On-line batch scheduling on tow parallel machines with wait

Abstract

It was studied with the problem of scheduling jobs in batches on-line on 2 identical parallel machines with objective to minimize the maximum completion time (the completion time of the last job: makespan), where batches arrive over list and every batch has exactly m jobs, and the processing times are constrained in some interval. When a batch arrives we schedule the jobs in this batch immediately and irrevocably without the knowledge of later batches. The pre-emption is not allowed. An algorithm with scheduling jobs in every batch by LPT rule was proposed. When all the jobs in pre-batch are scheduled we schedule the jobs in the following batch. The worst case was analyzed and the worst case ratio dependent with number of jobs in batch was given, and the conclusion was proved by procedure.