1. 15C Backward scanning and crashing

2. Rules for network construction
Two nodes can be connected directly by a maximum of one edge.
An activity must be represented by exactly one edge.

3. The latest start time is the time by which an activity must be started to avoid delaying the entire project.
Backward scanning starts at the end node and moves backward through the network, subtracting the time for each edge from the latest start time (LST) of each succeeding node. (note: textbook error on p.757).
Example, Ex 15C, Q.1

4. The earliest finish time (EFT) for an activity is the earliest start time for an activity plus the duration of the activity.
The float time for X = LSTY – ESTx - Tx
ESTY
ESTX
LSTX
LSTY
X, Tx
Y, TY
EFTX = ESTX + TX

5. The critical path consists of the nodes where the number in the ‘triangle’ equals the number in the ‘box’.
Crashing involves shortening the critical path to speed up completion of the project, resulting in a new, shorter, critical path.
Example, Ex 15C, Q.7

6. Remember, when you are…
Forward scanning: when two or more edges lead to the same node, enter the largest value as the earliest start time.
Backward scanning: when two or more edges lead to the same node, enter the smallest value as the latest start time.

7. Ex 15C, Q. 2, 4, 5, 6, 8, 9, 10, 11

8. Dummy activities
Dummy activities are used to avoid a network breaking the two rules of networks.
Two nodes can be connected directly by a maximum of one edge.
An activity must be represented by exactly one edge.
Example, Ex 15C, Q.12, 14

9. Crashing
To speed up an entire project, the critical path must be shortened. This results in a new critical path.
Example, Ex 15C, Q. 17

10. You do
Exercise 15C, Q. 13, 15, 18, 19, 21