D:\java\MinShip\my-minship-app>mvn package
[INFO] Scanning for projects...
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[INFO] Using the builder org.apache.maven.lifecycle.internal.builder.singlethreaded.SingleThreadedBuilder with a thread count of 1
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[INFO] Building my-minship-app 1.0-SNAPSHOT
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[INFO]
[INFO] --- maven-resources-plugin:2.6:resources (default-resources) @ my-minship-app ---
[WARNING] Using platform encoding (Cp1252 actually) to copy filtered resources, i.e. build is platform dependent!
[INFO] skip non existing resourceDirectory D:\java\MinShip\my-minship-app\src\main\resources
[INFO]
[INFO] --- maven-compiler-plugin:2.5.1:compile (default-compile) @ my-minship-app ---
[INFO] Nothing to compile - all classes are up to date
[INFO]
[INFO] --- maven-resources-plugin:2.6:testResources (default-testResources) @ my-minship-app ---
[WARNING] Using platform encoding (Cp1252 actually) to copy filtered resources, i.e. build is platform dependent!
[INFO] skip non existing resourceDirectory D:\java\MinShip\my-minship-app\src\test\resources
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[INFO] --- maven-compiler-plugin:2.5.1:testCompile (default-testCompile) @ my-minship-app ---
[INFO] Nothing to compile - all classes are up to date
[INFO]
[INFO] --- maven-surefire-plugin:2.12.4:test (default-test) @ my-minship-app ---
[INFO] Surefire report directory: D:\java\MinShip\my-minship-app\target\surefire-reports
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T E S T S
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Running com.smkltd.app.AppTest
Tests run: 1, Failures: 0, Errors: 0, Skipped: 0, Time elapsed: 0.005 sec
Results :
Tests run: 1, Failures: 0, Errors: 0, Skipped: 0
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[INFO] --- maven-jar-plugin:2.4:jar (default-jar) @ my-minship-app ---
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[INFO] BUILD SUCCESS
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[INFO] Total time: 1.654 s
[INFO] Finished at: 2015-01-07T23:57:03-05:00
[INFO] Final Memory: 9M/489M
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D:\java\MinShip\my-minship-app>java -cp target/my-minship-app-1.0-SNAPSHOT.jar com.smkltd.app.GraphFlow
Transportation at minimum cost in a directed network linear program
x >= 0 Tableau
Ax - b >= 0 [A ][-b] pivot to make [-b] >= 0 and [c'] >= 0
c'x = min [c'][ 0]
available supply equals demand
Simplex iterations = 0
V\E 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 -b
22 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -6
23 -1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -14
24 0 -1 0 -1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -18
25 0 0 -1 0 -1 0 -1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 -6
26 0 0 0 0 0 -1 0 -1 0 -1 0 1 1 1 1 1 0 0 0 0 0 0 -46
27 0 0 0 0 0 0 0 0 -1 0 0 -1 0 0 0 0 1 1 0 0 0 0 -14
28 0 0 0 0 0 0 0 0 0 0 -1 0 -1 0 0 0 -1 0 1 0 0 0 24
29 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 -1 0 1 1 0 -9
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 -1 -1 0 1 30
31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 -1 -1 59
c' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0
ship 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
VertexLabels 22 23 24 25 26 27 28 29 30 31
SupplyDemand -6 -14 -18 -6 -46 -14 24 -9 30 59
SupplyChange 0 0 0 0 0 0 0 0 0 0
InitialSupply 15 2 23 0 7 9 36 1 55 72
FinalSupply 15 2 23 0 7 9 36 1 55 72
