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
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