# 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?

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SapphireGirl
tigin44

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

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.
SapphireGirl

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.
tigin44

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SapphireGirl

The question was not the most well formed but I appreciate the help.
Thank you
SapphireGirl

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.
Project Management

Project management is the discipline of carefully projecting or planning, organizing, motivating and controlling resources to achieve specific goals and meet specific success criteria. A project is a temporary endeavor designed to produce a unique product, service or result with a defined beginning and end (usually time-constrained, and often constrained by funding or deliverables) undertaken to meet unique goals and objectives, typically to bring about beneficial change or added value.

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