Min-Max Scheduling of Batch or Drop-Line Jobs Under Agreeable Release and Processing Times

We study the Pareto optimization scheduling on an unbounded parallel-batch machine with jobs having agreeable release dates and processing times for minimizing makespan and maximum cost simultaneously. The jobs considered in this paper are of two types: batch jobs and drop-line jobs. For batch jobs, the completion time of a job is given by the completion time of the batch containing this job. For drop-line jobs, the completion time of a job is given by the starting time of the batch containing this job plus the processing time of this job. For both of batch jobs and drop-line jobs, we present polynomial-time algorithms for finding all Pareto optimal points.