Abstract
Two-agent scheduling problems with the general position-dependent processing time are studied in this paper. Under the constraint that the makespan of one agent is upper bounded, we show that the problem to minimize the other agent's makespan on a single machine is NP-hard. A polynomial time algorithm is proposed for the problem with learning or deteriorating effects. To minimize the total completion time of one agent's jobs on a single machine, we design a dynamic programming algorithm and an FPTAS. Moreover, we also provide dynamic programming algorithms and FPTASs for the problem to minimize one agent's makespan and the problem to minimize the total completion time of the other agent's jobs on parallel machines.
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