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Technical Report: UTEP-CS-20-111

Published in International Mathematical Forum, 2020, Vol. 15, No. 8, pp. 401-406.


In practice, we sometimes end up in a situation when we are late on several relatively small tasks. We cannot finish them all, so which ones should we do first? We show that in general, this is an NP-complete problem. In the typical situation when all the tasks are of approximately the same importance and requires approximately the same time to finish, we can have an explicit solution to this problem. In a nutshell, the resulting (somewhat counterintuitive) recommendation is to start with things which are not yet late or only a few days late. Actually, this recommendation makes sense: on a task on which we are already 30 days late, making it 31 days late will not change much, but if a task is due today, we want to finish it today, to avoid late penalty.

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