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How to solve transportation problem [north-west corner method]

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Test Question 6

Luminous lamps are produced in three factories – F1, F2, and F3, with production capacities 30, 50, and 20 units per week respectively. These units are to be shipped to four warehouses – W1, W2, W3 and W4 – with requirements of 20, 40, 30, and 10 units per week respectively. The transportation costs (in Naira) per unit between factories and warehouses are given below. Find an initial basic feasible solution of the given transportation problem using the North-West Corner Rule.

transportation problem in operations research 2

SOLUTION:

To solve this, follow the following steps:

Most importantly, check if the total supply = total demand.

Total supply = 30 + 50 + 20 = 100

Total demand = 20 + 40 + 30 + 10 = 100

This means we are good to go, otherwise, we would have introduced dummies to balance out.

  1. Next, we start balancing from the north-westernmost cell which is cell F1W1
  2. In cell F1W1, we will fill in 20 to balance the demand of 20 lamps.
  3. Remember 10 extra supplies are remaining for row F1, take this 10 to the next cell which is cell F1W2.
  4. Row F1 and column W1 are now balanced.
  5. Remember in column W2, cell F1W2 = 10, cell F2W2 will have to be 30 to balance out the demand of 40 down.
  6. For row F2, cell F2W2 = 30, and since we have a supply of 50, we would have to take the remaining 20 to the next cell which is F2W3, so, F2W3 = 20. This balances out row F2.
  7. But demand in column W3 = 30, and F2W3 = 20, this means we would have to balance the column by putting 10 in cell F3W3.
  8. Finally, in row F3, we would need to put 10 in cell F3W4 to balance everything out.
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The table will then become:

how to use north-west corner method to solve transportation problem

Our aim is basically to start allocating from the north-westernmost cell, and to ensure total allocations for each row and column are balanced with the supply and demand respectively.

Now the final step will be calculating the initial basic feasible solution by multiplying each allocated number with their cell values (costs in naira) like this:

Cost = 20(1) + 10(2) + 30(3) + 20(2) + 10(3) + 10(2) = 20 + 20 + 90 + 40 + 30 + 20 = 220 Naira.

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