Abstract This article discusses the precedence-constrained class sequencing problem (PCCSP). In scheduling terms, this is a single-machine problem with precedence constraints and family setups with the goal of minimizing the number of setups. From a practical perspective, PCCSP covers a wide range of applications such as, for example, scheduling problems in systems with job families where multipurpose processors need retooling to switch from a job of one family to a job of another family. Previous research has shown that PCCSP is NP-hard and that no polynomial-time algorithm with constant worst-case performance exists unless P = NP . So far, only little research has been conducted on the development of specific computational methods for PCCSP. This article bridges this gap by proposing a dynamic programming algorithm for solving PCCSP exactly. It comprises specialized lower bound computations, node merging and precedence reasoning algorithms, and heuristics that successfully exploit the problem’s structure. Based on extensive numerical experiments, we analyze the algorithm in detail and show that it outperforms mixed-integer programming and constraint programming models.

中文翻译：

---

优先约束类排序问题的精确动态规划算法

摘要 本文讨论了优先约束类排序问题（PCCSP）。在调度方面，这是一个具有优先约束和系列设置的单机问题，其目标是最小化设置数量。从实践的角度来看，PCCSP 涵盖了广泛的应用，例如，具有作业系列的系统中的调度问题，其中多用途处理器需要重新加工以从一个系列的作业切换到另一个系列的作业。先前的研究表明 PCCSP 是 NP-hard 并且不存在具有恒定最坏情况性能的多项式时间算法，除非 P = NP 。到目前为止，对于 PCCSP 的特定计算方法的开发只进行了很少的研究。本文通过提出一种用于精确求解 PCCSP 的动态规划算法来弥补这一差距。它包括专门的下界计算、节点合并和优先推理算法，以及成功利用问题结构的启发式算法。基于大量的数值实验，我们详细分析了该算法，并表明它优于混合整数规划和约束规划模型。