We prove that the bicriteria single-machine scheduling problem of minimizing total completion time and maximum cost simultaneously is solvable in polynomial time. Our result settles a long-standing open problem.

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doi.org/10.1016/0167-6377(95)00023-D, hdl.handle.net/1765/12348
ERIM Article Series (EAS)
Operations Research Letters
Erasmus Research Institute of Management

Hoogeveen, H., & van de Velde, S. (1995). Minimizing total completion time and maximum cost simultaneously is solvable in polynomial time. Operations Research Letters, 205–208. doi:10.1016/0167-6377(95)00023-D