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 $b<n$. 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.