Abstract:

The paper considers two two-agent scheduling problems on a single machine. For the first two-agent scheduling problem, the objective of agent A is to minimize the total weighted completion time of all jobs of agent A while the objective of agent B is to minimize the maximum cost of the jobs of agent B. For the second two-agent scheduling problem, the objective of agent A is to minimize the total completion time of all jobs of agent A while the objective of agent B is to minimize the makespan which is defined as the maximum completion time of all the jobs of agent B. In this paper, we prove that the first problem is NP-hard in the strong sense which improves the current complexity result and design a dynamic programming other than the previous known algorithm for the second problem.

Key words: two-agent scheduling, algorithm complexity, optimal algorithm