Abstract
We consider the single machine parallel batch scheduling problems to minimize makespan and total completion time, respectively, under precedence relations. The complexities of these two problems are reported as open in the literature. In this paper, we settle these open questions by showing that both problems are strongly NP-hard, even when the precedence relations are chains. When the processing times of jobs are directly agreeable or inversely agreeable with the precedence relations, there is an O(n2) time algorithm to minimize the makespan.
Original language | English |
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Pages (from-to) | 949-958 |
Number of pages | 10 |
Journal | Naval Research Logistics |
Volume | 51 |
Issue number | 7 |
DOIs | |
Publication status | Published - 1 Oct 2004 |
Keywords
- Parallel batching
- Scheduling
- Single machine
ASJC Scopus subject areas
- Modelling and Simulation
- Ocean Engineering
- Management Science and Operations Research