Records in MPS format

CPLEX supports indicator records and data records in MPS file format.

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

Indicator records separate the individual sections of the MPS file. Each indicator record contains a single word that begins in the first column. There are seven kinds of indicator records, each corresponding to sections of the MPS file. They are listed in Table 1.

Table 1. Indicator records
Section name/indicator record	Purpose
`NAME`	specifies the problem name; unlike other indicator records, the name record contains data
`ROWS`	specifies name and sense for each constraint
`COLUMNS`	specifies the name assigned to each variable (column) and the nonzero constraint coefficients corresponding to that variable
`RHS`	specifies the names of righthand side vectors and values for each constraint (row)
`RANGES`	specifies constraints that are restricted to lie in the interval between two values; interval endpoints are also specified
`BOUNDS`	specifies the limits within which each variable (column) must remain
`ENDATA`	signals the end of the data; always the last entry in an MPS file

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 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

Data records contain the information that describes the LP problem. Each data record comprises six fields, as in Table 2. The fields must be separated by white space (that is, blank space, tab, etc.), and the first field must begin in column 2 or beyond. Not all fields are used within each section of the input file.

Table 2. Fields of a data record in MPS file format
	Field 1	Field 2	Field 3	Field 4	Field 5	Field 6
Contents	Indicator	Name	Name	Value	Name	Value

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 use 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).

The ROWS section

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

Field 1 contains a single letter designating the sense of each row. Acceptable values are:

N indicates a free row.
G indicates a greater-than-or-equal-to row.
L indicates a less-than-or-equal-to row.
E indicates an equality row.

Field 2 contains a character identifier, maximum length of 255 characters, specifying the name of the row.

Fields 3-6 are not used in the ROWS section.

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

The 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.

Field 1: Blank

Field 2: Column identifier

Field 3: Row identifier

Field 4: Value of matrix coefficient specified by Fields 2 and 3

Field 5: Row identifier (optional)

Field 6: Value of matrix coefficient specified by Fields 2 and 5 (optional)

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

The RHS section

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

Field 1: Blank

Field 2: RHS identifier

Field 3: Row identifier

Field 4: Value of RHS coefficient specified by Field 2 and 3

Field 5: Row identifier (optional)

Field 6: Value of RHS coefficient specified by Field 2 and 5 (optional)

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

You can also declare an objective offset for a model in the RHS section of a file in MPS format. To do so, use the negative value of the offset, and declare it as the RHS of the objective function. For example, the following line declares an objective offset of 3.1415 (as in the example in the LP file format):


 rhs       obj     -3.1415

Notice particularly the reversal of the sign from 3.1415 to -3.1415.

The RANGES section

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

Field 1: Blank

Field 2: Righthand side range vector identifier

Field 3: Row identifier

Field 4: Value of the range applied to row specified by Field 3

Field 5: Row identifier (optional)

Field 6: Value of the range applied to row specified by Field 5 (optional)

The effect of specifying a righthand side range depends on the sense of the specified row and whether the range has a positive or negative coefficient. Table 3 specifies how range values are interpreted. For a given row, rhs is the righthand side value and range is the corresponding range value.

Table 3. How range values are interpreted in data records of MPS files
Row type	Range value sign	Resulting rhs upper limit	Resulting rhs lower limit
G	+ or -	rhs + \|range\|	rhs
L	+ or -	rhs	rhs - \|range\|
E	+	rhs + range	rhs
E	-	rhs	rhs + range

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.

The BOUNDS section

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

Field 1: Type of bound. Acceptable values are:

LO Lower bound
LI Lower bound, integer
UP Upper bound
UI Upper bound, integer
FX Fixed value (upper and lower bound the same)
FR Free variable (lower bound -∞ and upper bound +∞)
MI Minus infinity (lower bound = -∞)
PL Plus infinity (upper bound = +∞)
BV Binary variable, integer (0 or 1)
SC Upper bound of a semi-continuous variable, see What are semi-continuous variables?

Field 2: Bound identifier

Field 3: Column identifier to be bounded

Field 4: Value of the specified bound

Fields 5 and 6 are not used in the BOUNDS section.

In our example, the BOUNDS section looks like this:


BOUNDS
 UP BOUND     x1                  40

If no bounds are specified, 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 -∞. 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 -∞, CPLEX accepts both a lower and upper bound of 0, effectively fixing that variable at 0. 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.

Note:

Each of the bound types above specify the lower bound, the upper bound, or both, for a specific variable. CPLEX will reject an MPS file in which there is a variable for which multiple lower (or multiple upper) bounds are specified. For example, since FX specifies both the lower and upper bounds for a variable, it is invalid to have both an UP and an FX bound type for a variable (as there would be two upper bound specifications).