How to write a simple MPS file to submit to NEOS servers

Question

I'm trying to find an open source lp solver that is fast enough to my problem. I'm trying to build a MPS file so I can submit it to NEOS servers and compare the performance of different solvers.

My problem involves, at its most difficult cases, something around 150 integer variables but I'm starting with a simple case to help me figure out how the MPS file format works.

This is the problem:

minimize  : 330.3 * M1 + 1132.88 * M2 + 955.86 * M3
subject to:
         20 <= 60 * M2 <= 20.9
         20 <= 34 * M3 <= 20.9
         M1 + M2 + M3 = 1

and I wrote the following MPS file:

NAME problema1
ROWS
 L  K
 L  N
 E  ONE
 N  CUSTO
COLUMNS
    M1        ONE       1              CUSTO     330.3
    M2        K         60
    M2        ONE       1              CUSTO     1132.88
    M3        N         34
    M3        ONE       1              CUSTO     955.86
RHS
    KLESS     K         20.9
    NLESS     N         20.9
    ONEREST   ONE       1
RANGES
    RANGE1    K         0.9
    RANGE2    N         0.9
ENDATA

Using the linear solvers available at NEOS (https://neos-server.org/neos/solvers/index.html), just Gurobi can solve it. The others find the problem is infeasible (which it's not).

I'm pretty confident that this is a problem with my MPS file, but I just can't figure it out what it is. What am I doing wrong?

Answer 1

Indeed your MPS file has a problem. The lines in the RHS section should have one name e.g.

RHS
    RHS1      K         20.9
    RHS1      N         20.9
    RHS1      ONE       1

Basically the solver picks one RHS set. Similar for the RANGES section. I am not sure what you intended using the lines in the RANGES section.