Using the activity data below, identify the critical path and the total project duration.

Activity                       Duration (Days) Predecessors
A                                 4 -
B                                 2 A
C                                 4 A
D                                 2 B
E                                  5 B
F                                  3 D, E
G                                 2 F, C
H                                 3 G
I                                   4 E
J                                  2 H, I

Question

Using the activity data below, identify the critical path and the total project duration.

Activity                       Duration (Days)                 Predecessors 
A                                 4                                           -
B                                 2                                          A         
C                                 4                                          A
D                                 2                                          B
E                                  5                                         B
F                                  3                                         D, E
G                                 2                                         F, C
H                                 3                                        G
I                                   4                                       E
J                                  2                                        H, I

BlackTom AI · Accepted Answer

Critical Path Method finds the longest sequence of dependent activities that determines the project duration. Relevant concepts: forward pass (compute earliest finish times), when an activity has multiple predecessors the earliest start is the maximum of their finish times, and the critical path is the chain of activities that produces the project’s longest finish time (zero total float).

Step-by-step forward-pass calculation (showing intermediate steps):
- A: duration 4 → earliest finish (EF_A) = 4.
- B: successor of A, duration 2 → EF_B = EF_A + 2 = 4 + 2 = 6.
- C: successor of A, duration 4 → EF_C = 4 + 4 = 8.
- D: successor of B, duration 2 → EF_D = EF_B + 2 = 6 + 2 = 8.
- E: successor of B, duration 5 → EF_E = EF_B + 5 = 6 + 5 = 11.
- F: successors D and E → earliest start for F = max(EF_D, EF_E) = max(8, 11) = 11; duration 3 → EF_F = 11 + 3 = 14.
- G: successors F and C → earliest start for G = max(EF_F, EF_C) = max(14, 8) = 14; duration 2 → EF_G = 14 + 2 = 16.
- H: successor of G, duration 3 → EF_H = EF_G + 3 = 16 + 3 = 19.
- I: successor of E, duration 4 → EF_I = EF_E + 4 = 11 + 4 = 15.
- J: successors H and I → earliest start for J = max(EF_H, EF_I) = max(19, 15) = 19; duration 2 → EF_J = 19 + 2 = 21.

Why the correct path is A–B–E–F–G–H–J:
- The chain A (4) → B (2) → E (5) → F (3) → G (2) → H (3) → J (2) sums to 21 days (4+2+5+3+2+3+2 = 21) and produces the project EF of 21. At each convergence the longer predecessor determined the successor’s earliest start, so this chain controls the schedule and thus is the critical path.

Why other options are incorrect:
- A–C–G–H–J sums to 15 days (4+4+2+3+2 = 15) — shorter, not critical.
- A–B–D–F–G–H–J sums to 18 days (4+2+2+3+2+3+2 = 18) — shorter.
- A–B–E–I–J sums to 17 days (4+2+5+4+2 = 17) — shorter.
All three therefore do not determine the project completion time.

Conclusion: Critical Path = A – B – E – F – G – H – J; Project Duration = 21 days, which matches the provided correct answer.

Using the activity data below, identify the critical path and the total project duration. Activity Duration (Days) Predecessors A 4 - B 2 A C 4 A D 2 B E 5 B F 3 D, E G 2 F, C H 3 G I 4 E J 2 H, I单项选择题

类似问题

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