when a problem is read. Additional range vectors are discarded.

In our example, there are no ranged rows, but suppose we want to add the following constraint to our problem:

x1 - 3x2 + x3 >= 15

Instead of explicitly adding another row to the problem, we can represent this additional constraint by modifying row 2 of the example to make it a ranged row in this way:

15 <= x1 - 3x2 + x3 <= 30

The RANGES section of the MPS file to support this modification looks like this:

RANGES
    rhs       c2                  15

The name of each range vector appears in Field 2. However, only the first range vector is selected when a problem is read. Additional range vectors are discarded.

BOUNDS Section

In the BOUNDS section, bound values for variables may be specified.

In our example, the BOUNDS section looks like this:

BOUNDS
 UP BOUND     x1                  40

If no bounds are specified, ILOG CPLEX assumes a lower bound of 0 (zero) and an upper bound of +. If only a single bound is specified, the unspecified bound remains at 0 or +, whichever applies, with one exception. If an upper bound of less than 0 is specified and no other bound is specified, the lower bound is automatically set to -. ILOG CPLEX deviates slightly from a convention used by some MPS readers when it encounters an upper bound of 0 (zero). Rather than automatically set this variable's lower bound to -, ILOG CPLEX accepts both a lower and upper bound of 0, effectively fixing that variable at 0. ILOG CPLEX resets the lower bound to - only if the upper bound is less than 0. A warning message is issued when this exception is encountered.

More than one bound vector may exist. The name of each bound vector appears in Field 2. However, only the first bound vector is selected when a problem is read. Additional bound vectors are discarded.

Complete Example of MPS File Format

NAME example2.mps ROWS N obj L c1 L c2 COLUMNS x1 obj -1 c1 -1 x1 c2 1 x2 obj -2 c1 1 x2 c2 -3 x3 obj -3 c1 1 x3 c2 1 RHS rhs c1 20 c2 30 BOUNDS UP BOUND x1 40 ENDATA