  We deal with a challenging scheduling problem on parallel machines with
sequence-dependent setup times and release dates from a real-world application
of semiconductor work-shop production. There, jobs can only be processed by
dedicated machines, thus few machines can determine the makespan almost
regardless of how jobs are scheduled on the remaining ones. This causes
problems when machines fail and jobs need to be rescheduled. Instead of
optimising only the makespan, we put the individual machine spans in
non-ascending order and lexicographically minimise the resulting tuples. This
achieves that all machines complete as early as possible and increases the
robustness of the schedule. We study the application of Answer-Set Programming
(ASP) to solve this problem. While ASP eases modelling, the combination of
timing constraints and the considered objective function challenges current
solving technology. The former issue is addressed by using an extension of ASP
by difference logic. For the latter, we devise different algorithms that use
multi-shot solving. To tackle industrial-sized instances, we study different
approximations and heuristics. Our experimental results show that ASP is indeed
a promising KRR paradigm for this problem and is competitive with
state-of-the-art CP and MIP solvers. Under consideration in Theory and Practice
of Logic Programming (TPLP).
