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The scheduling problem in a multi-stage hybrid ﬂowshop has been the subject of considerable research. All the studies on this subject assume that each job has to be processed on all the stages, i.e., there are no missing operations for a job at any stage.
However, missing operations usually exist in many real-life production systems, such as a system in a stainless steel factory investigated in this note. The studied production system in the factory is composed of two stages in series. The ﬁrst stage contains only one machine while the second stage consists of two identical machines (namely a 1 • 2 hybrid ﬂowshop). In the system, some jobs have to be processed on both stages, but others need only to be processed on the second stage.
Accordingly, the addressed scheduling problem is a 1 • 2 hybrid ﬂowshop with missing operations at the ﬁrst stage.
In this note, we develop a heuristic for the problem to generate a non-permutation schedule (NPS) from a given permutation schedule, with the objective of minimizing the makespan. Computational results demonstrate that the heuristic can efficiently generate better NPS solutions.
- ChyiLv 41 decade agoFavorite Answer
I guess this is from this paper-
A note on two-stage hybrid flowshop scheduling with missing operations
Computers and Industrial Engineering archive Volume 54 , Issue 3 (April 2008) table of contents
Pages 695-704, 2008
permutation schedule - the order of performing the jobs in all stages. eg. if job1 proceeds job2 in stage 1, job1 continues to proceed jobs in other stages (stage,2,3,4...).
non-permutation schedule - permits an arbitary sequence of jobs at each stage.
2008-03-06 10:30:19 補充：
Sorry. typo on arbitary.
2008-03-06 10:37:50 補充：