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 knowledge representation and reasoning (KRR) paradigm for this problem and is competitive with state-of-the-art constraint programming (CP) and Mixed-Integer Programming (MIP) solvers.

我们处理并行机器上具有挑战性的调度问题，其设置时间和发布日期与半导体车间生产的实际应用有关。在那里，作业只能由专用机器处理，因此几乎没有机器可以确定完工时间，无论作业如何在剩余机器上调度。当机器出现故障并且需要重新安排作业时，这会导致问题。我们不是只优化完工时间，而是将各个机器的时间范围按非升序排列，并按字典顺序最小化生成的元组。这实现了所有机器尽早完成并提高了计划的稳健性。我们研究应用答案集编程（ASP）来解决这个问题。虽然 ASP 简化了建模，但时间约束和考虑的目标函数的结合对当前的求解技术提出了挑战。前一个问题是通过使用 ASP 的差分逻辑扩展来解决的。对于后者，我们设计了使用多镜头求解的不同算法。为了解决工业规模的实例，我们研究了不同的近似方法和启发法。我们的实验结果表明，ASP 确实是解决该问题的一种有前途的知识表示和推理 (KRR) 范式，并且与最先进的约束规划 (CP) 和混合整数规划 (MIP) 求解器具有竞争力。