Approximation schemes for two-agent scheduling on parallel machines

Two models of two-agent scheduling problem on identical machines are considered in this paper. In both models, the goal is to minimize the makespan and the total completion time of agent A respectively, subject to an upper bound on the makespan of agent B. We prove that these two problems are NP-hard and can be solved in pseudo-polynomial time. Furthermore, we design the fully polynomial time approximation schemes for both problems, respectively.