2)Construct the network.

3)Solve the network using forward and backward passes. Critical activities are those that have 0 slack.

ES_i = earliest start time for activity i assuming all predecessor activities started at their earliest start time

EF_i = earliest finish time for activity i

= ES_i + t_iwhere t_i is the time estimated for activity i

LF_i = latest finish time for activity i without delaying the project

LS_i = latest start time for activity i without delaying the project= LF_i - t_i

a) Forward Pass: Calculate the earliest start time and the earliest finish time for each activity. 

1) For all beginning activities i, set:ES_i = 0

2) In general, ES_j = max (EF_i), where i indexes all predecessors andEF_j = ES_j + t_j

b) Backward Pass: Calculate the latest start time and the latest finish time for each activity.

1)For all ending activities j, setLF_j = largest EF_j found in forward pass

2)In general, LF_i = min (LS_j) where j indexes all successors and LS_i = LF_i - t_i.

c) Slack time for each activity is calculated (difference between LS-ES or LF-EF).

d) Critical path is the sequence of activities that has zero slack time.

Example 1.Consider the information in the table.

 

Task	Immediate Predecessor	Estimated time (days)	# of People
A	-	5	2
B	-	4	3
C	A	3	1
D	B	7	3
E	C	2	3
F	D , E	1	1

a.Draw the network diagram for this project.

b.Using a forward and backward pass, find the critical path. 

c.What is the minimum project completion time ignoring resource constraints?

 

Activity	Earliest Start	Earliest Finish	Latest Start	Latest Finish	Slack
A
B
C
D
E
F

After completing the table above, you can see the Gantt chart of the solution.
 

Example #2:

Given the following information regarding a project:

 

Activity	Duration (weeks)	Predecessors
A	10	-
B	10	-
C	5	-
D	7	A
E	5	B
F	7	B
G	2	B
H	5	C
I	8	G, H
J	4	D, E

a.Draw the network.

b.Using a forward and backward pass, find the critical path. 

c.What is the minimum project completion time ignoring resource constraints?

 

Activity	Earliest Start	Earliest Finish	Latest Start	Latest Finish	Slack
A
B
C
D
E
F
G
H
I
J