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In a simple model of assigning workers to tasks, every solution thatminimizes the load difference between the most loaded worker and the leastloaded one actually minimizes the maximal load and maximizes the minimal load.This can be seen as a consequence of standard results of optimization overpolymatroids. We show that similar phenomena still occur in close models,simple to state, and that do not enjoy any polymatroid structure.

Maximal workload, minimal workload, maximal workload difference: optimizing all criteria at once