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A B C D E F G H I J
From To Ship Unit Cost Nodes Net Flow Supply/Demand
Source 1 Destination 1 0 $6 Source 1 40 =40
Source 1 Destination 2 10 $7 Source 2 60 =60
Source 1 Destination 3 30 $4 Destination 1 -30 = -30
Source 2 Destination 1 30 $5 Destination 2 -40 = -40
Source 2 Destination 2 30 $8 Destination 3 -30 = -30
Source 2 Destination 3 0 $6
Total Cost $580
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A B C D E F G H I J K
From To Ship Capacity Unit Cost Nodes Net Flow Supply/Demand
P1 WH1 125 <= 125 $425 P1 200 =200
P1 WH2 75 <= 150 $560 P2 300 =300
P2 WH1 125 <= 175 $510 WH1 0 = 0
P2 WH2 175 <= 200 $600 WH2 0 = 0
WH1 RO1 100 <= 100 $470 RO1 -150 = -150
WH1 RO2 50 <= 150 $505 RO2 -200 = -200
WH1 RO3 100 <= 100 $490 RO3 -150 = -150
WH2 RO1 50 <= 125 $390
WH2 RO2 150 <= 150 $410
WH2 RO3 50 <= 75 $440
Total Cost $488,125
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Fixed Per Total Total
Shipping Mile Miles to Miles to Cost to Cost to
Vendor Price Charge Charge WH1 WH2 WH1 WH2
1 $22,500 $300 $0.40 1600 400 $23,440 $22,960
2 $22,700 $200 $0.50 500 600 $23,150 $23,200
3 $22,300 $500 $0.20 2000 1000 $23,200 $23,000
From To Ship Capacity Unit Cost Nodes Net Flow Supply/Demand
V1 WH1 0 <= 6 $23,440 V1 10 =10
V1 WH2 6 <= 6 $22,960 V2 10 =10
V2 WH1 6 <= 6 $23,150 V3 10 =10
V2 WH2 0 <= 6 $23,200 WH1 0 = 0
V3 WH1 0 <= 6 $23,200 WH2 0 = 0
V3 WH2 4 <= 6 $23,000 F1 -10 = -10
WH1 F1 6<= 6$200 F2 -6 =-6
WH1 F2 0<= 6$700 D -14 = -14
WH2 F1 4<= 6$400
WH2 F2 6<= 6$500
V1 D 4 $0
V2 D 4 $0
V3 D 6 $0
Total Cost $374,460
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A B C D E F G H I J K
From To Ship Capacity Unit Cost Nodes Net Flow Supply/Demand
ST LI 30 <= 40 $3,200 ST 130 =130
ST BO 70 <= 70 $2,500 BE 50 =50
ST RO 30 <= 50 $2,900 LI 0 = 0
BE RO 20 <= 20 $2,400 BO 0 = 0
BE HA 30 <= 60 $2,000 RO 0 = 0
LI NO 30 <= 30 $6,100 HA 0 = 0
BO NO 30 <= 50 $6,800 NO 0 = 0
BO NY 40 <= 40 $5,400 NY 0 = 0
RO NY 50 <= 60 $5,900 BN 0 = 0
HA NY 0<= 30 $6,300 LA -130 = -130
HA BN 30 <= 40 $5,700 SE -50 = -50
NO LA 60 <= 70 $3,100
NY LA 60 <= 80 $4,200
NY SE 30 <= 40 $4,000
BN LA 10 <= 10 $3,400
BN SE 20 <= 20 $3,000
Total Cost $2,187,000
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A B C D E F G H I J K
From To Ship Capacity Unit Cost Nodes Net Flow Supply/Demand
ST LI 30 <= 40 $3,200 ST 130 =130
ST BO 70 <= 70 $2,500 LI 0 = 0
ST RO 30 <= 50 $2,900 BO 0 = 0
LI NO 30 <= 30 $6,100 RO 0 = 0
BO NO 30 <= 50 $6,800 NO 0 = 0
BO NY 40 <= 40 $5,400 NY 0 = 0
RO NY 30 <= 60 $5,900 LA -130 = -130
NO LA 60 <= 70 $3,100
NY LA 70 <= 80 $4,200
Total Cost $1,618,000
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A B C D E F G H I J K
From To Ship Capacity Unit Cost Nodes Net Flow Supply/Demand
BE RO 20 <= 20 $2,400 BE 50 =50
BE HA 30 <= 60 $2,000 RO 0 = 0
RO NY 20 <= 60 $5,900 HA 0 = 0
HA NY 10 <= 30 $6,300 NY 0 = 0
HA BN 20 <= 40 $5,700 BN 0 = 0
NY SE 30 <= 40 $4,000 SE -50 = -50
BN SE 20 <= 20 $3,000
Total Cost $583,000
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A B C D E F G H I J
From To Ship Capacity Nodes Net Flow Supply/Demand
A B 8 <= 9 A 15
A C 7 <= 7 B 0 = 0
B D 7 <= 7 C 0 = 0
B E 1 <= 2 D 0 = 0
C D 1 <= 4 E 0 = 0
C E 6 <= 6 F -15
D E 2 <= 3
D F 6 <= 6
E F 9 <= 9
Maximum Flow 15
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A B C D E F G H I J
