There’s a trendy classification of tasks into important and urgent, used to describe a common pitfall of focusing on the urgent but unimportant.
But the real question is: for any given task, what is the cost of delaying it by a day? Ideally you should draw out the whole function of dollars lost over time, then decide tasks by optimizing for dollars over time in the usual way. Of course this is hard to do in general, especially for big tasks with uncertain outcomes, but it’s not clear that splitting these ‘loss functions’ into the buckets of important and urgent is particularly useful.
When delegating tasks it’s especially important to be clear about your loss function. Usually managers will try to amplify the importance or urgency of the task they’re delegating, but not make clear the loss function - how bad is it exactly if the bugfix is shipped tomorrow instead of tonight? Deadlines and classifications into low/medium/high priority are the best tools we seem to have, but they’re very far from aligning the worker’s incentive with the true loss function.
Another instance is the california company that fixes highways ahead of time (Myers & Sons, https://www.ktvu.com/news/california-contractor-earns-8m-bonus-for-early-finish-on-san-francisco-overpass) by creating huge incentives for themselves to finish quickly. A new highway being completed 1 day early is potentially worth millions, obviously the construction company should internalize this loss function instead of being held to some binary deadline.
Tool idea: project management software or plugin that allows easy drawing of loss functions for tasks. Ideally denominated in dollars and the employee gets paid a fraction of $ saved by doing things earlier, but this runs into incentive problems like the equal compensation principle; just getting real clarity on what the costs of delaying are across tasks will help massively in prioritization.