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“学越千山（四三）：非标准指派问题”，
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Learning over a thousand mountains(43):Non-standard assignment problem，
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思维导图
Mind mapping
非标准指派问题
Non-standard assignment problem
最大化指派问题：在标准的指派问题中，我们通常是寻找总成本最小的方案。然而，在最大化指派问题中，我们的目标则是寻找总效率或总收益最大的方案。为了解决这个问题，一种常见的做法是将效率矩阵中的元素进行转换，使得最大化问题变为最小化问题，然后利用如匈牙利法等算法进行求解。
Maximizing assignment problem: In standard assignment problems, we usually search for the solution with the lowest total cost. However, in the maximization assignment problem, our goal is to find the solution with the highest total efficiency or total benefit. To solve this problem, a common approach is to transform the elements in the efficiency matrix, making the maximization problem a minimization problem, and then use algorithms such as the Hungarian method to solve it.
人数与事数不等的指派问题：当需要分配的任务数量与可用的人员数量不相等时，就会产生此类问题。在这种情况下，我们可以采取添加虚拟人员或虚拟任务的方式，使得任务数量和人员数量相等，然后应用标准的指派问题求解方法。
The assignment problem of unequal number of people and tasks: This type of problem arises when the number of tasks to be assigned is not equal to the number of available personnel. In this case, we can adopt the approach of adding virtual personnel or virtual tasks, so that the number of tasks and personnel is equal, and then apply standard assignment problem solving methods.
一个人可做几件事的指派问题：在某些情况下，一个人可能同时承担多个任务。为了处理这种情况，我们可以将这个人视为多个“虚拟人”，每个“虚拟人”负责一个任务，然后应用标准的指派问题求解方法。
The assignment problem of how many things a person can do: In some cases, a person may take on multiple tasks simultaneously. To handle this situation, we can consider this person as multiple "virtual humans", each responsible for a task, and then apply standard assignment problem solving methods.
某人一定不能做某事的指派问题：在实际应用中，可能存在某些限制条件，例如某个人不能执行某个任务。为了处理这种情况，我们可以在效率矩阵中将相应的元素设置为一个非常大的数M，表示这个人不能执行这个任务。在求解过程中，M将不会被选中。
The assignment problem where someone must not do something: In practical applications, there may be certain constraints, such as someone being unable to perform a task. To handle this situation, we can set the corresponding elements in the efficiency matrix to a very large number M, indicating that this person cannot perform the task. During the solving process, M will not be selected.
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翻译：百度翻译
参考资料：百度百科，
《管理运筹学》
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