Multi-agent scheduling on a single machine with max-form criteria

We consider multi-agent scheduling on a single machine, where the objective functions of the agents are of the max-form. For the feasibility model, we show that the problem can be solved in polynomial time even when the jobs are subject to precedence restrictions. For the minimality model, we show that the problem is strongly NP-hard in general, but can be solved in pseudo-polynomial-time when the number of agents is a given constant. We then identify some special cases of the minimality model that can be solved in polynomial-time.