Input Format for MILPs

Table of Contents

• Example (.lp and .mps)

Describes the input file format for MILPs.

For MILPs, idol_cl accepts .mps and .lp files.

These are standard formats used by solvers such as Gurobi, Cplex, GLPK, and HiGHS.

In most cases, the file parsing is performed by the underlying solver used by idol.

For more details, refer to the IBM page on the .lp format or the lpsolve page on the .mps format.

Example (.lp and .mps)

Example of a simple MILP:

\[\begin{align} \min_{x,y} \quad & 3x + 4y \\ \text{s.t.} \quad & 2x + y \ge 5 \\ & x + 2y \ge 6 \\ & x, y \in \mathbb{Z}_{\ge 0} \end{align} \]

Corresponding .lp file:

Minimize
 obj: 3 x + 4 y
 
Subject To
 c1: 2 x + y >= 5
 c2: x + 2 y >= 6
 
Bounds
 x >= 0
 y >= 0
 
Generals
 x
 y
 
End

Equivalent .mps file:

NAME          example
ROWS
 N  obj
 G  c1
 G  c2
COLUMNS
    x       obj     3
    x       c1      2
    x       c2      1
    y       obj     4
    y       c1      1
    y       c2      2
RHS
    rhs     c1      5
    rhs     c2      6
BOUNDS
 LO bnd     x       0
 LO bnd     y       0
ENDATA