Question

Critical Path Network: 

 a. Develop the critical path network.

 b. Show ES, EF, LS, LF, on the network. c. What are the critical path activities?

 d. What are the slack time of the activities?

 e. What is the completion time of the project?

 f. What are the expected times of the activities?

 g. What is the project variance?

 h. What is its standard deviation?

Answer 1

ACTIVITY	DURATION	ES	EF	LS	LF	SLACK
A	3	0	3	1	4	1
B	4	0	4	0	4	0
C	2	3	5	6	8	3
D	4	4	8	4	8	0
E	6	8	14	8	14	0

FORWARD PASS

We calculate the ES and EF values using a forward pass where the ES of an activity is the maximum EF of all the predecessor activities.

BACKWARD PASS

We calculate the LS and LF values using a backward pass where the LF of the activity is the minimum of all the successor activities.

SLACK

Slack is the value which is determined by subtracting EF from the LF or ES from the LS.

CRITICAL PATH

Critical path is the chain in the project network where the slack value of all the activities is 0, what this means is that any delay in these activities would result in delaying the entire project.

CRITICAL PATH & COMPLETION TIME

B + D + E = 14

PERT ANALYSIS

ACTIVITY	OPTIMISTIC a	MOST LIKELY m	PESSIMISTIC b	EXPECTED	VARIANCE
				(a + (4m) + b) / 6	((b - a) / 6) ^ 2
A	2	3	4	3	0.11
B	3	4	6	4	0.25
C	1	2	4	2	0.25
D	3	4	6	4	0.25
E	4	5	8	5	0.44

VARIANCE OF CRITICAL PATH = 0.25 + 0.25 + 0.44 = 0.94

STDEV OF CRITICAL PATH = SQRT(VARIANCE) = SQRT(0.94) = 0.9695