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 with precedence constraints, release times, and deadlines (i.e., the problem known as $1|\operatorname{prec},r_j,d_j|*$ in the three-field notation). 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 strongly XNLP-hard parameterized by the number of chains, even with only two prescribed processing times and two distinct time-window lengths. The problem remains XNLP-hard even 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 XNLP when parameterized by the width of the precedence relation either when the instance is encoded in unary or the processing times are bounded.

翻译：暂无翻译