Online parallel-batch scheduling to minimize total weighted completion time on single unbounded machine

• Design and analysis the online algorithms for 1|rj1|rj, B=+∞B=+∞, online|∑wjCjonline|∑wjCj.
• Obtain an online algorithm with competitive ratio 5+1 for the general case of processing time.
• Provide the optimal online algorithm when all jobs have identical processing times.

The online parallel-batch scheduling problem on single unbounded machine to minimize total weighted job completion time is studied. For the general case of processing time, we give an online algorithm with competitive ratio 5+1. When all jobs have identical processing times, we provide an optimal online algorithm.