Transportation at minimum cost in a directed network linear program
x >= 0 Tableau
Ax - b >= 0 [A ][-b] pivot to make [-b] >= 0 and [c'] >= 0
c'x = min [c'][ 0]
available supply equals demand
Simplex iterations = 28
V\E 22 23 24 11 12 25 13 27 26 3 0 6 1 28 29 30 8 4 18 17 20 21 -b
10 0 0 0 -1 -1 0 0 -1 0 0 0 0 0 -1 0 0 -1 0 1 1 0 0 10
7 0 0 1 0 0 0 0 0 0 1 0 -1 1 0 0 0 -1 0 0 0 0 0 18
2 1 0 0 0 0 0 0 0 0 0 -1 0 -1 0 0 0 0 0 0 0 0 0 6
5 0 1 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 -1 0 0 0 0 14
16 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 14
19 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 -1 0 9
9 1 0 0 1 1 1 0 1 0 0 -1 1 -1 1 0 0 1 1 -1 -1 0 0 2
14 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 -1 0 0 -1 -1 1 1 21
15 1 1 1 0 0 1 0 1 1 0 0 0 0 1 1 1 0 0 0 0 -1 -1 59
31 -1 -1 -1 0 0 -1 0 -1 -1 0 0 0 0 -1 -1 -1 0 0 0 0 0 0 0
c' 3 2 2 2 1 2 1 2 1 1 0 1 0 1 1 0 1 1 0 0 0 1 153
ship 0 0 6 0 0 14 0 18 0 2 10 0 0 0 21 59 14 0 0 9 0 0
VertexLabels 22 23 24 25 26 27 28 29 30 31
SupplyDemand -6 -14 -18 -6 -46 -14 24 -9 30 59
SupplyChange 6 14 18 6 46 14 -24 9 -30 -59
InitialSupply 15 2 23 0 7 9 36 1 55 72
FinalSupply 21 16 41 6 53 23 12 10 25 13
Transportation at minimum cost in a directed network linear program
x >= 0 Tableau
Ax - b >= 0 [A ][-b] pivot to make [-b] >= 0 and [c'] >= 0
c'x = min [c'][ 0]
adjusted for sinks with supply: available supply less than demand
Simplex iterations = 0
V\E 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 -b
22 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
23 1 0 0 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16
24 0 1 0 1 0 0 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 20
25 0 0 1 0 1 0 1 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 6
26 0 0 0 0 0 1 0 1 0 1 0 -1 -1 -1 -1 -1 0 0 0 0 0 0 46
27 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 -1 -1 0 0 0 0 14
28 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 -1 0 0 0 -24
29 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 -1 -1 0 9
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 -1 -30
31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 -51
c' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0
ship 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
VertexLabels 22 23 24 25 26 27 28 29 30 31
SupplyDemand 6 -16 -20 -6 -46 -14 24 -9 30 51
SupplyChange 0 0 0 0 0 0 0 0 0 0
InitialSupply 15 2 23 0 7 9 36 1 55 72
FinalSupply 15 2 23 0 7 9 36 1 55 72
Transportation at minimum cost in a directed network linear program
x >= 0 Tableau
Ax - b >= 0 [A ][-b] pivot to make [-b] >= 0 and [c'] >= 0
c'x = min [c'][ 0]
adjusted for sinks with supply: available supply less than demand
Simplex iterations = 12
V\E 0 1 29 3 22 12 23 4 8 9 28 11 25 13 30 31 26 17 18 27 20 21 -b
7 -1 0 1 1 0 1 1 1 0 -1 0 1 0 0 1 1 1 -1 -1 0 0 0 10
6 1 1 0 0 1 -1 0 -1 -1 1 1 -1 1 0 0 0 0 1 1 1 0 0 4
24 0 0 -1 0 -1 0 -1 0 0 0 -1 0 -1 0 -1 -1 -1 0 0 -1 0 0 6
19 0 0 -1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 -1 0 9
16 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 -1 0 -1 0 0 14
5 1 0 0 -1 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16
10 0 0 0 0 0 -1 0 0 -1 0 1 -1 0 0 0 0 0 1 1 1 0 0 10
2 -1 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14 0 0 1 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 -1 -1 0 1 1 21
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -1 -1 51
c' 1 1 1 1 0 0 0 0 0 1 2 1 1 1 2 2 1 1 1 1 0 1 135
ship 0 0 0 0 0 16 4 10 0 0 10 0 0 0 21 51 14 0 0 9 0 0
VertexLabels 22 23 24 25 26 27 28 29 30 31
SupplyDemand 6 -16 -20 -6 -46 -14 24 -9 30 51
