We consider a parallel-machine scheduling problem of minimizing the total completion time. The processing time of a job is a linear function of its starting time and deterioration rate. This problem is known to be NP-hard, even for the case with two machines. In this note, we generalize an existing lower bound for the two-machine case to the general case with an arbitrary number of machines. Despite the generalization concerning machine number, our bound has one extra term that makes our bound tighter than the existing one.Journal of the Operational Research Society (2007) 58, 824-826. doi:10.1057/palgrave.jors. 2602208 Published online 26 April 2006.
- Lower bound
- Parallel-machine scheduling
- Time-dependent processing time