Abstract
In this paper, we revisit a two-agent scheduling problem on a single machine with jobs of unit processing times. In this problem, we have two agents: agent A and agent B. Each agent has his/her own disjoint job set. The objective of agent A is to minimize the total weighted completion time, and the objective of agent B is to minimize the total weighted number of tardy jobs. The complexity of the decision version of the problem was proposed as open in Oron et al. (European Journal of Operational Research 244:86–99, 2015). We construct a reduction from a variant of Even-Odd Partition to show that this problem is NP-complete. Finally, we also propose a pseudo-polynomial algorithm and a dual FPTAS for the problem.
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