On-Line Scheduling Of Unit Time Jobs With Rejection: Minimizing The Total Completion Time

We consider on-line scheduling of unit time jobs on a single machine with job-dependent penalties. The jobs arrive on-line (one by one) and can be either accepted and scheduled, or be rejected at the cost of a penalty. The objective is to minimize the total completion time of the accepted jobs plus the sum of the penalties of the rejected jobs. We give an on-line algorithm for this problem with competitive ratio . Moreover, we prove that there does not exist an on-line algorithm with competitive ratio better than 1.63784.