Multiprocessor Scheduling with Rejection
SIAM Journal on Discrete Mathematics
Lower bounds for on-line single-machine scheduling
Theoretical Computer Science
Minimizing the total completion time on-line on a single machine, using restarts
Journal of Algorithms
Optimal Semi-online Algorithm for Scheduling on a Batch Processing Machine
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Best semi-online algorithms for unbounded parallel batch scheduling
Discrete Applied Mathematics
On-line scheduling on a batch machine to minimize makespan with limited restarts
Operations Research Letters
Semi-online two-level supply chain scheduling problems
Journal of Scheduling
Batching and delivery in semi-online distribution systems
Discrete Applied Mathematics
Hi-index | 5.23 |
We consider an online scheduling problem in a parallel batch processing system with jobs in a batch being allowed to restart. Online means that jobs arrive over time, and all jobs' characteristics are unknown before their arrival times. A parallel batch processing machine can handle up to several jobs simultaneously. All jobs in a batch start and complete at the same time. The processing time of a batch is equal to the longest processing time of jobs in the batch. We are allowed to restart a batch, that is, a running batch may be interrupted, losing all the work done on it. Jobs in the interrupted batch are released and become independently unscheduled jobs. We deal with an unbounded model where each batch's capacity is sufficiently large. We provide a linear online algorithm with competitive ratio 3/2 for the problem. We also show that the considered problem has no online algorithm using restarts with competitive ratio less than (5-5)/2.