If you're looking to solve a transportation problem, the North-West Corner Rule is a simple and efficient method to consider. But before diving into the details of this rule, it's necessary to grasp the concept of a transportation problem.

Transportation Problem

A transportation problem is a special kind of Linear Programming Problem (LPP). In this type of problem, we need to figure out the best way to move goods from several suppliers (called sources) to different buyers or places (called destinations). The main aim is to reduce the total cost of transporting those goods while making sure each place gets what it needs, and each supplier sends only as much as it can.

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Types of Transportation Problems:

1. Balanced Transportation Problem:
   In this case, the total supply equals the total demand. Everything produced can be delivered without any shortage or leftover.
    
2. Unbalanced Transportation Problem:
   Here, the supply and demand are not equal. To solve this, we may add a dummy row or column to balance the numbers and make it easier to calculate.

Methods to Find Initial Solution:

To start solving a transportation problem, we first need an initial feasible solution. This is like taking the first step in the right direction. There are three main methods to do this:

• North-West Corner Rule (also called North-West Corner Cell Method)
   
• Least Cost Method
   
• Vogel’s Approximation Method (VAM)

In this article, we’ll focus on the North-West Corner Rule, which is one of the easiest and commonly used methods to begin solving such problems.

The North-West Corner Rule is a simple method used to find a starting solution for a transportation problem. In this method, we begin with the top-left cell of the transportation table — this cell is called the North-West corner

North-West Corner Rule Steps

The following steps will guide you through the process of finding a feasible solution for a transportation problem using the North-West Corner Rule.

Step 1:
Start with the top-left cell of the table (this is the "North-West corner").
Put in the smaller number between the supply and demand values for that cell. That number becomes the amount to transport.

Step 2:
Now, subtract that number from the supply and demand of the row and column.

• If the supply becomes zero, cross out that row and move down to the next row.
   
• If the demand becomes zero, cross out that column and move right to the next column.
   
• If both supply and demand become zero at the same time, cross out both the row and column and move diagonally to the next cell.

Step 3:
Keep repeating the same process — fill in the cell, subtract, and move — until all the supply and demand values are used up.

North-West Corner Rule Solved Example

Let's apply the North-West Corner Rule to a hypothetical transportation problem to illustrate how it works.

Example 1: Balanced Transportation Problem

Supply & Demand Table

Step-by-Step Allocation:

1. Start at (A, D1) → min(20, 30) = 20 → assign 20, A exhausted → move down to B
    
2. At (B, D1) → min(30, 10) = 10 → assign 10, D1 done → move right to D2
    
3. At (B, D2) → min(20, 25) = 20 → assign 20, B done → move down to C
    
4. At (C, D2) → remaining demand = 5 → assign 5, D2 done → move right to D3
    
5. At (C, D3) → min(20, 20) = 20 → assign 20

Final Allocation Table:

Example 2: Unbalanced Transportation Problem

Supply & Demand Table

Here, total supply = 40, total demand = 30 → Add a dummy destination D4 = 10 to balance

Step-by-Step Allocation:

1. (A, D1) → min(15, 10) = 10 → assign 10, D1 done → move right to D2
    
2. (A, D2) → min(5, 10) = 5 → assign 5, A done → move down to B
    
3. (B, D2) → min(20, 5) = 5 → assign 5, D2 done → move right to D3
    
4. (B, D3) → min(20, 10) = 10 → assign 10, D3 done → move right to D4
    
5. (B, D4) → assign remaining 10

Final Allocation Table:

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