Scheduling Two Agents on a Single Machine: A Parameterized Analysis of NP-hard Problems.

•The tool of parametrized complexity is almost completely neglect when analyzing the complexity of scheduling problems.•We aim to study hard scheduling problems from parametrized point of view.•We do so by studying the parameterized complexity of nine different two-agents scheduling problems.•The selected parameter is the number of jobs that belongs to the second agent.•Our analysis determines the border between tractable and intractable variants of these problems.