NWCM

Based on the image you've provided, here's a detailed and easy-to-understand explanation of the Northwest Corner Method (NWCM) for solving transportation problems.

What is the Northwest Corner Method?

The Northwest Corner Method is a simple and straightforward way to find an initial basic feasible solution for a transportation problem. Think of it as a starting point. It's called the "northwest corner" because you begin the allocation process at the cell in the top-left corner of your transportation table.

Important Note: The NWCM is an easy-to-use method, but it does not consider the cost of transportation. This means the solution it provides is a valid starting point, but it's not guaranteed to be the most cost-effective solution. Other methods, like the Stepping-Stone Method, are then used to improve on this initial solution to find the optimal (lowest-cost) solution.

The Steps Explained: A Simple Breakdown

Imagine a grid or table where the rows represent your supply points (e.g., factories) and the columns represent your demand points (e.g., warehouses). The goal is to figure out how many units to ship from each supply point to each demand point.

Here are the rules, broken down into simple, logical steps:

Step 1: Start at the Northwest Corner

* Begin at the very first cell in the top-left corner of your table. This is your "northwest corner."

* Compare the supply available for that row with the demand required for that column.

* Allocate the smallest of these two values to that cell. This means you ship as many units as you can, up to the smaller of the two numbers.

Step 2: Subtract and Adjust

* After you've allocated units to the cell, subtract that allocated amount from both the row's supply and the column's demand.

* One of these will become zero.

Step 3: Move to the Next Cell

* If the column's demand becomes zero: This means that particular demand point is now fully supplied. You don't need to ship any more units there. So, you move to the next cell to the right in the same row.

* If the row's supply becomes zero: This means that particular supply point has sent out all its available units. You can't ship any more from there. So, you move to the next cell down in the same column.

Step 4: Repeat the Process

* You keep repeating Steps 1, 2, and 3 until you've satisfied all the demand and used up all the supply.

* You will continue to move across rows and down columns, always working with the new "northwest corner" of the remaining unallocated cells.

Step 5: The End

* The process is complete when the remaining supply and demand for all rows and columns are zero.

* The allocations you made in each cell represent your initial shipping plan.

Example Walkthrough

Let's say we have a supply of 50 units and a demand of 30 units for our first cell.

* Step 1: The smallest value is 30 (the demand). We allocate 30 units to that cell.

* Step 2:

* The demand for that column is now 30 - 30 = 0.

* The supply for that row is now 50 - 30 = 20.

* Step 3: Since the demand is now zero, that column is satisfied. We don't need to ship anything else there. We move to the next cell to the right in the same row and repeat the process.

This simple, step-by-step process ensures you fill the table systematically, from the top-left to the bottom-right, until all supply and demand requirements are met.