Re: [Fwd: GLPK doubt]

[Michael Hennebry]

On Thu, 8 Feb 2024, Manuel Muñoz Márquez wrote:

> You have a decision problem if and only if you have decision variables.

I think OP is using "decision variables" in a non-standard way:
binary auxilliary variables representing choices,
e.g., project p is done in month m.
OP wants to reduce it to one variable per project.
It won't work.
If q[p]=1 represents project p is done in month 1
and q[p]=37 represents project p is done in month 37,
then q[p]=19=(1+37)/2 allows project p to be half done in month 1
half in month 37.
OP could get it down to 6 binary variables per project,
but 'tain't obvious that it would help.
The LP relaxation might not be as tight.
The traditional TSP formulation has n*(n-1)/2 binary variables.
It could be got down to 2*n*lg(n),
but so far as I know, no one has tried to deal with the mess.

My suspicion is that OP's problem is equivalent to an assignment problem.
In that case, 12000 variables should not be difficult.

--
Michael   hennebry@mail.cs.ndsu.NoDak.edu
"SCSI is NOT magic. There are *fundamental technical
reasons* why it is necessary to sacrifice a young
goat to your SCSI chain now and then."   --   John Woods