Transportation Problems | North West Corner Method

Introduction

This tutorial will guide you through the North West Corner Method, a technique used to find the initial basic feasible solution for balanced transportation problems. Understanding this method is essential for efficiently solving logistics and supply chain challenges in operations research.

Step 1: Understand the Transportation Problem

Before applying the North West Corner Method, familiarize yourself with the components of a transportation problem, which include:

• Suppliers and Demanders: Identify the number of supply points (sources) and demand points (destinations).
• Supply and Demand Values: Each supplier has a supply capacity, and each demander has a demand requirement.
• Cost Matrix: Create a matrix that lists the transportation costs from each supplier to each demander.

Practical Tips

• Ensure that the total supply equals the total demand for the problem to be balanced.
• Use clear labeling for suppliers and demanders to avoid confusion.

Step 2: Set Up the Cost Matrix

Create a cost matrix based on the transportation costs associated with shipping goods from each supplier to each demander.

Steps to Create the Cost Matrix

1. List all suppliers in rows and all demanders in columns.
2. Fill in the corresponding transportation costs for each route in the matrix.

Common Pitfalls

• Double-check that all costs are accurately represented in the matrix.
• Ensure that the cost matrix is complete and does not contain any missing values.

Step 3: Apply the North West Corner Rule

This rule helps you determine the initial allocation of shipments. Follow these steps to apply the rule:

1. Start at the top-left corner of the cost matrix.
2. Allocate as much as possible to that cell, which represents shipping from the first supplier to the first demander.
3. Adjust the supply and demand values accordingly:
   • If supply exceeds demand, reduce the supplier’s supply and move to the next demander in the row.
   • If demand exceeds supply, reduce the demander’s demand and move to the next supplier in the column.
4. Repeat until you reach the bottom right of the matrix.

Example Allocation

• If Supplier A has a supply of 20 and Demander X has a demand of 15, allocate 15 units to that cell. Update the supply of Supplier A to 5 and the demand of Demander X to 0.
• Move to the next cell in the row or column as necessary.

Step 4: Verify the Solution

After completing the allocations, check that all supply and demand constraints are satisfied.

Verification Steps

• Sum all allocations for each supplier to confirm they do not exceed supply.
• Sum all allocations for each demander to ensure they meet demand.

Practical Advice

• If any adjustments are needed, revisit your allocations and modify them to meet the constraints.

Conclusion

The North West Corner Method is an effective way to find an initial basic feasible solution for transportation problems. By following these steps—understanding the problem components, setting up the cost matrix, applying the North West Corner rule, and verifying your solution—you can efficiently tackle logistics challenges. As a next step, consider exploring other optimization methods to improve your solution further.