Engm 732 network flow programming
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ENGM 732 Network 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 Month1234 Demand20253218 Available25202520

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ENGM 732 Network Flow Programming

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Engm 732 network flow programming

ENGM 732Network Flow Programming

Network Flow Models


Hire em fire em

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.


Hire em fire em1

Hire em, Fire em

  • Build a network flow model to capture this problem


Hire em fire em2

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

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

2709047000 40002500

3 10510065000 40004000

49510043000 60006000

5103 11043000 70004500


Amalgamated grain export1

Amalgamated Grain Export


Amalgamated grain export2

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 export3

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 export4

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 export5

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 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

Vermillion74925

Chamberlain66835

Rapid City76550

Available80 70 90


Generous electric1

Generous Electric

[Fixed]

M

Push available supply at

primary warehouses

[80]

[70]

L

D

[90]


Generous electric2

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 electric3

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 electric4

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 electric5

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 electric6

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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