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We propose a model for scheduling jobs in a parallel machine setting that takes into account the cost of migrations by assuming that the processing time of a job may depend on the specific set of machines among which the job is migrated. For the makespan minimization objective, the model generalizes classical scheduling problems such as unrelated parallel machine scheduling, as well as novel ones such as semi-partitioned and clustered scheduling. In the case of a hierarchical family ofdoi:10.1109/ipdps.2017.22 dblp:conf/ipps/BonifaciDM17 fatcat:aqf5so6qvfalfi62ouxnpkj6g4