1. ENGM 732 Network Flow Programming Network Flow Models

2. K Power K Power has 2 fields from which they obtain fuel for their plants. It is sent to one of two facilities for refinement before being sent to generating plants. Refinery A produces 1 unit from 2 units of input and has a capacity of 50 units per year. Refinery B produces 1 unit from 3 units of input and has a capacity of 75 units per year. Refined fuel is sent to one of two plants. Each unit of fuel produced by refinery B produces 1 unit of power. Each unit of fuel produced by refinery A produces 0.8 units of power.

3. K-Power Shipping cost for mineral ore is $0.01 per mile. Distances ore fields and refineries follow: FieldRefinery ARefinery B 1 100 200 2 80 70 Shipping cost for refined ore to generating station is $0.01 per mile. RefineryStation AStation B A 100 120 B 80 50 Costs for generating power at stations A and B are StationCostCapacity A$1.50 50 B$1.75 75

4. K-Power F1F2 F1 Mine field 1 Mine field 2 What does it cost us to mine the ore?

5. K-Power $1 $2 $3 $4 100 200300 100 200300 Field 1 Field 2 $1 $2 $3 $4 $5

6. K-Power F1F2 F1 Mine ore (100,1,1) (100,2,1) (200,4,1) (Capacity, cost, gain) [Fixed, slack, cost) (200,0.5,1) (100,2,1) (200,5,1) [0,500,0]

7. K-Power Shipping cost for mineral ore is $0.01 per mile. Distances ore fields and refineries follow: FieldRefinery ARefinery B 1 100 200 2 80 70 Shipping cost for refined ore to generating station is $0.01 per mile. RefineryStation AStation B A 100 120 B 80 50 Costs for generating power at stations A and B are StationCostCapacity A$1.50 10 B$1.75 30

8. K-Power F1F2 F1 Mine ore (100,1,1) (100,2,1) (200,4,1) (200,0.5,1) (100,2,1) (200,5,1) RBRA (M,1,1) (M,2,1) (M,.8,1) (M,.7,1) Ship to Refinery [0,500,0] (Capacity, cost, gain) [Fixed, slack, cost)

9. K-Power Shipping cost for mineral ore is $0.01 per mile. Distances ore fields and refineries follow: FieldRefinery ARefinery B 1 100 200 2 80 70 Shipping cost for refined ore to generating station is $0.01 per mile. RefineryStation AStation B A 100 120 B 80 50 Costs for generating power at stations A and B are StationCostCapacity A$1.50 10 B$1.75 30

10. K-Power F1F2 F1 Mine ore (100,1,1) (100,2,1) (200,4,1) (200,0.5,1) (100,2,1) (200,5,1) RBRA (M,1,1) (M,2,1) (M,.8,1) (M,.7,1) Ship to Refinery RBRA [0,500,0] (100,1,.5) (150,1,.33) Refine the ore (Capacity, cost, gain) [Fixed, slack, cost) SBSA Ship to Stations (M,1,.8) (M,1.2,.8) (M,.8,1) (M,.5,1)

11. K-Power Shipping cost for mineral ore is $0.01 per mile. Distances ore fields and refineries follow: FieldRefinery ARefinery B 1 100 200 2 80 70 Shipping cost for refined ore to generating station is $0.01 per mile. RefineryStation AStation B A 100 120 B 80 50 Costs for generating power at stations A and B are StationCostCapacity A$1.50 50 B$1.75 75

12. K-Power F1F2 F1 (100,1,1) (100,2,1) (200,4,1) (200,0.5,1) (100,2,1) (200,5,1) RBRA (M,1,1) (M,2,1) (M,.8,1) (M,.7,1) RBRA [0,500,0] (100,1,.5) (225,1,.33) (Capacity, cost, gain) [Fixed, slack, cost) SBSA (M,1,.8) (M,1.2,.8) (M,.8,1) (M,.5,1) Refined fuel is sent to one of two plants. Each unit of fuel produced by refinery B produces 1 unit of power. Each unit of fuel produced by refinery A produces 0.8 units of power.

13. K-Power F1F2 F1 Mine ore (100,1,1) (100,2,1) (200,4,1) (200,0.5,1) (100,2,1) (200,5,1) RBRA (M,1,1) (M,2,1) (M,.8,1) (M,.7,1) Ship to Refinery RBRA [0,500,0] (100,1,.5) (225,1,.33) Refine the ore (Capacity, cost, gain) [Fixed, slack, cost) SBSA Ship to Stations (M,1,.8) (M,1.2,.8) (M,.8,1) (M,.5,1) SBSA Station generation (50,1.5,1) (75,1.75,1)

14. K-Power A transmission connects the two stations and power may flow either direction. Line is 100 miles long, costs is $0.005 per unit per mile, and there is a 0.1% loss on the line per mile.

15. K-Power F1F2 F1 Mine ore (100,1,1) (100,2,1) (200,4,1) (200,0.5,1) (100,2,1) (200,5,1) RBRA (M,1,1) (M,2,1) (M,.8,1) (M,.7,1) Ship to Refinery RBRA [0,500,0] (100,1,.5) (150,1,.33) Refine the ore (Capacity, cost, gain) [Fixed, slack, cost) SBSA Ship to Stations (M,1,.8) (M,1.2,.8) (M,.8,1) (M,.5,1) SBSA Station generation (50,1.5,1) (75,1.75,1) (M,.5,.9) To Distribution

16. K-Binding K-Binding is considering a book binding operation at its RC plant. There are 9 steps that include open boxes, collate pages, trim pages, blue backs, attach binding, emboss binding, box books, attach mailing labels and load trucks. Mgmt has asked for a model of the process, the capacity, and recommendations for increasing capacity at minimal cost.

17. K-Binding StepNo. StationsCapacity 1 1 76 22 10,12 32 10,13 44 7,9,3,2 52 22,23 61 42 73 15,6,4 82 10,15 91 105

18. K-Binding 123456789 (76) (Capacity) (10) (12) (10) (13) (22) (23)