CMA Final · Strategic Cost Management · Transportation
A transportation problem has two sources and three destinations. Unit costs in rupees are S1: 8, 6, 10 and S2: 9, 7, 5 for D1, D2, D3. The current basic cells are S1D1, S1D2, S2D2 and S2D3. Using the MODI method, what is the opportunity cost (cij - ui - vj) of the empty cell S1D3?
With u1 set to zero, the basic cells give v1 = 8, v2 = 6, u2 = 1 and v3 = 4. The empty cell S1D3 then has an opportunity cost of 10 minus (0 plus 4), which equals 6. A positive value means the cell would not improve the solution.
- A-6
- B5
- C6Correct
- D4
Explanation
Set u1 = 0. Then v1 = 8 and v2 = 6 from the S1 basic cells. From S2D2, u2 = 7-6 = 1, and from S2D3, v3 = 5-1 = 4. For S1D3 the value is 10 - (0+4) = 6. The value -6 reverses the sign, and 4 forgets to deduct v3.
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