MHB Some works can be done simultaneously

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The discussion revolves around determining the minimum time required to complete a building project involving nodes A through I, where certain tasks can be performed simultaneously. The participants explore the dependencies between tasks, noting that completing tasks B, C, and D simultaneously can optimize the overall timeline. They emphasize the importance of tracking completion times for each task to ensure efficient scheduling. The conversation highlights the necessity of completing all tasks leading up to the final work, J, to finish the project. Ultimately, a strategic approach to managing task dependencies and simultaneous work is essential for minimizing project duration.
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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