Transportation simplex method

1
Transportation simplex method
2
Balanced?
B1 B1 B2 B2 B3 B3 B4 B4
R1 30
R1 8 2 4 7 30
R2 40
R2 7 4 3 2 40
R3 50
R3 2 5 5 9 50
20 20 16 16 42 42 42 42
120
120
120
3
Methods for finding basic feasible solution

• We need to find a feasible solution, which
  satisfy all the constraints (supply and demand).
• Northwest corner
• Minimum cost
• Vogels method

Solution
4
Northwest corner
B1 B1 B2 B2 B3 B3 B4 B4
R1 30
R1 8 2 4 7 30
R2 40
R2 7 4 3 2 40
R3 50
R3 2 5 5 9 50
20 20 16 16 42 42 42 42
20
10
10
34
6
34
42
42
8
120
6
8
5
Vogels method
B1 B1 B2 B2 B3 B3 B4 B4
R1 30
R1 8 2 4 7 30
R2 40
R2 7 4 3 2 40
R3 50
R3 2 5 5 9 50
20 20 16 16 42 42 42 42
1. row Penalty 4-2 2
2
14
3
2
12
16
2
2. row Penalty 3-2 1
1
40
30
3. row Penalty 5-2 3
20
30
3
0
4
120
12
40
6
Minimum cost
B1 B1 B2 B2 B3 B3 B4 B4
R1 30
R1 8 2 4 7 30
R2 40
R2 7 4 3 2 40
R3 50
R3 2 5 5 9 50
20 20 16 16 42 42 42 42
16
14
14
40
2
30
28
2
20
120
2
28
7
Solution
B1 B1 B2 B2 B3 B3 B4 B4
R1 30
R1 8 2 4 7 30
R2 40
R2 7 4 3 2 40
R3 50
R3 2 5 5 9 50
20 20 16 16 42 42 42 42
20
10
6
34
42
8
120
(11)
(12)
(22)
(23)
(33)
(34)
IB
8
8 U1 V1
U10
V18
6 equation 7 variable ? Fix U10
2 U1 V2
V22
U22
4 U2 V2
V31
U34
3 U2 V3
V45
5 U3 V3
9 U3 V4
(11)
(12)
(22)
(23)
(33)
(34)
IB
9
U10 V18 U22 V22 U34 V31
V45
B1 B1 B2 B2 B3 B3 B4 B4
R1 30
R1 8 2 4 7 30
R2 40
R2 7 4 3 2 40
R3 50
R3 2 5 5 9 50
20 20 16 16 42 42 42 42
d134-(U1V3)3
3
2
20
10
-3
-5
6
34
-10
-1
42
8
120
10
B1 B1 B2 B2 B3 B3 B4 B4
R1 30
R1 8 2 4 7 30
R2 40
R2 7 4 3 2 40
R3 50
R3 2 5 5 9 50
20 20 16 16 42 42 42 42
3
2
20
10
20-T
10T
-3
-5
6
34
34T
6-T
-10
-1
42
8
T
8-T
120
11
T 6
B1 B1 B2 B2 B3 B3 B4 B4
R1 30
R1 8 2 4 7 30
R2 40
R2 7 4 3 2 40
R3 50
R3 2 5 5 9 50
20 20 16 16 42 42 42 42
10T
20-T
34T
6-T
T
8-T
42
120
12
T 6
B1 B1 B2 B2 B3 B3 B4 B4
R1 30
R1 8 2 4 7 30
R2 40
R2 7 4 3 2 40
R3 50
R3 2 5 5 9 50
20 20 16 16 42 42 42 42
16
14
40
6
2
42
120
13
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