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 <= constraint <= u .
   The range of the constraint is  r = u - h .  The value of r is specified
   in the RANGES section, and the value of u or h is specified in the RHS
   section.  If b is the value entered in the RHS section, and r is the
   value entered in the RANGES section, then u and h are thus defined:

        row type       sign of r       h          u
        ----------------------------------------------
           G            + or -         b        b + |r|
           L            + or -       b - |r|      b
           E              +            b        b + |r|
           E              -          b - |r|      b


E. In the BOUNDS section, bounds on the variables are specified.  When
   bounds are not indicated, the default bounds ( 0 <= x < infinity )
   are assumed.  The code for indicating bound type is as follows:

                    type            meaning
                   -----------------------------------
                     LO    lower bound        b <= x
                     UP    upper bound        x <= b
                     FX    fixed variable     x = b
                     FR    free variable
                     MI    lower bound -inf   -inf < x
                     BV    binary variable    x = 0 or 1

F. Sections RANGES and BOUNDS are optional as are the fields 5 and 6.
   Everything else is required.  In regards to fields 5 and 6, consider
   the following 2 constraints:

                       const1:  2x + 3y < 6
                       const2:  5x + 8y < 20

   Two ways to enter the variable x in the COLUMNS section are:

     (Field:  2    3           4            5         6  )
   1.         x  const1       2.0         const2     5.0

   2.         x  const1       2.0
              x  const2       5.0

G. A mixed integer program requires the specification of which variables
   are required to be integer.  Markers are used to indicate the start
   and end of a group of integer variables.  The start marker has its
   name in field 2, 'MARKER' in field 3, and 'INTORG' in field 5.  The
   end marker has its name in field 2, 'MARKER' in field 3, and 'INTEND'
   in field 5.  These markers are placed in the COLUMNS section.