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

翻译：在将工人分配给任务的简单模型中，每一个最小化最高负载工人与最低负载工人之间负载差的解，实际上同时最小化了最大负载并最大化了最小负载。这可以看作是多拟阵优化标准结果的推论。我们证明，类似现象在表述简单且不具有任何多拟阵结构的相近模型中仍然存在。