1 Unit refining costs (per 100,000 barrels) Edmonton $1,500 Red Deer $1,200 Unit shipping costs (per 100,000 barrels) To Node index Grande Prairie Fort St. John Edmonton Red Deer From Grande Prairie 1 $2,000 $3,200 Fort St. John 2 $4,200 $4,900 Edmonton 3 $1,500 Red Deer 4 $1,500 Calgary 5 Lethbridge 6 Network formulation Origin Destination 1 3 1 4 2 3 2 4 3 4 3 5 3 6 4 3 4 5 4 6 5 6 6 5 Total cost $44,900 Unit Cost $2,000.00 $3,200.00 $4,200.00 $4,900.00 $1,500.00 $1,800.00 $2,900.00 $1,500.00 $1,000.00 $1,600.00 $1,200.00 $1,200.00 Flow 5.00 0.50 0.00 2.00 0.00 5.00 0.00 0.00 0.00 2.50 0.00 0.00 <= <= <= <= <= <= <= <= <= <= <= <= Capacity Total Cost 6.00 $10,000.00 3.00 $1,600.00 6.00 $0.00 3.00 $9,800.00 3.00 $0.00 5.00 $16,500.00 2.50 $0.00 6.00 $0.00 5.00 $0.00 2.50 $7,000.00 2.50 $0.00 5.00 $0.00 Calgary $1,800 $1,000 Lethbridge $2,900 $1,600 $1,200 $1,200 Node balance contraints Oil field constraints Node Oil Field net outflow 1 5.5 <= 2 2 <= Oil field capacity 5.5 4.5 Refinery constriants Node Refinery net outflow 3 0= 4 0= Refinery capacity 0 0 Node Customer net inflow 5 5 >= 6 2.5 >= Customer demand 5 2.5 Customer constraints Problem 2 Network formulation Orgin Destination 1 1 1 1 2 2 2 3 3 Total cost Unit Costs Flow 1 $0.40 2 $0.40 3 $0.40 4 $0.40 2 $0.20 3 $0.20 4 $0.20 3 $0.12 4 $0.12 $0.00 0 <= 0 <= 0 <= 0 <= 0 <= 0 <= 0 <= 0 <= 0 <= Capacity 3000 2400 3600 1200 2400 3600 1200 3600 1200 Node balance constraints Buy or Clean constraints Node Buy or clean net flow 1 0 >= 2 0 >= 3 0 >= Customer constraints Node Customer inflow 4 5 6 7 0 >= 0 >= 0 >= 0 >= Buy or clean capacity 0 0 0 Customer demand 3000 2400 3600 1200