Lecture_16_Vogal s Approximation method

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Find the initial basic feasible solution using vogel’s approximation method
1.
W1 W2 W3 W4 Availability
F1 19 30 50 10 7
F2 70 30 40 60 9
F3 40 8 70 20 18
Requirement 5 8 7 14
Solution
W1 W2 W3 W4 Availability Penalty
F1 19 30 50 10 7 19-10=9
F2 70 30 40 60 9 40-30=10
F3 40 8 70 20 18 20-8=12
Requirement 5 8 7 14
Penalty 40-19=21 30-8=22 50-40=10 20-10=10
W1 W2 W3 W4 Availability Penalty
F1 (19) (30) (50) (10) 7 9
F2 (70) (30) (40) (60) 9 10
F3 (40) 8(8) (70) (20) 18/10 12
Requirement 5 8/0 7 14
Penalty 21 22 10 10
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W1 W2 W3 W4 Availability Penalty
F1 5(19) (30) (50) (10) 7/2 9
F2 (70) (30) (40) (60) 9 20
F3 (40) 8(8) (70) (20) 18/10 20
Requirement 5/0 X 7 14
Penalty 21 X 10 10
W1 W2 W3 W4 Availability Penalty
F1 5(19) (30) (50) (10) 7/2 40
F2 (70) (30) (40) (60) 9 20
F3 (40) 8(8) (70) 10(20) 18/10/0 50
Requirement X X 7 14/4
Penalty X X 10 10
W1 W2 W3 W4 Availability Penalty
F1 5(19) (30) (50) 2(10) 7/2/0 40
F2 (70) (30) (40) (60) 9 20
F3 (40) 8(8) (70) 10(20) X X
Requirement X X 7 14/4/2
Penalty X X 10 50
W1 W2 W3 W4 Availability Penalty
F1 5(19) (30) (50) 2(10) X X
F2 (70) (30) 7(40) 2(60) X X
F3 (40) 8(8) (70) 10(20) X X
Requirement X X X X
Penalty X X X X
Initial Basic Feasible Solution
x11 = 5, x14 = 2, x23 = 7, x24 = 2, x32 = 8, x34 = 10
The transportation cost is 5 (19) + 2 (10) + 7 (40) + 2 (60) + 8 (8) + 10 (20) = Rs. 779
2.
Stores Availability
I II III IV
Warehouse
A 21 16 15 13 11
B 17 18 14 23 13
C 32 27 18 41 19
Requirement 6 10 12 15
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Solution
Stores Availability Penalty
I II III IV
Warehouse
A (21) (16) (15) (13) 11 2
B (17) (18) (14) (23) 13 3
C (32) (27) (18) (41) 19 9
Requirement 6 10 12 15
Penalty 4 2 1 10
Stores Availability Penalty
I II III IV
Warehouse
A (21) (16) (15) 11(13) 11/0 2
B (17) (18) (14) (23) 13 3
C (32) (27) (18) (41) 19 9
Requirement 6 10 12 15/4
Penalty 4 2 1 10
Stores Availability Penalty
I II III IV
Warehouse
A (21) (16) (15) 11(13) X X
B (17) (18) (14) 4(23) 13/9 3
C (32) (27) (18) (41) 19 9
Requirement 6 10 12 15/4/0
Penalty 15 9 4 18
Stores Availability Penalty
I II III IV
Warehouse
A (21) (16) (15) 11(13) X X
B 6(17) (18) (14) 4(23) 13/9/3 3
C (32) (27) (18) (41) 19 9
Requirement 6/0 10 12 X
Penalty 15 9 4 X
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Stores Availability Penalty
I II III IV
Warehouse
A (21) (16) (15) 11(13) X X
B 6(17) 3(18) (14) 4(23) 13/9/3/0 4
C (32) (27) (18) (41) 19 9
Requirement X 10/7 12 X
Penalty X 9 4 X
Stores Availability Penalty
I II III IV
Warehouse
A (21) (16) (15) 11(13) X X
B 6(17) 3(18) (14) 4(23) X X
C (32) 7(27) 12(18) (41) X X
Requirement X X X X
Penalty X X X X
Initial Basic Feasible Solution
x14 = 11, x21 = 6, x22 = 3, x24 = 4, x32 = 7, x33 = 12
The transportation cost is 11 (13) + 6 (17) + 3 (18) + 4 (23) + 7 (27) + 12 (18) = Rs. 796
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