Some works can be done simultaneously

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SUMMARY

The discussion focuses on project management involving nodes $A, B, C, D, E, F, G, H, I$, where tasks $B, C, D, E, F, G, H, I$ are interdependent. The cost function $p(a,b)$ indicates the days required for task $b$ to finish after task $a$ is completed. It is established that tasks can be executed simultaneously, allowing for optimization of the overall project timeline. The participants conclude that to finish the entire project, all tasks must be completed, but certain tasks can be done concurrently to minimize total completion time.

PREREQUISITES
  • Understanding of project management concepts, specifically task dependencies
  • Familiarity with graph theory, particularly directed acyclic graphs (DAGs)
  • Knowledge of scheduling algorithms for optimizing task completion
  • Experience with project management tools that track task timelines
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  • Research project scheduling techniques, such as Critical Path Method (CPM)
  • Learn about task dependency graphs and their applications in project management
  • Explore software tools for project management, like Microsoft Project or Asana
  • Study optimization algorithms for parallel task execution
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Project managers, software developers, and anyone involved in coordinating complex tasks that require efficient scheduling and resource allocation.

evinda
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Hello! (Wave)

The nodes $A,B,C,D,E,F,G,H,I$ are given and are related as follows:View attachment 5084

The nodes $B,C,D,E,F,G,H,I$ are tasks that are done so that a work is completed , for example a building, and the cost $p(a,b)$ are the days that are needed so that the work $b$ finishes if the work $a$ has already finished.
For example, $p(A,B)=22$: 22 days are needed so that the work B is done.
$p(B,E)$: 16 days are needed so that the work E is done if the work B has finished.

Of course, some works can be done simultaneously.

Find the minimum time needed so that the building gets finished.How do we use the fact that some works can be done simultaneously?
 

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Hey evinda! (Smile)

Suppose we would only need $A,B,C$.
How much time would that take? (Wondering)
 
I like Serena said:
Hey evinda! (Smile)

Suppose we would only need $A,B,C$.
How much time would that take? (Wondering)

22 days? (Thinking)
 
evinda said:
22 days? (Thinking)

Exactly!
So how long will it take to complete $D, E$ additionally? (Wondering)
 
I like Serena said:
Exactly!
So how long will it take to complete $D, E$ additionally? (Wondering)

So in this case do we have to complete all the works $B, C, \dots, I$ so that the whole work is completed?

If so, then don't we make $B, C, D$ simultaneously and if we have completed for example $D$ we start with one of $G$ or $F$ ? (Thinking)
 
evinda said:
So in this case do we have to complete all the works $B, C, \dots, I$ so that the whole work is completed?

If so, then don't we make $B, C, D$ simultaneously and if we have completed for example $D$ we start with one of $G$ or $F$ ? (Thinking)

How so?
Can't we complete just $B,C,D,E$? (Wondering)

And yes, we should indeed complete $B, C, D$ simultaneously.
 
I like Serena said:
How so?
Can't we complete just $B,C,D,E$? (Wondering)

Don't we have to reach at $J$ , which is the last work?
 
evinda said:
Don't we have to reach at $J$ , which is the last work?

Yes... we're building up to that...
We can create a timeline and keep track of the earliest time that each part can be completed. (Thinking)
 

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