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## 15C Backward scanning and crashing

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**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.**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 lateststart time (LST) of each succeeding node. (note: textbook error on p.757). • Example, Ex 15C, Q.1**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**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**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.**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**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**You do**• Exercise 15C, Q. 13, 15, 18, 19, 21