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 henne...@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
