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：在将工人分配至任务的简单模型中，每个最小化最繁忙工人与最空闲工人之间负载差异的解，实际上同时最小化了最大负载并最大化了最小负载。这可视作拟阵多面体优化标准结论的推论。我们证明，在表述简洁且不具备任何拟阵多面体结构的邻近模型中，类似现象依然存在。