The following LP format input defines an integer programming problem that contains four variables, each required to take on integer values, and three constraints. The first variable, x1, is bounded between 0 and 2, while the remaining three variables default to binary values, that is, they are bounded between 0 and 1.
Problem IntegerVars Maximize obj: 4x1 + x2 + 5x3 + 3x4 Subject To r1: x1 - x2 - x3 + 3x4 <= 1 r2: 5x1 + x2 + 3x3 + 8x4 <= 55 r3: -x1 + 2x2 + 3x3 - 5x4 <= 3 Bounds 0 <= x1 <= 2 Integer x1 x2 x3 x4 End
The same problem is defined by the following MPS format input. It uses MARKER lines to specify that the four variables are required to take on integer values.
NAME IntegerVars OBJSENSE MAX OBJNAME obj ROWS N obj L r1 L r2 L r3 COLUMNS MARK0qs 'MARKER' 'INTORG' x1 obj 4 r3 -1 r2 5 r1 1 x2 obj 1 r3 2 r2 1 r1 -1 x3 obj 5 r3 3 r2 3 r1 -1 x4 obj 3 r3 -5 r2 8 r1 3 MARK4qs 'MARKER' 'INTEND' RHS RHS r1 1 RHS r2 55 RHS r3 3 BOUNDS UP BOUND x1 2 ENDATA