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Comic Sans MS size 44

3/4”. Comic Sans MS size 44. First level bullet (size 32) Second level bullet (size 28) Third level bullet (size 24). 3/4”. 3/4”. Oil Shipping Example From Bazarra and Jarvis.

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Comic Sans MS size 44

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  1. 3/4” Comic Sans MS size 44 • First level bullet (size 32) • Second level bullet (size 28) • Third level bullet (size 24) 3/4” 3/4” Footer

  2. Footer

  3. 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 -> Suez -> Suez Canal -> 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 Footer

  4. 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) Footer

  5. 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) Footer

  6. Oil Shipping Example Continued • 30% of oil in Dhahran shipped in large tankers that can’t go through the Suez Canal • Pipeline from Suez to Alexandria has a capacity of 10 million barrels of oil • Formulate as MCNFP Footer

  7. Network Formulation R PS M S D A N Footer

  8. 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 Footer

  9. Arcs Lower bound = 0 for all arcs Upper bound = infinity for all arcs except (S,A) = 10 million (S,PS) = 14 million Footer

  10. LP Formulation for Oil Shipping Example Footer

  11. 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 <= 14000000 (At most 70% through canal) XSA <= 10000000 ( Pipeline capacity) Footer

  12. 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 Footer

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