FPT implicit enumeration of active schedules - Tarhan, İstenç; Hanen, Claire; Kordon, Alix Munier; Carlier, Jacques; Jouglet, Antoine (Discrete Applied Mathematics, 2025)
We consider in this paper the resource constrained scheduling problem with release times and deadlines. We develop an original dynamic programming algorithm generating a compact representation of all feasible active schedules for the decision problem inspired from classical branch-and-bound approaches with no time windows. This algorithm is proved to be fixed-parameter tractable (FPT in short) parameterized by the maximum number of jobs overlapping following time windows and the maximum processing time. New dominance rules are also presented to improve the time complexity of our algorithm. Lastly, we also develop an enhanced version of our algorithm to optimize any regular separable objective function. It is shown that this new version of our algorithm has the same time complexity and hence is FPT with the relevant two parameters. •A generic resource constrained scheduling problem with time windows is introduced.•Fixed-parameter tractable (FPT) algorithm is proposed to generate active schedules.•The FPT algorithm is enhanced to optimize regular objective functions.