MPS format small example The following example defines a linear programming problem in MPS format. The line numbers are included for reference, they are not part of the MPS input.

 
         0  * This is a comment
         1  NAME    smallExample
         2  OBJSENSE
         3    MAX
         4  OBJNAME
         5    obj
         6  ROWS
         7    N  obj 
         8    L  r1
         9    G  r2
        10  COLUMNS
        11    x    obj    1   r1  1  r2  2
        12    y    obj -2.3   r1 -1
        13    z    obj  0.5
        14    z    r2    -1
        15    s    r2    -1
        16    s    r1     1
        17  RHS
        18    RIGHT    r1 10.75
        19    RIGHT    r2  -100
        20  ENDATA

This example describes the same problem instance as the following LP-format input.

 
        Problem
         smallExample
        Maximize
         obj:   x - 2.3 y + 0.5 z
        Subject To
         r1:   x -  y +  s <= 10.75
         r2:  2.0 x -  z -  s >= -100.0
        End

Whereas the LP-format input specifies the objective function and constraints row by row, the MPS-format input describes these objects in a column by column fashion.

The following table summarizes the lines in the MPS input that define the different components of smallExample's objective and constraints.


	line 11	line 12	line 13	line 14	line 15	line 16	line 8	line 18	line 9	line 19

`obj`	`x`	`-2.3y`	`+0.5z`
`r1`	`x`	`-y`				`s`	`≤`	`10.75`
`r2`	`2x`			`-z`	`-s`				`≥`	`-100`

The remaining lines in the MPS input are interpreted as follows. Line 1 defines the problem's name to be "smallExample". Line 3 states that the objective value should be maximized. Line 5 picks the row "obj" as the objective and line 7 defines "obj" to be an "N" row, that is, "obj" has no right-hand-side.