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Hungarian Method

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Hungarian Method
HW5Q2)

The model:-
Optimize Z =
Where,
Xij= no of containers from distribution center I to customer j …..(i=1,2,3,4: j=A,B,C)
Cij= Shipping cost per container from distribution center I to customer j

Subject to, ∑XiA=600 ∑XiB=500 ∑XiC=500 ∑X1j=450 ∑X2j=600 ∑X3j=350
Xij= integer

The VAM penalty cost is given by,
The initial allocation in VAM method is made in the row or column that has the highest penalty cost. In following table, column C has highest penalty cost i.e. $350. and we choose cell 4C.

Iteration 1)

A
B
C

Hongkong
Singapore
Taipei
Supply
Penalty
1
LA
300

210

340

450
90
2
Savannah
490

520

610

600
30
3
Galveston
360

320

500

350
40
4
Dummy
0

0

0
200
200
200

Demand
600

500

500

1400

Penalty
60

110

350

Iteration 2)

A
B
C

Hongkong
Singapore
Taipei
Supply
Penalty
1
LA
300

210
450
340

450
90
2
Savannah
490

520

610

600
30
3
Galveston
360

320

500

350
40
4
Dummy
0

0

0
200
200

Demand
600

500

500

1400

Penalty
60

Iteration 3)

A
B
C

Hongkong
Singapore
Taipei
Supply
Penalty
1
LA
300

210
450
340

450

2
Savannah
490

520

610

600
30
3
Galveston
360

320
50
500

350
40
4
Dummy
0

0

0
200
200

Demand
600

500

500

1400

Penalty
60

160

Iteration 4)

A
B
C

Hongkong
Singapore
Taipei
Supply
Penalty
1
LA
300

210
450
340

450

2
Savannah
490

520

610

600
30
3
Galveston
360
300
320
50
500

350

4
Dummy
0

0

0
200
200

Demand
600

500

500

1400

Penalty

160

Iteration 5)

A
B
C

Hong Kong
Singapore
Taipei
Supply
Penalty
1
LA
300

210
450
340

450

2
Savannah
490

520

610
300
600
30
3
Galveston
360
300
320
50
500

350

4
Dummy
0

0

0
200
200

Demand
600

500

500

1400

Penalty

Iteration 6) INTIAL VAM SOLUTION:

A
B
C

Hong Kong
Singapore
Taipei
Supply
Penalty
1
LA
300

210
450
340

450

2
Savannah
490
300
520

610
300
600

3
Galveston
360
300
320
50
500

350

4
Dummy
0

0

0
200
200

Demand
600

500

500

1400

Penalty

Modified
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