dontesalgor 2bm angol - Budapest University of Technology ... · 2015.10.04. 1...
Transcript of dontesalgor 2bm angol - Budapest University of Technology ... · 2015.10.04. 1...
2015.10.04.
1
Algorithm for longest path
Generic shortest path algorithmSingle source shortest path algorithm
Bellman-Ford 1958
Construction Technology and Management, Mályusz Levente Decision Support models
Digraph
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source
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56
7
sink
Construction Technology and Management, Mályusz Levente Decision Support models
Theorem of Graph
• Leonhard Euler 1707-1783• Königsbergi hidak 1736
Construction Technology and Management, Mályusz Levente Decision Support models
2015.10.04.
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Shortest Path problem• Algorithms
– Ford 1956– Bellman 1958– Dantzig 1958– Dijkstra 1959
Construction Technology and Management, Mályusz Levente Decision Support models
Graph, network
• 1847 Kirchoff graph theory and application of electrical networks.1852 F. Guthrie: There are four colourproblem.1930 Kuratowski planar graph.1956-61 Ford-Fulkerson maximum flow, minimum cost flow1956 Polaris project, DuPont, RandCorporation, CPM, PERT, MPM, PDM
Construction Technology and Management, Mályusz Levente Decision Support models
The longest path 1-4, the earliest and latest date policy
1 2 3 4
1 7 9
2 8 9
3 12
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Construction Technology and Management, Mályusz Levente Decision Support models
2015.10.04.
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From 1. node
1 2 3 4
1 7 9
2 8 9
3 12
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97
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0
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Construction Technology and Management, Mályusz Levente Decision Support models
From 2. node
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1 7 9
2 8 9
3 12
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97
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9 15
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Construction Technology and Management, Mályusz Levente Decision Support models
From 3. node
1 2 3 4
1 7 9
2 8 9
3 12
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9 15
16 27
Construction Technology and Management, Mályusz Levente Decision Support models
2015.10.04.
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From 1., 2.,3., nodes
1 2 3 4
1 7 9
2 8 9
3 12
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0 0
7 7
15 8 15
27 16 27
Construction Technology and Management, Mályusz Levente Decision Support models
Backward from 4. node
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2 8 9
3 12
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0 0
7 7
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27 16 27
9 12 0Construction Technology and Management, Mályusz Levente Decision Support models
Backward from 3. node
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2 8 9
3 12
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21 9 20 12 0Construction Technology and Management, Mályusz Levente Decision Support models
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Backward from 2. node
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2 8 9
3 12
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21 27 9 20 12 0Construction Technology and Management, Mályusz Levente Decision Support models
Latest date policy
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0 7 15 27Construction Technology and Management, Mályusz Levente Decision Support models
Longest path 1-4 and lag times
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1 7 9
2 8 9
3 -10 12
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Construction Technology and Management, Mályusz Levente Decision Support models
2015.10.04.
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From 1. node
1 2 3 4
1 7 9
2 8 9
3 -10 12
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Construction Technology and Management, Mályusz Levente Decision Support models
From 2. node
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2 8 9
3 -10 12
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Construction Technology and Management, Mályusz Levente Decision Support models
From 3. node
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2 8 9
3 -10 12
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Construction Technology and Management, Mályusz Levente Decision Support models
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New iteration from 1,2,3. nodes
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3 -10 12
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0 0
7 7
15 8 15
27 16 27
Construction Technology and Management, Mályusz Levente Decision Support models
Backward from 4. node
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2 8 9
3 -10 12
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0 0
7 7
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27 16 27
9 12 0
Construction Technology and Management, Mályusz Levente Decision Support models
Backward from 3. node
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Construction Technology and Management, Mályusz Levente Decision Support models
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Backward from 2. node
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0 7 15 27Construction Technology and Management, Mályusz Levente Decision Support models
Result: scheduling
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0 7 15 27Construction Technology and Management, Mályusz Levente Decision Support models
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Longest path 1-4 and lag times
1 2 3 4
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2 8 9
3 -7 12
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Construction Technology and Management, Mályusz Levente Decision Support models
2015.10.04.
