Teach you to easily calculate AOE Network critical path

Original link: http://blog.csdn.net/wang379275614/article/details/13990163

This combination of system Analyst-operations Method-network planning technology-critical Path section, the original link description is not accurate where the correction.

Know AoE Network

　　In a direction diagram, a vertex is used to represent an activity, and a forward edge is used to indicate the order in which the activity begins, which is called the AoV (activity on Vertex) network, and the AOV network can react to the sequencing of task completion (topological ordering).

By adding weights to the edge of the AOV network to indicate the time required to complete the activity, the AOV network is called the AOE (activity on Edge) network, such as:

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In the figure, the vertex represents the event (which can be triggered, two characteristic attributes: The earliest occurrence of the VE (j); The late occurrence of VL (J)), the edge represents the activity (can be started, two characteristic attributes: The earliest start time E (i); the latest start time L (i)), the right represents the activity duration, Usually use AOE net to estimate the time of project completion

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Two principles:

?? Only events that are represented by a vertex can start with activities from that vertex

?? Only events that enter a vertex end, and the event that the vertex represents can occur

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Calculate critical paths

First, in the AOE network, the path from the beginning to the end with the maximum path length (the sum of the time that each activity on that path lasts) is the critical path.

To calculate the critical path, only the above four feature attributes are required, and the edges of E (i) =l (i) are the edges on the critical path (more than one critical path may be).

Let's take a look at the meaning of the four feature attributes:

?? Ve (j): Refers to the maximum path length from the start point to the vertex VJ

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Calculation techniques:

(1) from front to back, take large value: Ve (j) of direct precursor node + weight of reaching edge (edge to vertex), larger of multiple values

(2) First node ve (j) known, is 0

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ve (j) for each vertex (event): (Starting from V1)

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?? Vl (j): The last occurrence time allowed by event VJ without postponing the entire duration

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Calculation techniques:

(1) from the back forward, take the small value: the direct successor node of the VL (j)-Emit the edge (from the vertex from the edge) of the weight, there are multiple values of the smaller;

(2) The end point VL (J) is known to be equal to its ve (j))

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VL (j) for each vertex (event): (Starting with V7, it has the same earliest and latest occurrences, all of which are ten):

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?? E (i): If the active AI is represented by arc <vk,vj>, then the earliest start time of the active AI should be equal to the earliest occurrence of the event VK. Thus, there is: E (i) =ve (k); ( i.e.: The earliest start time of an edge (activity) equals the earliest occurrence of its emitted vertex )

E (i) for each side (activity):

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?? L (i): If the active AI is represented by Arc <vk,vj>, the latest start time of the AI is to ensure that the latest occurrence of the event VJ is not delayed. Thus there is: L (i) =VL (j)-len<vk,vj> (the last occurrence time of the arrival vertex of the edge (activity) minus the weight of the edge )

As L (i) for each side (activity):

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At this point, we have introduced the four characteristics of the method of the attribute, also find the middle side of E (i) and L (i), take out E (i) =l (i) is A1, A2, A4, A8, A9, which is the edge on the critical path, so the critical path has two: A1 A4 A9 and A2 A8 A9

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Summarize

To find the critical path, just understand the vertex (event) and Edge (activity) of the respective two feature attributes and the method can be:

?? The earliest occurrence time of each vertex is calculated first based on the VE (j) =0 of the first node.

?? Then the VL (j) of the endpoint is equal to its ve (J ) to solve the last occurrence time of each vertex sequentially

?? The earliest start time of each edge is calculated based on the E (i) of the Edge and the VE (j) that is equal to its emitted vertex (earliest beginning, corresponding to the earliest occurrence)

?? Calculates the latest start time of each edge, based on the Edge's L (i) minus the weight of the edge by a VL (j) that is equal to its reach vertex (the latest start, corresponding to the latest occurrence)

Teach you to easily calculate AOE Network critical Path (RPM)