Single machine scheduling with two competing agents, arbitrary release dates and unit processing times

We study various single machine scheduling problems with two competing agents, unit processing times and arbitrary integer release dates. The problems differ by the scheduling criterion used by each of the two agents, and by the variant of the bicriteria problem that has to be solved. We prove that when the scheduling criterion of either one of the two agents is of a max-type, then all considered variants of the bicriteria problem are solvable in polynomial time. However, when the two agents have a sum-type of scheduling criterion, several variants of the bicriteria problem become (Formula presented.) -hard.