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Question 2
A project consists of nine activities, A to I. The durations (in days) of the activities, and the precedence relations, are given in the following table.
Activity    Duration    Preceding activities
A                     8                         −
B                     5                         −
C                     3                      A, B
D                   10                        B
E                     4                      A, B
F                     7                      A, E
G                   2                         B
H                   6                        C, D
I                      8                     B, D, G
(a) Use the activity network construction algorithm to find an activity network for this project. [5]
(b) List any redundant arcs in your activity network. (You should ignore them when applying the subsequent algorithms.) [1]
(c) Use the critical path construction algorithm to compile a table showing the earliest starting time for each activity. Hence find a critical path in the activity network, and state the length of this path. [4]
(d) Use the algorithm for calculating latest starting times to compile a table showing the latest starting time for each activity. [3]
(e) Use the critical path scheduling algorithm to find a schedule for the above project for two workers. Is the resulting schedule an optimum one? If so, explain why; if not, write down an improved schedule.

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