Question

Examine this transportation table: To=> 2 3 Dummy_Supply LO | 10 | 8 | 12 From A 100 80 | 7 16 20 | 4 10 B 150 120 | 10 30 16 19 10 с 150 100 250 Demand 120 80 200 100 Which cell should be filled in the next iteration? O Cell ADummy O Cell A1 Cell B2 O Cell C1

Answer 1

ANSWER: Cell ADummy

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Explanation:

Compute Improvement index of empty cells by alternatively adding and subtracting the cost of cells which form a close loop the empty cell at one of its corner and non-empty cells at all the other corners. For example close loop for empty cell A1 in clockwise direction is formed by cells A1-A3+B4-B1. So, improvement index of A1 is = 10-12+4-6 = -4

Improvement index of ADummy = 0-0+6-12 = -6

Improvement index of B2 = 7-8+12-4 = 7

Improvement index of BDummy = 0-0+6-4 = 2

Improvement index of C1 = 10-6+4-6 = 2

Improvement index of C2 = 9-8+12-6 = 7

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We see that improvement index of ADummy is the most negative (-6)

Therefore, cell ADummy should be filled in the next iteration

Resulting tableau , after next iteration, is following:

To From 1 2 3 Dummy Supply 10 00 12 + 0 A 100 80 20 LD 7 4 0 B 150 120 30 10 9 + 6 0 с 250 170 80 Demand 120 80 200 100 0 Total Cost = 2500