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SapphireGirlFlag for United States of America asked on

Math behind scheduling parallel tasks to minimize the performance time

Does anyone know the math behind how I can figure out how to scheduling parallel tasks to minimize the time to perform all of the required tasks.

Is this an optimization problem.  Where can I find out how to do this type if problem?

Thanks in advance
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8/22/2022 - Mon

you can use round robin approach. Some operating systems uses this apprach to process the simultaneous works.

I am not clear as to what round robin approach is.  What I need is a way basically using logic to understand the idea behind how to solve this type of problem.  For example.  If I have shared resources and I have tasks on these shared resources to complete,  What kind of problem, some type of optimization I am guessing, can I set up to solve this type of scheduling problem.

Does that make sense.  I am looking for some examples of problems like this so I can understand the idea behind the logic of solving this type of problem.

For a basic optimization problem, I used the Hungarian method of minimizing.  That could work given no constraints.

What happens if I have constraints?

For example, Find the minimum amount of processing time to run 3 programs on 3 computers simultaneously given the fact that computer 1 must be run between 7-9 am and computer 3 must be run between 6-7 pm.

Say the following is true
                                  Computer 1              Computer 2                   Computer 3
Application 1 takes    10 minutes                     20                                    30  
Application 2 takes    20                                  10                                      40
Application 3 takes    5                                     5                                     10

Using the Hungarian method to solve the minimize problem I get the following:

Run A1 on C1
Run A2 on C2
Run A3 on C3

Now, given constraints on Computer 1, Computer 2 and Computer 3 and only 1 solution for optimization where do I go from here.  Has anyone done this type of problem?  I hope I am looking at it in the correct way.
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The question was not the most well formed but I appreciate the help.
Thank you

To answer a minimum question, I set up the problem in a matrices ( must be a square matrices) and used the Hungarian method that can be found in any linear algebra book.