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CMA Intermediate · Operations Management and Strategic Management · Transportation

A transportation problem has 3 sources and 4 destinations. The initial basic feasible solution obtained has only 5 occupied cells. Before applying the MODI test, what should be done?

The solution is degenerate because it needs m + n - 1 = 6 occupied cells but has 5. A tiny quantity epsilon is allocated to an unoccupied cell that forms no closed loop with the occupied cells, so MODI numbers can be calculated.

  1. AAdd a dummy row and a dummy column
  2. BAllocate a very small quantity epsilon to an unoccupied cell that does not form a closed loop with occupied cells, making 6 occupied cellsCorrect
  3. CRemove one occupied cell to make it 4 cells
  4. DProceed with MODI, since 5 cells are enough

Explanation

MODI requires m + n - 1 = 3 + 4 - 1 = 6 occupied cells in independent positions so all ui and vj can be found. With 5 cells the solution is degenerate, so epsilon is placed in an independent unoccupied cell. Proceeding with 5 leaves the u and v values undetermined.

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