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Transportation simplex Transportation simplex methodmethod
B1B1 B2B2 B3B3 B4B4
R1R1 303088 22 44 77
R2R2 404077 44 33 22
R3R3 505022 55 55 99
2020 1616 4242 4242
120
120
120
Balanced?
Methods for finding basic feasible solutionMethods for finding basic feasible solution
We need to find a feasible solution, which satisfy all the We need to find a feasible solution, which satisfy all the constraints (supply and demand).constraints (supply and demand).
- Northwest cornerNorthwest corner
- Minimum costMinimum cost
- Vogel’s methodVogel’s method
Solution:
Northwest cornerNorthwest corner
B1B1 B2B2 B3B3 B4B4
R1R1 303088 22 44 77
R2R2 404077 44 33 22
R3R3 505022 55 55 99
2020 1616 4242 4242 120
20
42
10
6
6 34
|10
|34
8
|428
B1B1 B2B2 B3B3 B4B4
R1R1 303088 22 44 77
R2R2 404077 44 33 22
R3R3 505022 55 55 99
2020 1616 4242 4242 120
20
12
30
16
12 40
|30
2|141. row: Penalty: 4-2 = 2
2. row: Penalty: 3-2 = 1 1
3. row: Penalty: 5-2 = 3 30
3
4
2 |2
40
Vogel’s methodVogel’s method
Minimum costMinimum cost
B1B1 B2B2 B3B3 B4B4
R1R1 303088 22 44 77
R2R2 404077 44 33 22
R3R3 505022 55 55 99
2020 1616 4242 4242 120
16
|2|30
|14
28
2
2
28
14
20
40
SolutionSolution
B1B1 B2B2 B3B3 B4B4
R1R1 303088 22 44 77
R2R2 404077 44 33 22
R3R3 505022 55 55 99
2020 1616 4242 4242 120
20
42
10
6 34
8
(1;1) (1;2) (2;2) (2;3) (3;3) (3;4)IB=
(1;1) (1;2) (2;2) (2;3) (3;3) (3;4)IB=
8 = U1 + V1
2 = U1 + V2
4 = U2 + V2
3 = U2 + V3
5 = U3 + V3
9 = U3 + V4
6 equation 7 variable
Fix U1=0
U1=0 V1=8
V2=2U2=2
V3=1U3=4
V4=5
U1=0 V1=8
U2=2 V2=2
U3=4 V3=1
V4=5B1B1 B2B2 B3B3 B4B4
R1R1 303088 22 44 77
R2R2 404077 44 33 22
R3R3 505022 55 55 99
2020 1616 4242 4242 120
20
42
10
6 34
8
d13=4-(U1+V3)=3 3
-10
-3 -5
2
-1
B1B1 B2B2 B3B3 B4B4
R1R1 303088 22 44 77
R2R2 404077 44 33 22
R3R3 505022 55 55 99
2020 1616 4242 4242 120
20
42
10
6 34
8
3
-10
-3 -5
2
-1Θ
34+Θ
8-Θ
6-Θ
20-Θ 10+Θ
B1B1 B2B2 B3B3 B4B4
R1R1 303088 22 44 77
R2R2 404077 44 33 22
R3R3 505022 55 55 99
2020 1616 4242 4242
Θ 8-Θ
34+Θ6-Θ
10+Θ20-Θ
120
42
Θ =6
B1B1 B2B2 B3B3 B4B4
R1R1 303088 22 44 77
R2R2 404077 44 33 22
R3R3 505022 55 55 99
2020 1616 4242 4242
6 2
40
1614
120
42
Θ =6
