Problem 17
Problem 16.1-2:
Activity Time Immediate
Activity (weeks) Predecessor(s)
A 3 none
B 4 A
C 2 B
D 5 B
E 4 C
F 3 D
G 2 E, F
[pic]
A-B-C-E-G 15 weeks
A-B-D-F-G 17 weeks
2. a. completion time for the project is 17 weeks
2. b. critical path: A-B-D-F-G
Problem 16.4-8:
|Activity |Immediate |Optimistic |Most Likely |Pessimistic |Expected |Variance |
| |Predecessor(s) |Time |Time |Time |Time | |
| | |(weeks) |(weeks) |(weeks) |(weeks) | |
|A |None |3 |6 |9 |6.00 |1.00 |
|B |A |3 |5 |7 |5.00 |0.44 |
|C |A |4 |7 |12 |7.33 |1.78 |
|D |B |4 |8 |10 |7.67 |1.00 |
|E |C |5 |10 |16 |10.17 |3.36 |
|F |D, E |3 |4 |5 |4.00 |0.11 |
|G |D, E |3 |6 |8 |5.83 |0.69 |
|H |F |4 |6 |10 |6.33 |1.00 |
|I |G |5 |8 |11 |8.00 |1.00 |
|J |H, I |3 |3 |3 |3.00 |0.00 |
| | | | | | | |
| | | | | | | |
| | | | | | | |
[pic]
|Path |Expected |Variance |38 week |38 week |42 week |42 week |
| |Completion | |z-value |probability |z-value |probability |
| |Time | | | | | |
|ABDFHJ |32.00 |3.56 |3.17 |0.99+ |5.29 |0.99+ |
|ABDGIJ |35.50 |4.13 |1.23 |0.89 |3.20 |0.99+ |
|ACEFHJ |36.83 |7.58 |0.42 |0.66 |1.88 |0.97 |
|ACEGIJ* |40.33** |7.83 |-0.83 |0.20 |0.60*** |0.73**** |
* Critical path is A-C-E-G-I-J.
** Expected project completion time 40.33 weeks.
*** Probability of completing project in 38 weeks or less is .20 or 20%.
**** Probability of completing project in 42 weeks or less is 0.73 or 73%.
Problem 16.9-10:
|Activity |Normal |Normal |Crash |Crash |Maximum |Crash Cost per Week |
| |Time |Cost |Time |Cost |Weeks |($) |
| |(weeks) |($) |(weeks) |($) |Reduced | |
|A |4 |800 |3 |1,200 |1 |400 |
|B |3 |900 |2 |1,000 |1 |100 |
|C |5 |1,250 |3 |2,250 |2 |500 |
|D |2 |800 |2 |800 |0 |0 |
|E |5 |1,500 |4 |2,000 |1 |500 |
|F |6 |2,000 |5 |3,000 |1 |1,000 |
|G |4 |600 |3 |900 |1 |300 |
|H |3 |900 |3 |900 |0 |0 |
[pic]
A-B-E-G-H 19 weeks
A-C-E-G-H 21 weeks
A-C-F-G-H 22 weeks critical path
A-D-F-G-H 19 weeks
Crashing:
1. Consider A, C, F, and G; reduce G by 1 week at a cost of $300.
ABEGH: 18 weeks. ACEGH: 20 weeks; ACFGH: 21 weeks; ADFGH: 18 weeks.
2. Consider A, C, and F; reduce A by 1 week at a cost of $400.
ABEGH: 17 weeks. ACEGH: 19 weeks; ACFGH: 20 weeks; ADFGH: 17 weeks.
3. Consider C and F; reduce C by 1 week at a cost of $500.
ABEGH: 17 weeks. ACEGH: 19 weeks; ACFGH: 19 weeks; ADFGH: 18 weeks.
Thus, crashing activities G, A, and C reduces the project completion time by 3 weeks (22 weeks down to 19 weeks) at a cost of $1,200.
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