Question

activity	immediate processor	activity time (days)
A	-	6
B	-	8
C	A,B	5
D	B	4
E	C	7
F	C,D	3
G	D	6
H	E,F,G	5

Given the following information for a project. SHOW ALL WORK.

a) Draw the AON(Activity-On-Node) project network

b) Write the estimated slack times for activities A-H

c) Identify the critical path

d) Determine the total completion time of the project.

Answer 1

Methodology followed: From the given information, AON project network diagram will be drawn first. From the project network diagram, activity schedule is determined. Using the activity schedule, Slack time of each activity is calculated. The activities with 0 slack time forms the critical path and the total length of the critical path forms the total completion time of the project.

Solution:

(a) From the given information, AON project network is drawn as below:

From the network diagram, ES, EF, LS, LF are computed as,

ES - Earliest Start

EF - Earliest Finish

LS - Latest Start

LF - Latest Finish

In forward pass,

ES of an activity = Higher value of EF of all the preceding activities

EF of an activity = ES + Activity duration

In backward pass,

LF of an activity = Lower value of ES of all the succeeding activities

LS of an activity = LF - Activity duration

(b) Slack time is calculated as,

Slack = (LS - ES) or (LF - EF)

The values of ES, EF, LS, LF and Slack are summarized in the table below:

(c) Critical path consists of activities with same (ES and LS) or same (EF and LF) or slack = 0

In the given scenario, activities with 0 slack are: B, C, E, H.

Critical path = B - C - E - H

(d) Project completion time = Length of the critical path

Length of critical path = B + C + E + H = 8 + 5 + 7 + 5 = 25

Project completion time = 25 days