The North-West Corner Method (NWCM) is a simple and straightforward approach used to find an initial feasible solution for a transportation problem in operations research. It is called the North-West Corner Method because it starts allocating supply from the top-left (north-west) corner of the transportation table.

Steps to Apply the North-West Corner Method:

1. Start at the North-West Corner (Top-Left Cell) of the cost matrix.

2. Allocate as much as possible to this cell, either:

   • The minimum of supply and demand for that row/column.

   • If supply is exhausted, move down to the next row.

   • If demand is met, move right to the next column.

3. Repeat the process for the next available cell until all supply and demand constraints are met.

Example:

Given Transportation Table

Step-by-Step Solution:

1. Start at S1-D1 (North-West Corner):

   • Allocate 20 (as demand for D1 is 20).

   • Reduce S1 supply to 10, D1 demand becomes 0.

   • Move right to D2.

2. Move to S1-D2:

   • Allocate 10 (remaining S1 supply).

   • Reduce S1 supply to 0, D2 demand becomes 40.

   • Move down to S2.

3. Move to S2-D2:

   • Allocate 40 (as supply for S2 is 40).

   • Reduce S2 supply to 0, D2 demand becomes 0.

   • Move right to D3.

4. Move to S3-D3:

   • Allocate 50 (remaining supply for S3).

   • Demand for D3 becomes 0, and supply for S3 becomes 0.

Final Allocations Table:

Advantages of North-West Corner Method:

✔️ Simple and easy to use
✔️ Requires no complex calculations
✔️ Provides a basic feasible solution quickly

Disadvantages of North-West Corner Method:

❌ Ignores transportation costs (May not be the most cost-efficient solution)
❌ May require further optimization using the MODI method or Stepping Stone Method