On-Line Scheduling on a Single Bounded Batch Processing Machine with Restarts

The problem of on-line job scheduling on a single batch processing machine with bounded batch size is attacked. Jobs arrive dynamically over time, the characteristics of jobs are unknown before their arrivals. A batch processing machine can handle up to b jobs simultaneously. The processing time of a batch is given by the longest processing time of some job in the batch. The objective of on-line scheduling problem is to minimize the time makespan. An on-line algorithm with restarts for a bounded batch machine scheduling is presented, and it is shown that the competitive ratio is 3/2. This model has not been considered previously.