SupplyChange 0 16 14 6 46 14 -24 9 -30 -51
InitialSupply 15 2 23 0 7 9 36 1 55 72
FinalSupply 15 18 37 6 53 23 12 10 25 21
Transportation at minimum cost in a directed network linear program
x >= 0 Tableau
Ax - b >= 0 [A ][-b] pivot to make [-b] >= 0 and [c'] >= 0
c'x = min [c'][ 0]
available supply greater than demand
Simplex iterations = 0
V\E 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 -b
22 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -6
23 -1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -14
24 0 -1 0 -1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -18
25 0 0 -1 0 -1 0 -1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 -6
26 0 0 0 0 0 -1 0 -1 0 -1 0 1 1 1 1 1 0 0 0 0 0 0 -46
27 0 0 0 0 0 0 0 0 -1 0 0 -1 0 0 0 0 1 1 0 0 0 0 -14
28 0 0 0 0 0 0 0 0 0 0 -1 0 -1 0 0 0 -1 0 1 0 0 0 40
29 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 -1 0 1 1 0 -9
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 -1 -1 0 1 37
31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 -1 -1 68
c' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0
ship 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
VertexLabels 22 23 24 25 26 27 28 29 30 31
SupplyDemand -6 -14 -18 -6 -46 -14 40 -9 37 68
SupplyChange 0 0 0 0 0 0 0 0 0 0
InitialSupply 15 2 23 0 7 9 36 1 55 72
FinalSupply 15 2 23 0 7 9 36 1 55 72
Transportation at minimum cost in a directed network linear program
x >= 0 Tableau
Ax - b >= 0 [A ][-b] pivot to make [-b] >= 0 and [c'] >= 0
c'x = min [c'][ 0]
available supply greater than demand
Simplex iterations = 25
V\E 22 23 24 11 12 25 9 27 26 3 0 5 1 28 29 30 8 17 18 13 20 21 -b
10 0 0 0 -1 -1 0 0 -1 0 0 0 0 0 -1 0 0 -1 1 1 0 0 0 26
7 1 1 1 1 1 1 -1 1 0 0 0 -1 0 1 0 0 0 -1 -1 0 0 0 18
2 1 0 0 0 0 0 0 0 0 0 -1 0 -1 0 0 0 0 0 0 0 0 0 6
6 -1 -1 0 -1 -1 -1 1 -1 0 1 0 1 1 -1 0 0 -1 1 1 0 0 0 0
16 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 14
4 0 1 0 0 0 0 0 0 0 -1 1 -1 0 0 0 0 0 0 0 0 0 0 14
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 -1 0 9
14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 -1 -1 -1 1 1 28
15 1 1 1 0 0 1 0 1 1 0 0 0 0 1 1 1 0 0 0 0 -1 -1 36
31 -1 -1 -1 0 0 -1 0 -1 -1 0 0 0 0 -1 -1 -1 0 0 0 0 0 0 32
c' 2 2 2 1 0 1 1 1 1 1 1 0 1 0 1 0 0 1 1 1 0 1 151
ship 0 0 6 0 14 0 0 18 0 0 26 0 0 0 28 36 14 0 0 9 0 0
VertexLabels 22 23 24 25 26 27 28 29 30 31
SupplyDemand -6 -14 -18 -6 -46 -14 40 -9 37 68
SupplyChange 6 14 18 6 46 14 -40 9 -37 -36
InitialSupply 15 2 23 0 7 9 36 1 55 72
FinalSupply 21 16 41 6 53 23 -4 10 18 36
Maximum flow from source to destination in a directed network linear program
z <= 0 Tableau
-A'z - c <= 0 [A ][-c] here c contains the edge capacities with remaining entries zero
b'z = min [b'][ 0] here b is destination row in Incidence matrix
setting up as dual program
x >= 0 Tableau
Ax - b >= 0 [A ][-b] pivot to make [-b] >= 0 and [c'] >= 0
c'x = min [c'][ 0]
Simplex iterations = 0
E\V 23 24 25 26 27 28 29 30 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 -22
0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1
1 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1
2 0 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1
3 -1 1 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 -1 0 1 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 -1 0 0 1 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 -1 1 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 0 -1 0 1 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 -1 0 0 1 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 0 0 -1 1 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 -1 0 0 1 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 -1 1 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
