Question 1. Task scheduling

(a) For the task schedule restrictions shown in the table below
(a) What is the length of the critical path for the project tasks, and what are the tasks along that path?

Task id Time estimate (hours) Depends on ... Assigned to
A 5 - Beri
B 5 A Finn
C 5 A Beri
D 10 B Finn
E 5 B Huc
F 5 C Beri
G 10 C Lee
H 10 F Beri
I 5 E, H Beri
J 5 D, G Finn
K 7 I, J Finn 

SAMPLE SOLUTION

Here's an outline of the task ordering, and (based on it)
   a table of the earliest start/end times for each task
                                    task  start  end
      (from B)-->E                    A     0      5
                  \                   B     5     10
                   \                  C     5     10
A--->C--->F--->H--->I--->K            D    10     20  
 \    \                 /             E    10     15
  \    \               /              F    10     15
   \    G-------.     /               G    10     20
    \            \   /                H    15     25
     \            \ /                 I    25     30 (had to wait for H)
      B---->D----->J                  J    20     25
       \                              K    30     37 (had to wait for I)
        \
        (to E above)

The critical path (tasks where any delay also delays the project as 
   a whole) is A,C,F,H,I,K and has length 37 (the sum of the times
   taken at each stage on the path).

(b)Suppose you are managing the project, but the time estimates above were provided by the people assigned to the tasks (Huc, Lee, Barry, and Finn).

You know that Huc and Lee's estimates tend to be pretty accurate, and Beri often comes in under her estimates, but Finn has a tendency to take up to 50% longer than his estimates.

Does this change your assessment of what the critical path is and what the projected completion time would be? Justify your answer. 
SAMPLE SOLUTION

We aren't given any specific metrics for speeding up anyone's estimates,
   but we are given reason to take Finn's estimates with a healthy dose 
   of caution.   If we take the cautious approach and assume Finn will
   take 50% longer for each of his tasks while everyone else comes in on
   time, then we get the following revised table:

   task  time  start   end
     A    5.0   0.0    5.0
     B    7.5   5.0   12.5
     C   10.0   5.0   10.0
     D   15.0  12.5   27.5
     E    5.0  12.5   17.5
     F    5.0  10.0   15.0
     G   10.0  10.0   20.0
     H   10.0  15.0   25.0
     I    5.0  25.0   30.0
     J    7.5  27.5   35.0 (had to wait for D)
     K   10.5  35.0   45.5 (had to wait for J)

Note that we now have a new critical path, A->B->D->J->K
   with length 45.5, significantly slower than the original.

(It is also worth noting that the only two tasks NOT on either
   critical path are E and G ... those look like the only two
   tasks we can safely delay or take extra time on without 
   delaying the project completion under either model.)