Understanding Critical Path and Crashing

Why are the durations for the paths calculated as the sum of the activity durations without considering the interdependencies? The durations given are:

  • A-D-F-H = 22 weeks
  • B-D-F-H = 21 weeks
  • C-E-G-H = 23 weeks
  • C-E-G-I = 21 weeks.

Shouldn’t the durations instead be:

  • A-D-F-H = 23 weeks
  • B-D-F-H = 23 weeks
  • C-E-G-H = 23 weeks
  • C-E-G-I = 21 weeks?

Shouldnt the durations for the paths instead be:

A-D-F-H=23 weeks
B-D-F-H-23 weeks
C-E-G-H=23 weeks
C-E-G-I=21 weeks

For example, if we take the path A-D-F-H, activity H cannot start until both F and G are completed. Since G finishes last, at 19 weeks, H should start at 19 weeks and end at 23 weeks.

Since crashing is only applied to the critical path, and C-E-G-H is initially the critical path, we might consider crashing activity E because it costs less and would save indirect costs. However, reducing the duration of E will cause C-E-G-H to no longer be the critical path, as the first 3 paths also have a duration of 23 weeks.

so shouldnt the activity that should be crashed must be common to the first three critical paths (A-D-F-H, B-D-F-H, and C-E-G-H), which is activity H?