12 0 0 0 -1 0 1 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
13 0 0 0 -1 0 0 1 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
14 0 0 0 -1 0 0 0 1 0 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
15 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
16 0 0 0 0 -1 1 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
17 0 0 0 0 -1 0 1 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
18 0 0 0 0 0 -1 0 1 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
19 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
20 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
21 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
c' 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 17 28 7 23 17 9 19 10 18 8 5 21 6 27 16 5 29 19 7 18 19 0
ship 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
VertexLabels 22 23 24 25 26 27 28 29 30 31
SupplyChange 0 0 0 0 0 0 0 0 0 0
InitialSupply 15 2 23 0 7 9 36 1 55 72
FinalSupply 15 2 23 0 7 9 36 1 55 72
Maximum flow from source to destination in a directed network linear program
z <= 0 Tableau
-A'z - c <= 0 [A ][-c] here c contains the edge capacities with remaining entries zero
b'z = min [b'][ 0] here b is destination row in Incidence matrix
setting up as dual program
x >= 0 Tableau
Ax - b >= 0 [A ][-b] pivot to make [-b] >= 0 and [c'] >= 0
c'x = min [c'][ 0]
Simplex iterations = 16
E\V 0 1 2 5 8 10 13 14 33 34 35 36 37 38 39 40 15 17 43 44 45 46 47 48 9 21 51 52 53 20 55 7 57 58 59 60 11 18 -22
23 0 0 1 -1 0 1 0 -1 1 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 0 -1 0 0 0 1 0 0 0 -1 0 0 1 1
24 0 0 1 0 0 1 0 -1 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 0 1 0 0 -1 0 0 0 1 -1 0 0 -1 0 0 1 1
25 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
3 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0
4 0 0 0 1 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 1 0 0 0 -1 0 0 0 1 0 0 -1 0
26 0 0 1 0 0 1 0 -1 0 0 0 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 0 0 0 1 0 0 0 -1 0 0 1 1
6 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 1 0 0 0 -1 1 0 0 1 0 0 -1 0
56 0 0 1 0 0 1 0 -1 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 -1 0 0 0 1 0 0 0 -1 0 0 1 1
27 0 0 1 0 0 1 0 -1 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 -1 0 0 1 0 0 0 -1 0 1 1 1
49 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 -1 0 0 0 0 -1 0 0
28 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 -1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 1
61 0 0 1 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 -1 -1 0 1 1 0 0 -1 -1 0 1 1 1
12 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 1 0 0 -1 0
29 0 0 1 0 0 1 0 -1 0 0 0 0 0 0 1 0 0 1 -1 0 0 0 0 0 0 0 -1 -1 0 0 1 0 0 -1 -1 0 1 1 1
30 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 0 0 1 1
41 1 0 -1 1 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 1 0 0 0 -1 0 0 0 1 0 0 -1 0
16 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 0 1 0 1 0 -1 -1 0
42 0 1 -1 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -1 0 0 1 0 0 0 -1 1 0 0 1 0 0 -1 0
62 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 -1 0 0 1 1
19 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 1 0 1 -1 0 0
54 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 -1 0 0
50 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 -1 0 0 0 1 0 0 -1 0
