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CMA Final · Strategic Cost Management · Transportation

A transportation problem has 3 sources and 4 destinations. An initial feasible solution by the North-West Corner method has only 5 occupied (allocated) cells. Before testing for optimality using MODI, the correct step is to:

Add a single epsilon allocation in an unoccupied cell that forms no closed loop with the existing cells. A 3 by 4 problem needs 3 plus 4 minus 1, that is 6, occupied cells, but only 5 exist, so the solution is degenerate by one cell.

  1. AAdd one very small allocation (epsilon) in an unoccupied cell that does not form a closed loop with the occupied cellsCorrect
  2. BAdd a dummy source and a dummy destination to restore balance
  3. CDelete one occupied cell so that the number of cells equals the number of sources
  4. DAdd two epsilon allocations so that the cells equal the number of destinations

Explanation

A non-degenerate solution needs m + n - 1 = 3 + 4 - 1 = 6 occupied cells. With 5, the solution is degenerate and one epsilon allocation is required, placed in an independent (loop-free) cell so that all u and v values can be computed. Adding two would give 7 cells, which is more than needed.

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