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From 1. node
1 2 3 4
1 7 9
2 8 9
3 -7 12
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Construction Technology and Management, Mályusz Levente Decision Support models
From 2. node
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Construction Technology and Management, Mályusz Levente Decision Support models
From 3. node
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Construction Technology and Management, Mályusz Levente Decision Support models
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New iteration from 1. node
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0 0
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27 16 27
Construction Technology and Management, Mályusz Levente Decision Support models
New iteration from 2. node
1 2 3 4
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Construction Technology and Management, Mályusz Levente Decision Support models
New iteration from 3. node
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Construction Technology and Management, Mályusz Levente Decision Support models
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3. Iteration from 1. node
1 2 3 4
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9 8 9 7 8
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Construction Technology and Management, Mályusz Levente Decision Support models
3. Iteration from 2. node
1 2 3 4
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0 0 0
9 8 9 7 8
16 17 15 16 9 15
28 27 28 16 27
Construction Technology and Management, Mályusz Levente Decision Support models
3. Iteration from 3. node
1 2 3 4
1 7 9
2 8 9
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16 17 15 16 9 15
28 29 27 28 16 27
Construction Technology and Management, Mályusz Levente Decision Support models
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Result: cycle, there is no solution
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Construction Technology and Management, Mályusz Levente Decision Support models
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Scheduling with calendar
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M T W Th F Sat Su M T W
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M T W Th F Sat Su M T W
5 5 5 5 5 5 5 5 5 5
M T W Th F Sat Su M T W
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SS2
FS0
maxFF6
Construction Technology and Management, Mályusz Levente Decision Support models
MPM network and the relationship with digraph
5 5K B
-5
MPM networkdigráfban
Construction Technology and Management, Mályusz Levente Decision Support models
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Relationship between MPM and a digraph
5 5S F
-5
PDM networkdigraph
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FS2
7S F
-7
2
Construction Technology and Management, Mályusz Levente Decision Support models
Relationships of MPM and digraph
5 5S F
-5
PDM networkdigraph
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SS3
7S F
-7
3maxSS4
3-4
Construction Technology and Management, Mályusz Levente Decision Support models
Relationships of MPM and a digraph
5 5K B
-5
PDM networkdigraph
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SS3
7K B
-7
3maxFF5
-5
Construction Technology and Management, Mályusz Levente Decision Support models
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Construction Technology and Management, Mályusz Levente Decision Support models
Normal critical activityactivity time increasing project
duration time increasing
FS0 FS0 FS0
FS0 FS0 FS0
0 3 3
3 3 6
6 3 9
0 3 3
3 2 5
5 3 8
0 3 3
3 4 7
7 3 10
Construction Technology and Management, Mályusz Levente Decision Support models
activity time increasing project duration time decreasing
FF10 FF10 FF10
SS10 SS10 SS10
0 3 3
10 3 13
20 3 23
0 3 3
11 2 13
21 3 24
0 3 3
9 4 13
19 3 22
Construction Technology and Management, Mályusz Levente Decision Support models
SS10 FF10 SS10 FF10 SS10 FF10
0 3 3
10 3 13
20 3 23
0 3 3
11 2 13
21 3 24
0 3 3
10 4 14
21 3 24
Bi- critical activityactivity time dec/increasing
project duration time increasing
SS10 FF10 SS10 FF10 SS10 FF10
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Construction Technology and Management, Mályusz Levente Decision Support models
SS10 SS10 SS10
0 3 3
10 3 13
20 3 23
0 3 3
10 2 12
20 3 23
0 3 3
10 4 14
20 3 23
Neutral critical activityactivity time dec/increasing
project duration time does not change
SS10 SS10 SS10