The North West Corner Method is a heuristic algorithm used in operations research and linear programming for solving transportation and distribution problems. These problems involve the optimal distribution of goods from several suppliers to several consumers, considering factors such as cost, distance, or time.
The method gets its name from the starting point in the allocation table, which is the northwest corner. The algorithm is relatively simple and intuitive, making it easy to understand and implement. Here's a step-by-step explanation of the North West Corner Method:
The North-West Corner Method is a simple approach for solving transportation problems.
Steps to apply the North West Corner Method
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| Steps to apply the North West Corner Method |
Setup:
Create a transportation tableau, which is a matrix that represents the costs or quantities associated with transporting goods from suppliers to consumers. Identify the northwest corner of the tableau as the starting point.
Allocation:
Allocate as much as possible to the cell in the northwest corner without exceeding the supply or demand constraints. Update the supply and demand values accordingly, reducing them as allocations are made.
Move to the Next Cell:
Move to the next cell either horizontally or vertically, depending on which direction allows for the most efficient allocation. Repeat the allocation process until either supply or demand is exhausted.
Continue Allocation:
Repeat the allocation process for each remaining row or column, moving to the next available cell in the same manner. Continue until all supply and demand requirements are satisfied.
Optimality Check:
Check whether the obtained solution is optimal. This involves assessing whether all constraints are met and evaluating the total cost associated with the allocations. If the solution is not optimal, further optimization methods may be applied, such as the Modified Distribution Method or the stepping-stone method.
Final Solution:
The final solution is reached when all supplies are exhausted and demands are met. The allocations in the tableau represent the optimal distribution of goods from suppliers to consumers.
To illustrate these steps, let's consider a simple example. Suppose you have a transportation tableau with supply values for three suppliers (S1, S2, S3) and demand values for three consumers (C1, C2, C3):
| C1 | C2 | C3 | Supply
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S1 | 3 | 1 | 4 | 30
S2 | 2 | 6 | 8 | 50
S3 | 5 | 7 | 2 | 20
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Demand | 20 | 60 | 30 |
Starting at the northwest corner (S1, C1), allocate 20 units, and update supply and demand values. Move to the next cell (S1, C2) and allocate, then continue until all requirements are satisfied. The North-West Corner Method provides an initial feasible solution but may require further optimization.
Example of North West Corner Method
| C1 | C2 | C3 | Supply
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S1 | 3 | 1 | 4 | 30
S2 | 2 | 6 | 8 | 50
S3 | 5 | 7 | 2 | 20
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Demand | 20 | 60 | 30 |
Using the North-West Corner Method
- Start at the northwest corner (S1, C1) and allocate 20 units (minimum of supply and demand).
- Move to the next cell (S1, C2) and allocate 10 units.
- Move to the next cell (S1, C3) and allocate 4 units.
- Move to the next row (S2, C3) and allocate 20 units.
- Move to the next row (S3, C3) and allocate 6 units.
The allocations satisfy the supply and demand constraints, and the transportation problem is partially solved. Further optimization methods may be applied for the final optimal solution.
Advantages Of North West Corner Method
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| Advantages Of North West Corner Method |
Simplicity:
The North-West Corner Method is easy to understand and implement. It doesn't require complex computations, making it accessible for those new to transportation problem-solving.Quick Initial Solution:
The method provides a quick initial feasible solution. It efficiently distributes goods based on the basic principle of starting at the northwest corner and moving to the next available cell.Intuitive:
The allocation process is intuitive, involving a systematic movement through the tableau. This makes it easy for practitioners to follow and apply the method without extensive training.Basis for Further Optimization:
While the initial solution may not be optimal, the North-West Corner Method serves as a foundation for more advanced optimization methods. It provides a starting point that can be refined through techniques like the Modified Distribution Method or the stepping-stone method.Useful for Educational Purposes:
The simplicity of the North-West Corner Method makes it valuable for educational purposes. It is often introduced in operations research courses to help students grasp the basic concepts of transportation problems before moving on to more complex algorithms.For more visit KMBN 206
