1. AOE-Net
Corresponding to the AOV-net is the AOE-net (Activity On Network), which is a network that uses edges to represent activities. AOE-Net is a directed acyclic graph with weights, where fixed points represent time, arcs represent activities, and weights represent the duration of activities. Usually AOE-Net can be used to estimate the completion time of the project.
Since the entire project has only one start point and completion point, under normal conditions (no loop), there is only one point with an in-degree of 0 in the network, which is called the source point, and there is only one point with an out-degree of 0, called the source point . As a meeting point . In the AOE network, the sum of the weights on each arc of a path becomes the weighted path length of the path (hereinafter referred to as the path length). To estimate the shortest time for the completion of the entire project, it is to find a path with the longest weighted path length from the origin to the sink, which is called the critical path .
2. Steps to find the critical path
a topological sort
b Calculation indicators
c to identify key activities
eg：
Event Metrics:
Earliest start time vi (early)
x<ix is the predecessor of i vi(e)=MAX{vi(e)+weight(i,x)}
Because it is sorted according to topology, all time items pointing to it must be completed before doing one thing.
The latest start time vi (late)
x >ix is the successor of i, vi=MIN{vi(late)-weight(x,i)}
Suppose the latest time of the successor x is a, so the latest start time of its previous node is a-wight
If i has two successor nodes, subtract the smallest one, because it is necessary to ensure that the next two successors must be completed in the latest time.
Activity Metrics:
Earliest start time li (early)
li(e) = v start(e) (v eraly of the originating node of the arc)
The latest start time l (late)
li=v end-weight (accepting node v late minus weight of the arc)
Key Activities:
l(l) - l(e) = time margin = 0.
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a Topological sort:
v1-v2-v3-v4-v5-v6-v7-v8
b Calculation metrics: (event: the latest start time of the last one = its earliest start time)
Event Metrics Activity Metrics
Critical Path: (find the critical path based on the critical activities)
public events can be shortened
The picture comes from station b: TyrantLucifer