One lower bound for the modified problem proceeds by allowing preemption. We specify their parameters and precedence relations such that the optimal solution value of the modified problem obtained by ignoring the setup times, not the setup jobs, is no larger than the optimal solution value of the original problem. We develop several sufficient conditions to derive setup jobs. The key idea is to see a setup time as a setup job with a specific processing time, release date, due date, and precedence relations. The main algorithmic contribution is our lower bounding strategy to deal with family setup times. We develop a branch-and-bound algorithm, and our computational results show that it solves almost all instances with up to about 40 jobs to optimality. This problem arises from the constant tug-of-war going on in manufacturing between efficient production and delivery performance, between maximizing machine utilization by batching similar jobs and maximizing customers' satisfaction by completing jobs before their due dates. We address the NP-hard problem of scheduling n independent jobs with release dates, due dates, and family setup times on a single machine to minimize the maximum lateness.