From To Ship Capacity Nodes Net Flow Supply/Demand
R1 A65 <= 75 R1 95
R1 B30 <= 65 R2 150
R2 A40 <= 40 R3 150
R2 B50 <= 50 A 0 = 0
R2 C60 <= 60 B 0 = 0
R3 B80 <= 80 C 0 = 0
R3 C70 <= 70 D 0 = 0
A D 60 <= 60 E 0 = 0
A E 45 <= 45 F 0 = 0
B D 60 <= 70 T -395
B E 55 <= 55
B F 45 <= 45
C E 45 <= 70
C F 85 <= 90
D T 120 <= 120
E T 145 <= 190
F T 130 <= 130
Maximum Flow 395
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A B C D E F G H I J
From To Ship Capacity Nodes Net Flow Supply/Demand
Texas New Orleans 11 <= 11 Texas 28
Texas Charleston 7 <= 7 California 24
Texas Seattle 2 <= 2 Alaska 28
Texas St. Louis 8 <= 8 Middle East 28
California New Orleans 5 <= 5 New Orleans 0 = 0
California Charleston 4 <= 4 Charleston 0 = 0
California Seattle 8 <= 8 Seattle 0 = 0
California St. Louis 7 <= 7 St. Louis 0 = 0
Alaska New Orleans 7 <= 7 Pittsburgh -26
Alaska Charleston 3 <= 3 Atlanta -33
Alaska Seattle 12 <= 12 Kansas City -25
Alaska St. Louis 6 <= 6
San Francisco
-24
Middle East New Orleans 1 <= 8
Middle East Charleston 9 <= 9
Middle East Seattle 3 <= 4
Middle East St. Louis 15 <= 15
New Orleans Pittsburgh 5 <= 5
New Orleans Atlanta 9 <= 9
New Orleans Kansas City 6 <= 6
New Orleans San Francisco 4 <= 4
Charleston Pittsburgh 8 <= 8
Charleston Atlanta 7 <= 7
Charleston Kansas City 3 <= 9
Charleston San Francisco 5 <= 5
Seattle Pittsburgh 4 <= 4
Seattle Atlanta 6 <= 6
Seattle Kansas City 7 <= 7
Seattle San Francisco 8 <= 8
St. Louis Pittsburgh 9 <= 12
St. Louis Atlanta 11 <= 11
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A B C D E F G H I J K L M N
Littletown Fire Department Shortest Path Problem
From To On Route Distance Nodes Net Flow Supply/Demand Range Name Cells
Fire St. A 0 3 Fire St. 1 = 1 Distance F4:F27
Fire St. B 0 6 A 0 = 0 From B4:B27
Fire St. C 1 4 B 0 = 0 NetFlow I4:I13
A B 0 4 C 0 = 0 Nodes H4:H13
A D 0 6 D 0 = 0 OnRoute D4:D27
B A 0 1 E 0 = 0 SupplyDemand K4:K13
B C 0 2 F 0 = 0 To C4:C27
B D 0 4 G 0 = 0 TotalDistance D29
B E 0 5 H 0 = 0
C B 0 2
Farm Com.
-1 =-1
C E 1 7
D E 0 3
D F 0 8
E D 0 3
E F 1 6
E G 0 5
E H 0 4
F G 0 3
F Farm Com. 1 4
G F 0 3
G H 0 2
G Farm Com. 0 6
H G 0 2
H Farm Com. 0 7
Total Distance 21
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A B C D E F G H I J
From To
On Route
Distance (miles) Nodes Net Flow Supply/Demand
Origin A 1 40 Origin 1 = 1
Origin B 0 60 A 0 = 0
Origin C 0 50 B 0 = 0
A B 1 10 C 0 = 0
A D 0 70 D 0 = 0
B A 0 10 E 0 = 0
B C 0 20 Destination -1 =-1
B D 0 55
B E 1 40
C B 0 20
C N 0 20
C E 0 50
D A 0 70
D B 0 55
D E 0 10
D Destination 1 60
E D 1 10
E Destination 0 80
Total Distance (miles) 160
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A B C D E F G H I J
From To
On Route
Cost Nodes Net Flow Supply/Demand
Year 0 Year 1 1 $8,000 Year 0 1 = 1
Year 0 Year 2 0 $18,000 Year 1 0 = 0
Year 0 Year 3 0 $31,000 Year 2 0 = 0
Year 1 Year 2 0 $10,000 Year 3 -1 =-1
Year 1 Year 3 1 $21,000
Year 2 Year 3 0 $12,000
Total Cost $29,000
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A B C D E F G H I J
From To
On Route
Time (hours) Nodes Net Flow Supply/Demand
Seattle A 0 4.6 Seattle 1 = 1
Seattle B 0 4.7 A 0 = 0
Seattle C 1 4.2 B 0 = 0
A D 0 3.5 C 0 = 0
A E 0 3.4 D 0 = 0
B D 0 3.6 E 0 = 0
B E 0 3.2 F 0 = 0
B F 0 3.3 London -1 =-1
C E 1 3.5
C F 0 3.4
DLondon 03.4
ELondon 13.6
FLondon 03.8
Total Time (hours) 11.3