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Northwest Corner Method Calculator

Enter supplies, demands and unit costs to apply the northwest corner method.

How it is calculated

The tool handles only a 2 × 2 transportation problem: two sources with supplies s1, s2, two destinations with demands d1, d2, and unit costs c11, c12, c21, c22 (row = source, column = destination). It must be balanced, s1 + s2 = d1 + d2, otherwise it returns nothing. Starting at the top-left cell, it ships min(supply, demand), subtracts that from both, then moves down if the supply is used up or right if the demand is. Total cost is Σ xij × cij. Costs are ignored when choosing cells, so the answer is a starting solution, not necessarily the cheapest one.

Worked example

Supplies are 30 and 40, demands are 25 and 45, and the costs are 8, 6 in row 1 and 10, 9 in row 2. Cell (1,1): min(30, 25) = 25, leaving supply 5 and demand 0, so move right. Cell (1,2): min(5, 45) = 5, using up supply 1, so move down. Cell (2,2): min(40, 40) = 40. Cost: 25 × 8 + 5 × 6 + 40 × 9 = 200 + 30 + 360 = 590.00.

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Common mistakes

  • Entering an unbalanced problem, such as supplies adding to 70 and demands to 65. The tool rejects it; add a dummy destination yourself first, but note that this tool only takes a 2 × 2 table.
  • Putting costs in the wrong orientation. The first digit of c12 is the source and the second the destination, so swapping rows and columns changes the total cost.
  • Assuming 590.00 is the minimum cost. The rule ignores costs, so a method like Vogel's or MODI can find a cheaper plan on the same data.
  • Entering costs where supplies belong. The first four values are quantities and cannot be negative; the costs come last.

About this calculator

The northwest corner method is a simple algorithm for generating an initial basic feasible solution to a transportation problem — the classic operations research task of shipping goods from multiple supply points to multiple demand points at minimum total cost. Starting at the top-left ("northwest") cell of the cost table, the method allocates as much as possible to that cell, then moves right or down depending on whether supply or demand was exhausted first, repeating until all supply and demand is assigned.

This calculator applies the rule to a balanced 2×2 transportation problem, returning the allocation and its total cost. While the northwest corner method doesn't account for cost at all — it's later improved with methods like Vogel's approximation or the stepping-stone method — it's the standard starting point taught in operations research and logistics courses for understanding how transportation problems are set up and solved, and it's still used in practice as a fast first feasible allocation before optimization.

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Comments (1)

  • Editorial team

    The method never looks at the costs, which you can verify directly. With supplies 30 and 20 and demands 25 and 25, two different cost tables produce the identical allocation (x11=25, x12=5, x22=20) yet totals of 190.00 and 270.00. So the answer is a starting plan to improve with a later optimality step, not a recommendation. The tool handles a 2 × 2 table only. Would a 3 × 3 table or the improvement step be more useful to you?

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