Decision Optimization

The only difference between the classical HFS and the classical Flow-shop scheduling problem is that there are several parallel machines (say C[s]) for each stage s instead of a single one. So with CP Optimizer, you only need to use a cumul function instead of a no-overlap constraints. In OPL, it looks like:

using CP;

int N                       = ...; // Number of jobs
int M                       = ...; // Number of operations per jobs
int D[i in 1..N][s in 1..M] = ...; // Processing time of operation s of job i
int C[s in 1..M]            = ...; // Number of machines for stage s (in 1..M)

dvar interval op[i in 1..N][s in 1..M] size D[i][s];
minimize max(i in 1..N) endOf(op[i][M]);
subject to {
  forall(i in 1..N, s in 2..M) {
    endBeforeStart(op[i][s-1], op[i][s]);
  }
  forall(s in 1..M) {
    sum(i in 1..N) pulse(op[i][s],1) <= C[s];
  }
}