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Transportation simplex method
B1B2B3B4 R R R Balanced?
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 - Vogel’s method Solution:
Northwest corner Northwest cornerB1B2B3B4 R R R |10 |34 8 |42 8
B1B2B3B4 R R R |30 2 |14 1. row: Penalty: 4-2 = 2 2. row: Penalty: 3-2 = row: Penalty: 5-2 = |2 40 Vogel’s method
Minimum cost B1B2B3B4 R R R |2|30 |
Solution SolutionB1B2B3B4 R R R (1;1)(1;2)(2;2)(2;3)(3;3)(3;4) IB=IB=
(1;1) (1;2)(2;2)(2;3)(3;3)(3;4) IB=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=0V1=8 V2=2U2=2 V3=1U3=4 V4=5
U1=0 V1=8 U2=2 V2=2 U3=4 V3=1 V4=5 B1B2B3B4 R R R d 13 =4-(U1+V3)=
B1B2B3B4 R R R Θ 34+ Θ 8- Θ 6- Θ 20- Θ 10+ Θ
B1B2B3B4 R R R Θ 8- Θ 34+ Θ 6- Θ 10+ Θ 20- Θ Θ =6
B1B2B3B4 R R R Θ =6
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