Answer-Set Programming for Lexicographical Makespan Optimisation in Parallel Machine Scheduling

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