Comic Sans MS size 44

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Comic Sans MS size 44
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• First level bullet (size 32)
• Second level bullet (size 28)
• Third level bullet (size 24)

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(No Transcript)
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Oil Shipping Example From Bazarra and Jarvis

• Transport 20,000,000 barrels of oil from Dhahran,
  Saudi Arabia to Rotterdam (4 Mil.), Marseilles
  (12 Mil) and Naples (4 Mil.) in Europe
• Routes
• Ship oil around Africa to
• Rotterdam 1.20/barrel
• Marseilles 1.40/barrel
• Naples 1.40/barrel
• Dhahran -gt Suez -gt Suez Canal -gt Port Said
• 0.30/barrel from Dhahran to Suez
• 0.20/barrel through Suez Canal
• Port Said to
• Rotterdam 0.25
• Marseilles 0.20
• Naples 0.15

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Oil Shipping Example From Bazarra and Jarvis

• Transport 20,000,000 barrels of oil from Dhahran,
  Saudi Arabia to Rotterdam (4 Mil.), Marseilles
  (12 Mil) and Naples (4 Mil.) in Europe
• Route 1 ship oil around Africa to
• Rotterdam (cost 1.20/barrel)
• Marseilles (cost 1.40/barrel)
• Naples (cost 1.40/barrel)

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Oil Shipping Example Continued

• Route 2 Dhahran to Suez then pipeline to
  Alexandria
• 0.15/barrel through pipeline
• Alexandria to
• Rotterdam (cost 0.22/barrel)
• Marseilles (cost 0.20/barrel)
• Naples (cost 0.15/barrel)

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Oil Shipping Example Continued

• 30 of oil in Dhahran shipped in large tankers
  that cant go through the Suez Canal
• Pipeline from Suez to Alexandria has a capacity
  of 10 million barrels of oil
• Formulate as MCNFP

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Network Formulation
R
PS
M
S
D
A
N
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Network Formulation Continued

• Supply Node
• Dharhan has a supply of 20 M
• Demand Nodes
• Rotterdam, Marseilles and Naples have demands of
  4 M, 12 M and 4M, respectively
• Transshipment Nodes
• Suez, Alexandria and Port Said

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Arcs
Lower bound 0 for all arcs Upper bound
infinity for all arcs except (S,A) 10
million (S,PS) 14 million
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LP Formulation for Oil Shipping Example
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minimize 1.2 XDR 1.4 XDM 1.4 XDN 0.3 XDS
0.2 XSPS 0.15 XSA 0.25 XPSR 0.2 XPSM
0.15 XPSN 0.25 XAR 0.2 XAM 0.15 XAN subject
to XDR XDM XDN XDS 20000000 D XSPS
XSA - XDS 0 S XPSR XPSM XPSN - XSPS
0 PS XAR XAM XAN - XSA 0 PA -XPSR -
XAR - XDR - 4000000 R -XPSM - XAM - XDM -
12000000 M -XPSN - XAN - XDN -
4000000 N XSPS lt 14000000 (At most 70
through canal) XSA lt 10000000 ( Pipeline
capacity)
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Optimal Solution
Cost 13,500,000 Arc Flow XDS
20,000,000 XSPS 10,000,000 XSA
10,000,000 XPSR 4,000,000 XPSM
6,000,000 XAM 6,000,000 XAN 4,000,000