What is the duration of the entire project?

Computer Science
What is the duration of the entire project?

ScanSolve AI Answer

Answer

20 weeks

To determine the duration of the entire project, we need to identify the critical path using the Early Start (ES) and Early Finish (EF) times for each activity. The critical path is the longest sequence of activities in the project network, and its duration determines the minimum project completion time.

Step 1: Calculate the Early Start (ES) and Early Finish (EF) for each activity. The ES for an activity is the maximum EF of its immediate predecessors. If an activity has no predecessors, its ES is 0. The EF for an activity is its ES plus its duration.

ActivityDuration(weeks)PredecessorsES(weeks)EF(weeks)A2−00+2=2B3A22+3=5C4A22+4=6D2A22+2=4E1C,Dmax⁡(EFC,EFD)=max⁡(6,4)=66+1=7F2D44+2=6G4E77+4=11H2G1111+2=13I4F,Hmax⁡(EFF,EFH)=max⁡(6,13)=1313+4=17J3B,Imax⁡(EFB,EFI)=max⁡(5,17)=1717+3=20\begin{array}{|c|c|c|c|c|} \hline Activity & Duration (weeks) & Predecessors & ES (weeks) & EF (weeks) \\ \hline A & 2 & - & 0 & 0+2=2 \\ B & 3 & A & 2 & 2+3=5 \\ C & 4 & A & 2 & 2+4=6 \\ D & 2 & A & 2 & 2+2=4 \\ E & 1 & C, D & \max(EF_C, EF_D) = \max(6, 4) = 6 & 6+1=7 \\ F & 2 & D & 4 & 4+2=6 \\ G & 4 & E & 7 & 7+4=11 \\ H & 2 & G & 11 & 11+2=13 \\ I & 4 & F, H & \max(EF_F, EF_H) = \max(6, 13) = 13 & 13+4=17 \\ J & 3 & B, I & \max(EF_B, EF_I) = \max(5, 17) = 17 & 17+3=20 \\ \hline \end{array}

Step 2: Identify the critical path. The critical path is the sequence of activities that results in the latest Early Finish time for the project. By tracing back from the final activity (J) through the predecessors that determined its ES, we find the critical path.

  • J's ES is 17, which comes from I (since EFI=17>EFB=5EF_I = 17 > EF_B = 5).
  • I's ES is 13, which comes from H (since EFH=13>EFF=6EF_H = 13 > EF_F = 6).
  • H's ES is 11, which comes from G.
  • G's ES is 7, which comes from E.
  • E's ES is 6, which comes from C (since EFC=6>EFD=4EF_C = 6 > EF_D = 4).
  • C's ES is 2, which comes from A.
  • A's ES is 0.

Therefore, the critical path is A →\to C →\to E →\to G →\to H →\to I →\to J.

Step 3: Calculate the duration of the critical path. Sum the durations of the activities on the critical path:

Duration=Duration(A)+Duration(C)+Duration(E)+Duration(G)+Duration(H)+Duration(I)+Duration(J)Duration=2weeks+4weeks+1week+4weeks+2weeks+4weeks+3weeksDuration=20weeksDuration = Duration(A) + Duration(C) + Duration(E) + Duration(G) + Duration(H) + Duration(I) + Duration(J) \\ Duration = 2 weeks + 4 weeks + 1 week + 4 weeks + 2 weeks + 4 weeks + 3 weeks \\ Duration = 20 weeks

The duration of the entire project is 20weeks\boxed{20 weeks}.

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Quick Answer

To determine the duration of the entire project, we need to identify the critical path using the Early Start (ES) and Early Finish (EF) times for each activity.

What is the duration of the entire project?
Computer Science

This computer science problem involves algorithmic thinking and programming concepts. The solution below explains the approach, logic, and implementation step by step.

ScanSolve AI Answer
To determine the duration of the entire project, we need to identify the critical path using the Early Start (ES) and Early Finish (EF) times for each activity. The critical path is the longest sequence of activities in the project network, and its duration determines the minimum project completion time. Step 1: Calculate the Early Start (ES) and Early Finish (EF) for each activity. The ES for an activity is the maximum EF of its immediate predecessors. If an activity has no predecessors, its ES is 0. The EF for an activity is its ES plus its duration. |c|c|c|c|c| Activity & Duration (weeks) & Predecessors & ES (weeks) & EF (weeks) \\ A & 2 & - & 0 & 0+2=2 \\ B & 3 & A & 2 & 2+3=5 \\ C & 4 & A & 2 & 2+4=6 \\ D & 2 & A & 2 & 2+2=4 \\ E & 1 & C, D & (EF_C, EF_D) = (6, 4) = 6 & 6+1=7 \\ F & 2 & D & 4 & 4+2=6 \\ G & 4 & E & 7 & 7+4=11 \\ H & 2 & G & 11 & 11+2=13 \\ I & 4 & F, H & (EF_F, EF_H) = (6, 13) = 13 & 13+4=17 \\ J & 3 & B, I & (EF_B, EF_I) = (5, 17) = 17 & 17+3=20 \\ Step 2: Identify the critical path. The critical path is the sequence of activities that results in the latest Early Finish time for the project. By tracing back from the final activity (J) through the predecessors that determined its ES, we find the critical path. J's ES is 17, which comes from I (since EF_I = 17 > EF_B = 5). I's ES is 13, which comes from H (since EF_H = 13 > EF_F = 6). H's ES is 11, which comes from G. G's ES is 7, which comes from E. E's ES is 6, which comes from C (since EF_C = 6 > EF_D = 4). C's ES is 2, which comes from A. A's ES is 0. Therefore, the critical path is A C E G H I J. Step 3: Calculate the duration of the critical path. Sum the durations of the activities on the critical path: Duration = Duration(A) + Duration(C) + Duration(E) + Duration(G) + Duration(H) + Duration(I) + Duration(J) \\ Duration = 2 weeks + 4 weeks + 1 week + 4 weeks + 2 weeks + 4 weeks + 3 weeks \\ Duration = 20 weeks The duration of the entire project is 20 weeks.