On the Sitters–Fishkin hypothesis

We consider the problem of minimal number of migrations in the optimal schedule of problem $Pm|pmtn(delay=d)|C_\mathrm{max}$ on parallel machines with interruptions and constant delay in job migrations. In particular, we consider the Sitters–Fishkin hypothesis that for every instance of this problem there exists an optimal schedule with at most $m-1$ migrations where $m$ is the number of machines. This hypothesis has been proven in [1] for the case when $m\leqslant3$. In this work, we prove this hypothesis for the case of four machines.