A data storage system is provided in which a migration plan generates migration plans for reaching a goal configuration from an initial configuration in a predetermined period of time. The migration plan initially makes terminal moves until no further terminal moves can be made. A shunt move is then made based on reducing the contention (the total size of the data stores that need to be moved onto a particular data stores device divided by the amount of excess capacity on the data storage device). The shunt is selected to lead to the lowest contention for the data storage system. Subsequently, the migration plan returns to making terminal moves to develop a migration plan. By determining existence and utilization dependencies of the various moves, independent moves are determined to be implemented in parallel with moves having dependencies. This produces parallelized migration plans which run much faster than sequential migration plans.