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 (ILP) formulation for the job assignment subproblem, and show how to turn arbitrary ILP solutions into valid schedules. We also derive a polynomial-time 2-approximation algorithm for the problem. Extensions that incorporate memory capacity constraints are also discussed.

我们提出一种用于在并行计算机设置中调度作业的模型，该模型通过假设作业的处理时间可能取决于要在其中迁移作业的特定计算机集来考虑迁移成本。对于makepan最小化目标，该模型概括了经典的调度问题（例如无关的并行机器调度）以及新颖的问题（例如半分区和集群调度）。对于分层的机器族，我们为作业分配子问题推导了紧凑的整数线性规划（ILP）公式，并说明了如何将任意ILP解决方案转换为有效的计划。我们还导出了该问题的多项式时间2逼近算法。还讨论了包含内存容量限制的扩展。