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CMA Intermediate · Operations Management and Strategic Management · Transportation

A transportation problem has 3 sources and 4 destinations. The initial solution by the North-West Corner method has these allocations: 30 in (S1,D1), 20 in (S1,D2), 40 in (S2,D2), 10 in (S2,D3), 50 in (S3,D3). Which statement is correct?

The solution is degenerate because m + n - 1 equals 6 but only 5 cells are occupied. To proceed, a very small epsilon allocation is placed in an independent unoccupied cell that forms no closed loop with the existing allocations.

  1. AThe solution is non-degenerate because 5 cells are occupied, and 5 is less than 6
  2. BThe solution is degenerate; one more cell must receive an epsilon allocation placed so that no closed loop formsCorrect
  3. CThe solution is degenerate; one occupied cell must be removed
  4. DThe solution is non-degenerate because the sum of allocations is balanced

Explanation

Required occupied cells = 3 + 4 - 1 = 6, but only 5 are occupied, so the solution is degenerate. A tiny quantity epsilon is placed in an unoccupied cell that forms no closed loop with existing allocations, for example (S3,D4). Removing a cell would worsen the shortfall.

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