What would be the optimal algorithm for allocating the correct amount of time to each entry in a series of tasks?

[Eludium]

Given a series of daily tasks, each with a known deadline, for example:
- 1. Study for math exam - 19th of January
- 2. Study for language exam - 21th of January
- 3. Practice piano for event - 15th of March
- 4. Train for soccer match - 3rd of May

what would be the best algorithm for allocating daily work time to each task, so that the closer a deadline for a certain task is, the more time will be allocated for that particular task? The total amount of daily work is subjective, let's suppose this particular person spends 12 hours in total every day on their tasks.

For example, if you had two tasks and the deadline for the first one was tomorrow, the deadline for the second one was two days from now (double the amount of time left when compared to first task), it would mean you'd have to spend 75% of your today's working time on the first task and 25% on the second task (or, for the case of our particular person who works 12 hours each day: 9 hours on first task and 3 hours on the second task). If both tasks had the same deadline, the working time would be evenly split amongst them (50% both).

Other mention is that this algorithm would only run once per day (so every new day, the calculations are performed again based on the (new) amount of tasks and the updated time left until each of them's deadline (so in the example presented in the previous paragraph, it would mean that tomorrow, when the calculations are made again, only the 2nd task exists anymore and this task will be allocated 100% of the working time).

 

[tkhunny]

You'll have to be SUBSTANTIALLY more clear on what you consider "optimal". Depends on your goals.

Looks like you already have a plan based on the number of days until each event. Can you measure the optimality of that in ANY meaningful way?

Seems it should include more feedback on how things are actually going. One cannot simply let piano performance or on-field performance go to the last minute when it all becomes urgent.

May need to include penalties. If you totally choke the math exam, will you be ineffective in your other studies for two days?

 

[lev888]

Given a series of daily tasks, each with a known deadline, for example:
- 1. Study for math exam - 19th of January
- 2. Study for language exam - 21th of January
- 3. Practice piano for event - 15th of March
- 4. Train for soccer match - 3rd of May

what would be the best algorithm for allocating daily work time to each task, so that the closer a deadline for a certain task is, the more time will be allocated for that particular task? The total amount of daily work is subjective, let's suppose this particular person spends 12 hours in total every day on their tasks.

For example, if you had two tasks and the deadline for the first one was tomorrow, the deadline for the second one was two days from now (double the amount of time left when compared to first task), it would mean you'd have to spend 75% of your today's working time on the first task and 25% on the second task (or, for the case of our particular person who works 12 hours each day: 9 hours on first task and 3 hours on the second task). If both tasks had the same deadline, the working time would be evenly split amongst them (50% both).

Other mention is that this algorithm would only run once per day (so every new day, the calculations are performed again based on the (new) amount of tasks and the updated time left until each of them's deadline (so in the example presented in the previous paragraph, it would mean that tomorrow, when the calculations are made again, only the 2nd task exists anymore and this task will be allocated 100% of the working time).

Please clarify what calculation led you to the 75% - 25% split. If you have 2 days until the 2nd deadline, wouldn't you want to work 1 day on the first task and 1 day on the second task?

 

[Eludium]

I agree that my way of explaining the problem is unclear. I gave the OP an entire read again and there are indeed unclear passages that cannot be mathematically determined.

I will try to explain my problem in a simpler way: I am looking for a way to split the total daily working time amongst tasks, when there are multiple tasks with different deadlines. If I have an exam tomorrow and an exam two days from now, I don't want to study only for the first exam today. I want to study for both, but I definitely want to allocate more time to study for the first exam since it is tomorrow. I couldn't come up with a solution when it comes to exactly how much time I should spend on both of these tasks. I am unsure if there is a mathematical solution to my problem, but going by intuition alone feels like it will result in running out of time.

A day-to-day example that I can think of is software industry crunching. Sometimes, when the deadline for a product is closing in and the product is not ready for delivery, employess will begin to work extra hours each day in order to meet the expected deadline. As a result, this also means that the other projects are usually postponed. I am generally curious about the calculus performed by the head-of-operations. How do companies calculate exactly how much more hours of work to add daily when they enter crunch state? If they don't add extra work hours, but instead they cut hours from other projects and put these hours into the main project, how do they calculate the required amount of hours that they need to cut from the other projects?

 

[lev888]

I agree that my way of explaining the problem is unclear. I gave the OP an entire read again and there are indeed unclear passages that cannot be mathematically determined.

I will try to explain my problem in a simpler way: I am looking for a way to split the total daily working time amongst tasks, when there are multiple tasks with different deadlines. If I have an exam tomorrow and an exam two days from now, I don't want to study only for the first exam today. I want to study for both, but I definitely want to allocate more time to study for the first exam since it is tomorrow. I couldn't come up with a solution when it comes to exactly how much time I should spend on both of these tasks. I am unsure if there is a mathematical solution to my problem, but going by intuition alone feels like it will result in running out of time.

A day-to-day example that I can think of is software industry crunching. Sometimes, when the deadline for a product is closing in and the product is not ready for delivery, employess will begin to work extra hours each day in order to meet the expected deadline. As a result, this also means that the other projects are usually postponed. I am generally curious about the calculus performed by the head-of-operations. How do companies calculate exactly how much more hours of work to add daily when they enter crunch state? If they don't add extra work hours, but instead they cut hours from other projects and put these hours into the main project, how do they calculate the required amount of hours that they need to cut from the other projects?

Easy - we are required to provide estimates and current status of each project. Both of these measures are absent from your setup.