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This paper studies a hierarchical optimization problem of scheduling  n  jobs on a serial-batching machine, in which two objective functions are maximum costs. By a hierarchical optimization problem, we mean the problem of optimizing the secondary criterion under the constraint that the primary criterion is optimized. A serial-batching machine is a machine that can handle up to  b  jobs in a batch and jobs in a batch start and complete respectively at the same time and the processing time of a batch is equal to the sum of the processing times of jobs in the batch. When a new batch starts, a constant setup time  s  occurs. We confine ourselves to the bounded model, where  b  &lt;  n . We present an  O ( n  4 )-time algorithm for this hierarchical optimization problem. For the special case where two objective functions are maximum lateness, we give an  O ( n  3  log  n )-time algorithm.

Hierarchical minimization of two maximum costs on a bounded serial-batching machine