Minimizing Total Weighted Completion Time on Parallel Unbounded Batch Machines
极小化加权完工时间和的无界批量机器并行调度问题

This paper considers the problem of scheduling n jobs on m parallel unbounded batch machines to minimize the total weighted completion time. Each job is characterized by a positive weight, a release time and a processing time. Each unbounded batch machine can process up to B (B≥n) jobs as a batch simultaneo usly. The processing time of a batch is the longest processing time among jobs in the batch. Jobs processed in the same batch have the same completion time, I.e., their common starting time plus the processing time of the batch. A polynomial time approximation scheme (PTAS) for this problem is presented.