PERTCPM algorithm Compute topological order of vertices A

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PERT/CPM algorithm. Compute topological order of vertices: A B C D E F G

PERT/CPM algorithm. Compute topological order of vertices: A B C D E F G H I. n F D 3 6 E time 5 A B C G H I 0 4 2 4 6 0 1

PERT/CPM Algorithm. Compute topological order of vertices: A B C D E F G

PERT/CPM Algorithm. Compute topological order of vertices: A B C D E F G H I. Initialize fin[v] = 0 for all vertices v. n n earliest finish time 0 0 F D 0 6 3 E 5 0 0 0 A B C G H I 0 4 2 4 6 0 2

PERT/CPM algorithm. Compute topological order of vertices: A B C D E F G

PERT/CPM algorithm. Compute topological order of vertices: A B C D E F G H I. Initialize fin[v] = 0 for all vertices v. Consider vertices v in topological order: – for each edge v-w, set fin[w] = max(fin[w], fin[v] + time[w]) n n n 0 0 F D 0 6 3 E 5 0 4 0 X 0 0 A B C G H I 0 4 2 4 6 0 3

PERT/CPM algorithm. Compute topological order of vertices: A B C D E F G

PERT/CPM algorithm. Compute topological order of vertices: A B C D E F G H I. Initialize fin[v] = 0 for all vertices v. Consider vertices v in topological order: – for each edge v-w, set fin[w] = max(fin[w], fin[v] + time[w]) n n n 10 0 X 0 F D 0 6 3 E 0 4 0 X 6 X 0 5 0 0 0 A B C G H I 0 4 2 4 6 0 4

PERT/CPM algorithm. Compute topological order of vertices: A B C D E F G

PERT/CPM algorithm. Compute topological order of vertices: A B C D E F G H I. Initialize fin[v] = 0 for all vertices v. Consider vertices v in topological order: – for each edge v-w, set fin[w] = max(fin[w], fin[v] + time[w]) n n n 10 0 X 0 F D 0 6 3 E 0 4 0 X 6 X 0 5 10 0 X 12 0 X 0 A B C G H I 0 4 2 4 6 0 5

PERT/CPM algorithm. Compute topological order of vertices: A B C D E F G

PERT/CPM algorithm. Compute topological order of vertices: A B C D E F G H I. Initialize fin[v] = 0 for all vertices v. Consider vertices v in topological order: – for each edge v-w, set fin[w] = max(fin[w], fin[v] + time[w]) n n n 13 0 X 10 0 X F D 15 0 X 6 3 E 0 4 0 X 6 X 0 5 10 0 X 12 0 X 0 A B C G H I 0 4 2 4 6 0 6

PERT/CPM algorithm. Compute topological order of vertices: A B C D E F G

PERT/CPM algorithm. Compute topological order of vertices: A B C D E F G H I. Initialize fin[v] = 0 for all vertices v. Consider vertices v in topological order: – for each edge v-w, set fin[w] = max(fin[w], fin[v] + time[w]) n n n 13 0 X 10 0 X F D 15 0 X 6 3 E 0 4 0 X 6 X 0 5 10 X 19 0 X 12 X 21 0 X 0 A B C G H I 0 4 2 4 6 0 7

PERT/CPM algorithm. Compute topological order of vertices: A B C D E F G

PERT/CPM algorithm. Compute topological order of vertices: A B C D E F G H I. Initialize fin[v] = 0 for all vertices v. Consider vertices v in topological order: – for each edge v-w, set fin[w] = max(fin[w], fin[v] + time[w]) n n n 13 0 X 10 0 X F D 15 0 X 6 3 E 0 4 0 X 6 X 0 5 10 X 19 0 X 12 X 21 0 X 13 0 X A B C G H I 0 4 2 4 6 0 8

PERT/CPM algorithm. Compute topological order of vertices: A B C D E F G

PERT/CPM algorithm. Compute topological order of vertices: A B C D E F G H I. Initialize fin[v] = 0 for all vertices v. Consider vertices v in topological order: – for each edge v-w, set fin[w] = max(fin[w], fin[v] + time[w]) n n n 13 0 X 10 0 X F D 15 0 X 6 3 E 0 4 0 X 6 X 0 5 10 X 19 0 X 12 X 21 X 25 0 X 13 0 X A B C G H I 0 4 2 4 6 0 9

PERT/CPM algorithm. Compute topological order of vertices: A B C D E F G

PERT/CPM algorithm. Compute topological order of vertices: A B C D E F G H I. Initialize fin[v] = 0 for all vertices v. Consider vertices v in topological order: – for each edge v-w, set fin[w] = max(fin[w], fin[v] + time[w]) n n n 13 0 X 10 0 X F D 15 0 X 6 3 E 0 4 0 X 6 X 0 5 10 X 19 0 X 12 X 21 X 25 0 X 13 X 25 0 X A B C G H I 0 4 2 4 6 0 10

PERT/CPM algorithm. Compute topological order of vertices: A B C D E F G

PERT/CPM algorithm. Compute topological order of vertices: A B C D E F G H I. Initialize fin[v] = 0 for all vertices v. Consider vertices v in topological order: – for each edge v-w, set fin[w] = max(fin[w], fin[v] + time[w]) n n n 13 0 X 10 0 X F D 15 0 X 6 3 E 0 4 0 X 6 X 0 5 10 X 19 0 X 12 X 21 X 25 0 X 13 X 25 0 X A B C G H I 0 4 2 4 6 0 11

PERT/CPM algorithm. Compute topological order of vertices: A B C D E F G

PERT/CPM algorithm. Compute topological order of vertices: A B C D E F G H I. Initialize fin[v] = 0 for all vertices v. Consider vertices v in topological order: – for each edge v-w, set fin[w] = max(fin[w], fin[v] + time[w]) n n n 13 10 F D 15 6 E critical path 0 4 3 5 6 19 25 25 A B C G H I 0 4 2 4 6 0 12

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