Abstract
This paper studies a hierarchical optimization problem on an unbounded parallel-batching machine, in which two objective functions are maximum lateness induced by two sets of due dates, representing different purposes of two decision-makers. By a hierarchical optimization problem, we mean the problem of optimizing the secondary criterion under the constraint that the primary criterion is optimized. A parallel-batching machine is a machine that can handle several jobs in a batch in which all jobs start and complete respectively at the same time. We present an $$O(n\log P)$$ -time algorithm and an $$O(n^3)$$ -time algorithm for this hierarchical scheduling problem, where P is the total processing time of all jobs.
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