Question

# QUESTION 2. The following table explain the logical relationship of activities of a given project, including...

QUESTION 2. The following table explain the logical relationship of activities of a given project, including the duration in weeks of each activity.

 Activity Follows Duration (Weeks) M G, F 4 F Start 6 G Start 3 D Start 7 K D, G 5 L K, J 8 J D 3 S L, M, F 4 Finish S
1. Draw the network
2. Perform the forward path as determine the project duration (5 Marks)
3. Perform the back path and determine the critical path (5 Marks)

a. Network Diagram

b. Project Duration : 24 Days

ES = Earliest Start, EF = Earliest Finish, LS = Latest Start, LF = Latest Finish

Forward Path:

Activities F,G,D has no any predecessor so all these activities start on Day 0.

ES =0, EF = Project Duration

For all other activities

E: (ES, EF)
ES = Latest Earliest Finish time of predecessors.

EF = ES + Duration

c. Critical path: D-K-L-S

Backward Path:

L: (LS, LF)

LF = Lowest Latest Start time (LS)  of Following activities.

LS = LF - Project Duration

Activity S is the last activity in the project so for S, LS= ES and LF = EF.

S has three predecessors F, M and L

LF for M = LS for S  = 20

LS for M = 20 - 4 = 16

LF for F = min (LS for S or LS for M) = min (20,16) = 16

LS for F = 16-6 =10

LF for L = LS for S = 20

LS for L = 20-12 =8

Now, L had two predecessors K and J

LF for K = LS for L = 12

LS for K = 12-5 = 7

LF for J = LS for L =12

LS for J = 12-3 =9

Now for remaining two activities D & G.

LF for D = min (LS for K, LS for J) = 7

LS for D = 7-7 =0

LF for G = min(LS for M, LS for K) = 7

LS for G = 7-3 =4.

All activities are critical for which ES = LS.

In this project, D K L and S are critical activities.

And Critical Path = D-K-L-S

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