This paper studies the growing domain of Robotic Process Automation (RPA) problems. Motivated by scheduling problems arising in RPA, we study the parameterized complexity of the single-machine problem $1|\text{prec},r_j,d_j|*$. We focus on parameters naturally linked to RPA systems, including chain-like precedences, the number of distinct processing times, and the structure of the time windows. We show that the problem is W[2]-hard parameterized by the number of chains, even with only two prescribed processing times and two distinct time-window lengths. This hardness remains even for distinct processing times and time windows under prec-consistent time windows. On the positive side, we obtain polynomial-time algorithm when all jobs share a single time-window length and FPT when the processing times, release times and deadlines are chain-uniform. We also show that the problem lies in XP when parameterized by the width of the precedence relation.

翻译：本文研究了机器人流程自动化（RPA）这一日益发展的领域中的问题。受RPA中出现的调度问题启发，我们研究了单机调度问题 $1|\text{prec},r_j,d_j|*$ 的参数化复杂度。我们重点关注与RPA系统自然关联的参数，包括链式优先关系、不同处理时间的数量以及时间窗口的结构。我们证明了该问题在链的数量参数化下是W[2]-难的，即使仅有两个指定的处理时间和两个不同的时间窗口长度。即使在优先关系一致的时间窗口条件下，且处理时间和时间窗口各不相同，该困难性依然成立。在积极方面，当所有作业共享单一时间窗口长度时，我们获得了多项式时间算法；当处理时间、释放时间和截止时间均为链一致时，我们获得了固定参数可解（FPT）算法。我们还证明了当以优先关系的宽度为参数时，该问题属于XP类。