Question

Problem 9-19 (Algorithmic)

The product development group at Landon Corporation has been working on a new computer software product that has the potential to capture a large market share. Through outside sources, Landon's management learned that a competitor is working to introduce a similar product. As a result, Landon's top management increased its pressure on the product development group. The group's leader turned to PERT/CPM as an aid to scheduling the activities remaining before the new product can be brought to the market. The project network is as follows:

The activity time estimates (in weeks) are as follows:

Activity		Optimistic		Most Probable		Pessimistic
A		2.0		4.0		6.0
B		4.0		4.5		8.0
C		3.0		5.0		7.0
D		1.0		3.0		5.0
E		6.0		11.0		16.0
F		6.5		8.5		13.5
G		3.5		6.0		8.5
H		4.0		6.0		14.0
I		1.0		2.5		7.0
J		4.0		5.0		6.0

1. Develop an activity schedule for this project and identify the critical path activities.
   If required, round your answers to two decimal places. If your answer is zero enter “0”.
   

   Activity		Expected Time		Variance
   A
   B
   C
   D
   E
   F
   G
   H
   I
   J

   Earliest

   Latest

   Earliest

   Latest

   Critical

   Activity

   Start

   Start

   Finish

   Finish

   Slack

   Activity

   A

   No

   B

   Yes

   C

   No

   D

   No

   E

   Yes

   F

   No

   G

   No

   H

   Yes

   I

   No

   J

   Yes

   
   Critical Path: B-E-H-J
   
2. What is the probability that the project will be completed so that Landon Corporation may introduce the new product within 25 weeks? Within 30 weeks?
   
   Expected project completion time =  weeks. If required, round your answer to two decimal places.
   
   . If required, round your answer to two decimal places.
   
   P(25 weeks) = . If required, round your answer to four decimal places.
   
   P(30 weeks) = . If required, round your answer to four decimal places.

Answer 1

It is given that the critical path is B-E-H-J

Following may be noted :

Expected duration of an activity = ( Most probable duration + 4 x Pessimistic duration + Pessimistic duration)/6

Variance of an activity = ( Pessimistic duration – Most probable duration)^2/36

Refer below table which highlights data about calculated expected duration and variance of activities on critical path.

Expected duration of critical path = Sum of expected durations of B,E,H,J = 28

Variance of critical path = Sum of variances of B,E,H,J = 6.11

Therefore, Standard deviation of critical path = Square root ( variance ) = Square root ( 6.11) = 2.47

Activity	Optimistic	Most probable	Pessimistic	Expected duration	Variance
B	4	4.5	8	5	0.44
E	6	11	16	11	2.78
H	4	6	14	7	2.78
J	4	5	6	5	0.11
			Total:	28	6.11

Let Z value of probability that project will be completed in 25 weeks = Z1

Therefore,

28 + 6.11.Z1 = 25

Or, 6.11.Z1 = - 3

Or, Z1 = - 3/6.11 = - 0.491

Corresponding probability for Z1 s derived from Z table = 0.3121

P( 25 weeks ) = 0.3121

Let Z value of probability that the project will be completed in 30 weeks = Z2

Therefore ,

28 + 6.11.Z2 = 30

Or, 6.11.Z2 = 2

Or, Z2 = 2/6.11 = 0.327 ( 0.33 rounded to 2 decimal places)

Corresponding probability for Z = 0.33 as derived from Z table is 0.6293

P( 30 weeks ) = 0.6293