1. ENGM 732 Network 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 Month1234 Demand20253218 Available25202520 Costs to hire and / layoff each month are Month1234 Hire170200200150 Fire220240200200 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 2 3 4 5 6 [0,20,200] [0,25,200] [0,20,50] [0,0,170] [0,-M,0] (0,M,220) (0,M,240 (0,M,200) (0.M,200) (18,M,250) (22,M,250) (25,M,250) (20,M,250) (lower bound, capacity, cost() [Fixed, Max Slack, Cost]

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 TonsWarehouse Month Cost Price Cost Available CapacityDemand 1 85 95 2 6000 5000 3500 2 70 90 4 7000 4000 2500 3 105 100 6 5000 4000 4000 4 95 100 4 3000 6000 6000 5 103 110 4 3000 7000 4500

6. Amalgamated Grain Export

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

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

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

10. Amalgamated Grain Export 1 2 3 4 5 [0,60,85] [0,70,70] [0,50,105] [0,30,95] [0,30,103] [Fixed, Slack Flow, Cost] (Capacity, Cost) Purchase the wheat each month Include a model for holding some wheat from month to month Sell the wheat Meet the demand (50,2) (40,4) (40,6) (60,4) 6 7 8 9 10 (M,-95) (M,-110) (M,-100) (M,-90) [-35] [-25] [-40] [-60] [-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 MinneapolisLincoln Denver Demand Aberdeen4 5 830 Vermillion7 4 925 Chamberlain6 6 835 Rapid City7 6 550 Available80 70 90

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

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

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

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

16. Generous Electric M L D A V C R [80] [70] [90] [Fixed] (cost) 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? (4) (7) (6) (7) [-30] [-25] [-35] [-50]

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