 Dummy-job reduction for sequence-dependent setup times

Add a dummy job $0$. Give the arc $0\to i$ cost equal to job $i$'s initial setup, the arc $i\to j$ its changeover cost, and every arc $i\to 0$ zero cost. A Hamiltonian cycle through the dummy represents a schedule, starting just after $0$ and ending just before it. The total processing time is constant on a single machine, so minimizing cycle cost minimizes completion time. Dropping subtour elimination constraints gives an assignment problem lower bound.