miplib

MPS input format was originally introduced by IBM to express linear
and integer programs in a standard way. The format is a fixed column
format, so care must be taken that all information is placed in the
correct columns as described below.

The following is not intended as a complete description of MPS format,
but only as a brief introduction. For more information, the reader is
directed to:

“Advanced Linear Programming,” by Bruce A. Murtagh
“Computer Solutions of Linear Programs,” by J.L. Nazareth

It may be useful to look at an example MPS file while reading this
MPS information.

The following template is a guide for the use of MPS format:

———————————————————————
Field: 1 2 3 4 5 6
Columns: 2-3 5-12 15-22 25-36 40-47 50-61

NAME problem name

ROWS

type name

COLUMNS
column row value row value
name name name
RHS
rhs row value row value
name name name
RANGES
range row value row value
name name name
BOUNDS

type bound column value
name name
ENDATA
———————————————————————

NOTES:

A. In the ROWS section, each row of the constraint matrix must have a
row type and a row name specified. The code for indicating row type
is as follows:

type meaning
—————————
E equality
L less than or equal
G greater than or equal
N objective
N no restriction

B. In the COLUMNS section, the names of the variables are defined along
with the coefficients of the objective and all the nonzero constraint
matrix elements. It is not necessary to specify columns for slack or
surplus variables as this is taken care of automatically.

C. The RHS section contains information for the right-hand side of the problem.

D. The RANGES section is for constraints of the form: h