Casesolutions09 (1)Pert Coleman

Solutions to Case Problems

Chapter 9 Project Scheduling: PERT/CPM Case Problem: R.C. Coleman 1.

R.C. R.C. Col Coleman eman's 's Pro Project ject Net Network  work 

D

A

Start

C

B

E

F

G

Activity A B C D E F G H I J K

Activity A B C D E F G H I J K

I

Earliest Start 0 0 9 13 13 23 13 29 29 35 39

K

H

J

Expected Time 6 9 4 12 10 6 8 6 7 4 4

Latest Start 3 0 9 17 13 23 21 29 32 35 39

Earliest Finish 6 9 13 25 23 29 21 35 36 39 43

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Finish

Variance 0.44 2.78 0.44 7.11 1.00 0.44 7.11 0.44 2.78 0.11 0.44

Latest Finish 9 9 13 29 23 29 29 35 39 39 43

Slack   3 0 0 4 0 0 8 0 3 0 0

Critical Activity Yes Yes Yes Yes Yes Yes Yes

Chapter 9

The expected project completion time is 43 weeks. The critical path activities are B-C-E-F-H-J-K. The variance of the critical path is 5.67.

 z  =

40 − 43 5.67

= −1.26

Area = 0.3962 P(T  ≤ 40) = 0.5000 - 0.3962 = 0.1038

Given the above calculations, we can conclude that there is about a 10% chance that the project can be completed in 40 weeks or less. Coleman should consider crashing project activities. 2.

20' 0'

Planne! pro"e#t #ompletion time

$esires 40-%ee&  #ompletion time

For 80% chance,  z = +0.84 Thus 40 −  E (T ) 5.67

=

0.4

Solve for  E (T ) = 38 weeks. R.C. Coleman should crash activities to reduce the expected project completion time to 38 weeks. 3.

In this section, we will use expected activity times as normal times and use a linear programming model based on expected times to make the crashing decisions. Let

xi = the completion time for activity i  yi = the amount of crash time for activity i

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Solutions to Case Problems

Min 450 yA  + 400 yB  + 600 yC  + 300 yD  + 1000 yE  + 550 yF  + 750 yG  + 700 yH  + 800 yI + 400 yJ + 500 yK s.t.  xA +  yA

≥

6

 xK

≤

38

 xB +  yB

≥

9

 yA

≤

2

 xC +  yC –  xA

≥

4

 yB

≤

2

 xC +  yC –  xB

≥

4

 yC

≤

2

 xD +  yD –  xC

≥

12

 yD

≤

4

 xE +  yE –  xC

≥

10

 yE

≤

3

 xF +  yF –  xE

≥

6

 yF

≤

2

 xG +  yG –  xC

≥

8

 yG

≤

3

 xH +  yH –  xF

≥

6

 yH

≤

2

 xH +  yH –  xG

≥

6

 yI

≤

3

≤

1

 xI +  yI –  xD

≥

7

 yJ

 xI +  yI –  xF

≥

7

 yK

 xJ +  yJ –  xH

≥

4

All  xi, yi

 xK +  yK –  xI

≥

4

 xK +  yK –  xJ

≥

4

≤

1 ≥

0

The optimal crashing decisions are as follows: Crash Activity B F J K

Weeks 2 1 1 1 Total

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Cost 800 550 400 500 2250

Chapter 9

A revised activity schedule based on these crashing decisions is as follows:

Activity A B C D E F G H I J K

Earliest Start 0 0 7 11 11 21 11 26 26 32 35

Latest Start 1 0 7 14 11 21 18 26 28 32 35

Earliest Finish 6 7 11 23 21 26 19 32 33 35 38

Latest Finish 7 7 11 26 21 26 26 32 35 35 38

Slack   1 0 0 3 0 0 7 0 2 0 0

Critical Activity Yes Yes Yes Yes Yes Yes Yes

The student should comment on the fact that the crashing decisions may alter the variance in the project completion time. By defining revised optimistic, most probable, and pessimistic times for crashed activities B, F, J, and K, a revised variance in the project completion time can be found. Using this result, a revised probability of a 40-week completion time can be computed.

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