Volume 55, Number 1, January-February 2021
|Page(s)||135 - 140|
|Published online||12 March 2021|
Hierarchical minimization of two maximum costs on a bounded serial-batching machine
School of Science, Henan University of Technology, Zhengzhou, Henan 450001, P.R. China
* Corresponding author: email@example.com
Accepted: 18 December 2020
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(n4)-time algorithm for this hierarchical optimization problem. For the special case where two objective functions are maximum lateness, we give an O(n3 log n)-time algorithm.
Mathematics Subject Classification: 90C27 / 90B35
Key words: Hierarchical scheduling / serial-batching / maximum cost
© EDP Sciences, ROADEF, SMAI 2021
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