Question

(a). State TWO contrasts between Pure Project Teams and Matrix Project Teams. Give an example of each.

3(b). The following data relates to the activities required for a project. Since exact duration for each activity is not known for certain, three time estimates were made, namely: - the optimistic, most likely and pessimistic time estimates. The precedence relationships are also shown in the data below. You will need to analyze this problem using what you learned in Chapter 18 of the text as well as in your statistics class on probability distributions. A table of Normal distribution will be provided to you.

		TIME ESTIMATES (days)
ACTIVITY	PREDECSOR
		OPTIMISTIC	MOST LIKELY	PESSIMISTIC
A	--	36	50	56
B	--	45	60	84
C	A	36	45	46
D	A,B	26	40	42
E	C	24	36	36
F	D,E	58	70	82

        

Complete the following information

Activity	Expected Duration	Variance of Duration
A
B
C
D
E
F

Draw (electronically) the AON network for this project. Using the expected durations as the activity duration, conduct CPM analysis of the network.

What is the estimated (i) expected (mean) time and (ii) Standard Deviation for project completion? What is the probability distribution of the project completion time? Why?

What is the probability that the critical path for this project will be completed within 210 days? 200 days?

If the client is comfortable with a 98.50 % of completing the project, what completion time would you recommend? [Please show your work].

Answer 1

a)  

Characteristics	Pure project teams	Matrix Project Team
Reporting	Team members report to only project manger	Team memebers report to both Functional and Project Manager
Skills	Pure project teams does not develop very specific skill of particular field or department	In strong matrix structure, team has strong functional knowledge and return to same function post completion of project.

b)

PERT (BETA) Estimates = (optimistic duration + 4* Most Likely + pessimistic duration)/6

Variance = [( Pessimistic - optimistic duration)/6]²

ACTIVITY	PREDECSOR	OPTIMISTIC	MOST LIKELY	PESSIMISTIC	Beta (PERT) Estimate	Variance
A	--	36	50	56	48.67	11.11
B	--	45	60	84	61.50	42.25
C	A	36	45	46	43.67	2.78
D	A,B	26	40	42	38.00	7.11
E	C	24	36	36	34.00	4.00
F	D,E	58	70	82	70.00	16.00

Table :

ACTIVITY	Beta (PERT) Estimate	Variance
A	48.67	11.11
B	61.50	42.25
C	43.67	2.78
D	38.00	7.11
E	34.00	4.00
F	70.00	16.00

AON Network Diagram

Three paths are in network diagram

calculated sum of duration of each activities in path

Path	Duration
Start- A-C-E-F-Finish	196.33
Start-A-D-F-Finish	156.67
Start- B-D-F-Finish	169.50

Longest path = Critical path = Duration of project

Critical Path = Start- A-C-E-F-Finish

i) Expected (Mean) time = critical path duration = 196.33

ii) Standard Deviation of project = sqrt ( Sum of Variance of Critical path activities) = sqrt(33.89) = 5.8

iii) Probability distribution is Normal districution with mean 196.3 & std dev 5.8 and range = (Mean-3*Std.dev, Mean+std.dev) =(196.33-3*5.8 , 196.33+3*5.8) = (178.8 , 213.8)

Z = (X-Mean)/Std. dev

at X= 210

z = (210- 196.33)/5.8 = 2.34

Refer Z table to find the Proablility

P(X<210) = Value probability of Z at 2.34 = 0.9904 = 99.04%

At X =200

Z = (200 - 196.33)/5.8 = 0.63

P(X<200) = 0.7357 = 73.57 %

At probability of 98.50 % i.e 0.9850 , z value from table = 2.17

Z = (X-Mean)/Std. dev

2.17 = (x-196.33)/5.8

X = 196.33 +2.17*5.8 = 208.9 = 209 days