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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