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ENGM 732 Network Flow ProgrammingPowerPoint Presentation

ENGM 732 Network Flow Programming

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### ENGM 732Network Flow Programming

Network Flow Models

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.

Hire em, Fire em

- Build a network flow model to capture this problem

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]

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

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

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

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

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]

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

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

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

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]

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]

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]

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