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CMA Intermediate · Operations Management and Strategic Management · Transportation

Two plants supply 40 and 60 units to three markets needing 40, 30 and 30 units. Applying the North-West Corner Rule, the first allocation of 40 units to plant 1 and market 1 exhausts both the row and the column. What does this indicate?

The solution is degenerate. Exhausting a row and a column together leaves only three allocated cells (40, 30, 30), whereas m + n - 1 requires four for 2 sources and 3 destinations. A small epsilon allocation is added to a suitable empty cell.

  1. AThe problem is unbalanced and needs a dummy source
  2. BThe solution is degenerate, with fewer than 4 allocated cellsCorrect
  3. CThe solution is optimal and no further test is needed
  4. DThe solution is non-degenerate with 4 allocated cells

Explanation

Supply equals demand (100 each), so the problem is balanced. Allocations are 40, 30 and 30, only 3 cells, while m + n - 1 = 4 are needed. Simultaneous exhaustion of a row and column causes degeneracy, which is handled by adding a small epsilon allocation.

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