ENGM 732 Network Flow Programming

1. ENGM 732Network Flow Programming Network Flow Models

2. Hire em, Fire em Hirem-Firem supplies clerical employees upon demand to various business concerns in the area. The best available estimates are Month 1 2 3 4 Demand 20 25 32 18 Available 25 20 25 20 Costs to hire and / layoff each month are Month 1 2 3 4 Hire 170 200 200 150 Fire 220 240 200 200 Pay equals $250 per month.

3. Hire em, Fire em • Build a network flow model to capture this problem

4. Hire em, Fire em [0,25,170] 1 (lower bound, capacity, cost() [Fixed, Max Slack, Cost] (20,M,250) [0,20,200] 2 (0,M,220) (25,M,250) (0,M,240 [0,25,200] [0,-M,0] 3 6 (0,M,200) (22,M,250) [0,20,50] 4 (0.M,200) (18,M,250) 5 [0,0,170]

5. Amalgamated Grain Export AGE is based in RC, SD with branch offices in every major grain producing country in the world. Recent crop failures in ADXP have given rise for humanitarian service (and profit). Since it is probable the next wheat harvest will be successful, AGE believes it has a five month window to distribute grain to ADXP. Costs and revenues follow. Purchase Sale Holding Tons Warehouse Month Cost Price Cost Available Capacity Demand 1 85 95 2 6000 5000 3500 2709047000 40002500 3 10510065000 40004000 49510043000 60006000 5103 11043000 70004500

6. Amalgamated Grain Export

7. Amalgamated Grain Export [0,60,85] 1 [Fixed, Slack Flow, Cost] Purchase the wheat each month [0,70,70] 2 [0,50,105] 3 [0,30,95] 4 [0,30,103] 5

8. Amalgamated Grain Export [0,60,85] 1 [Fixed, Slack Flow, Cost] (Capacity, Cost) (50,2) Purchase the wheat each month Include a model for holding some wheat from month to month [0,70,70] 2 (40,4) [0,50,105] 3 (40,6) [0,30,95] 4 (60,4) [0,30,103] 5

9. Amalgamated Grain Export (M,-95) [0,60,85] 1 6 [Fixed, Slack Flow, Cost] (Capacity, Cost) (50,2) (M,-90) Purchase the wheat each month Include a model for holding some wheat from month to month Sell the wheat [0,70,70] 2 7 (40,4) (M,-100) [0,50,105] 3 8 (40,6) (M,-100) [0,30,95] 4 9 (60,4) (M,-110) [0,30,103] 5 10

10. Amalgamated Grain Export (M,-95) [0,60,85] [-35] 1 6 [Fixed, Slack Flow, Cost] (Capacity, Cost) (50,2) (M,-90) Purchase the wheat each month Include a model for holding some wheat from month to month Sell the wheat Meet the demand [0,70,70] 2 7 [-25] (40,4) (M,-100) [0,50,105] 3 8 [-40] (40,6) (M,-100) [0,30,95] 4 9 [-60] (60,4) (M,-110) [0,30,103] 5 10 [-45]

11. Generous Electric Generous owns primary warehouses in Minneapolis, Lincoln, and Denver. We want to resupply secondary warehouses from these three at lowest cost while meeting the demand. Transport costs are Minneapolis Lincoln Denver Demand Aberdeen 4 5 8 30 Vermillion 749 25 Chamberlain 668 35 Rapid City 765 50 Available 80 70 90

12. Generous Electric [Fixed] M Push available supply at primary warehouses [80] [70] L D [90]

13. Generous Electric [Fixed] (cost) A (4) (7) M Push available supply at primary warehouses Ship to secondary [80] V (6) (7) [70] L C D [90] R

14. Generous Electric [Fixed] (cost) A (4) (7) M Push available supply at primary warehouses Ship to secondary [80] V (6) (7) [70] L C D [90] R

15. Generous Electric [Fixed] (cost) A [-30] (4) (7) M Push available supply at primary warehouses Ship to secondary Meet demand at secondary [80] V [-25] (6) (7) [70] L C [-35] D [90] R [-50]

16. Generous Electric [Fixed] (cost) A [-30] (4) (7) M Push available supply at primary warehouses Ship to secondary Meet demand at secondary We have 80+70+90=240 flow in And 30+25+35+50=140 out. Flow in must = flow out How do we resolve? [80] V [-25] (6) (7) [70] L C [-35] D [90] R [-50]

17. Generous Electric [Fixed] (cost) A [-30] (4) (7) M Push available supply at primary warehouses Ship to secondary Meet demand at secondary Add a dummy node [80] V [-25] (6) (7) [70] L C [-35] D [90] R [-50] (0) (0) (0) D [-100]