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 of machines, we derive a compact integer linear programming formulation of the problem and leverage its fractional relaxation to obtain a polynomial-time 2-approximation algorithm. Extensions that incorporate memory capacity constraints are also discussed.
Bonifaci, V., D'Angelo, G., & Marchetti-Spaccamela, A. (2017). Algorithms for Hierarchical and Semi-Partitioned Parallel Scheduling. In Proc. of the 31st Int. Parallel and Distributed Processing Symposium (pp.738-747). New York, NY : IEEE [10.1109/IPDPS.2017.22].