A note on parallel-machine scheduling with deteriorating jobs

Abstract

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.

Keywords:

• parallel-machine scheduling
• time-dependent processing time
• lower bound

Acknowledgements

We are grateful to the referees for their constructive comments that have improved the presentation of the paper. This research was partially supported by the National Science Council of the ROC under grant NSC-93-2416-H-009-026.