c' 13 17 23 13 10 5 6 14 0 0 0 0 0 0 0 0 16 12 5 7 23 4 9 12 18 19 3 3 21 18 13 7 5 17 14 7 2 5 53
ship 13 17 23 0 0 13 0 7 10 18 5 2 0 6 14 16 0 12 5 0 18 19
VertexLabels 22 23 24 25 26 27 28 29 30 31
SupplyChange 53 0 0 0 0 0 0 0 0 -53
InitialSupply 15 2 23 0 7 9 36 1 55 72
FinalSupply 68 2 23 0 7 9 36 1 55 19
Transportation at minimum cost in a directed network linear program
x >= 0 Tableau
Ax - b >= 0 [A ][-b] pivot to make [-b] >= 0 and [c'] >= 0
c'x = min [c'][ 0]
available supply equals demand
Simplex iterations = 0
V\E 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 -b
22 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -53
23 -1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
24 0 -1 0 -1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
25 0 0 -1 0 -1 0 -1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0
26 0 0 0 0 0 -1 0 -1 0 -1 0 1 1 1 1 1 0 0 0 0 0 0 0
27 0 0 0 0 0 0 0 0 -1 0 0 -1 0 0 0 0 1 1 0 0 0 0 0
28 0 0 0 0 0 0 0 0 0 0 -1 0 -1 0 0 0 -1 0 1 0 0 0 0
29 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 -1 0 1 1 0 0
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 -1 -1 0 1 0
31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 -1 -1 53
c' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0
ship 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
VertexLabels 22 23 24 25 26 27 28 29 30 31
SupplyDemand -53 0 0 0 0 0 0 0 0 53
SupplyChange 0 0 0 0 0 0 0 0 0 0
InitialSupply 15 2 23 0 7 9 36 1 55 72
FinalSupply 15 2 23 0 7 9 36 1 55 72
Transportation at minimum cost in a directed network linear program
x >= 0 Tableau
Ax - b >= 0 [A ][-b] pivot to make [-b] >= 0 and [c'] >= 0
c'x = min [c'][ 0]
available supply equals demand
Simplex iterations = 9
V\E 22 23 24 3 4 25 6 7 26 9 27 11 12 28 29 30 16 17 18 19 20 21 -b
0 1 0 1 1 1 1 0 -1 0 -1 1 1 1 1 0 0 0 -1 -1 0 0 0 53
1 0 0 -1 -1 0 0 1 1 0 0 -1 -1 0 0 0 0 1 1 0 0 0 0 0
2 0 0 0 0 -1 -1 -1 0 0 1 0 0 -1 -1 0 0 -1 0 1 0 0 0 0
5 1 1 1 0 0 1 0 -1 0 -1 1 1 1 1 0 0 0 -1 -1 0 0 0 53
8 0 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 1 1 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 0 -1 0 1 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 0 1 1 0 0
14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 -1 0 1 0
15 1 1 1 0 0 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 -1 -1 53
31 -1 -1 -1 0 0 -1 0 0 -1 0 -1 0 0 -1 -1 -1 0 0 0 0 0 0 0
c' 3 2 2 1 1 2 1 0 1 0 1 1 1 1 0 0 1 0 0 1 1 1 159
ship 53 0 0 0 0 53 0 0 0 0 0 0 0 0 0 53 0 0 0 0 0 0
VertexLabels 22 23 24 25 26 27 28 29 30 31
SupplyDemand -53 0 0 0 0 0 0 0 0 53
SupplyChange 53 0 0 0 0 0 0 0 0 -53
InitialSupply 15 2 23 0 7 9 36 1 55 72
FinalSupply 68 2 23 0 7 9 36 1 55 19
shortest path 31, 15, 26, 5, 23, 0, 22,
Testing the TwoBit object rep of the incidence matrix:
1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 -1 0 -1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 -1 0 -1 0 -1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 -1 0 -1 0 -1 0 1 1 1 1 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 -1 0 0 -1 0 0 0 0 1 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 -1 0 -1 0 0 0 -1 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 -1 0 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 -1 -1 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 -1 -1
Printing Laplacian Matrix for Network
3 -1 -1 -1 0 0 0 0 0 0
-1 4 -1 -1 -1 0 0 0 0 0
-1 -1 5 -1 -1 -1 0 0 0 0
-1 -1 -1 5 -1 0 -1 0 0 0
0 -1 -1 -1 8 -1 -1 -1 -1 -1
0 0 -1 0 -1 4 -1 -1 0 0
0 0 0 -1 -1 -1 4 0 -1 0
0 0 0 0 -1 -1 0 4 -1 -1
0 0 0 0 -1 0 -1 -1 4 -1
0 0 0 0 -1 0 0 -1 -1 3
D:\java\MinShip\my-minship-app>