Least Cost Method

The Least Cost Method is another heuristic approach used to solve transportation problems in the field of operations research and linear programming. Similar to the North-West Corner Method, it is employed to find an initial feasible solution for distributing goods from suppliers to consumers. The method focuses on minimizing the transportation cost associated with allocations.

Steps to Apply the Least Cost Method

Steps to Apply the Least Cost Method

Setup:

Begin with a transportation tableau representing costs or quantities for transporting goods. Identify the cell with the lowest cost. If there are ties, choose the cell arbitrarily.

Allocation:

Allocate as much as possible to the cell with the lowest cost without exceeding the supply or demand constraints. Update the supply and demand values accordingly.

Repeat:

Repeat the process by identifying the next cell with the lowest cost, allocating as much as possible, and updating the tableau.Continue until all supply and demand requirements are satisfied.

Optimality Check:

Check whether the obtained solution is optimal. If necessary, apply further optimization methods to refine the solution.

Example of Least Cost Method

Consider the following transportation problem with costs and supply/demand constraints:

       | C1 | C2 | C3 | Supply -------------------------------- S1 | 3 | 1 | 4 | 30 S2 | 2 | 6 | 8 | 50 S3 | 5 | 7 | 2 | 20 -------------------------------- Demand | 20 | 60 | 30 |

Using the Least Cost Method:

Start with the cell (S1, C2) with the lowest cost of 1. Allocate 20 units (minimum of supply and demand) to this cell. Update supply and demand values, and identify the next lowest cost cell, which is (S1, C1). Allocate 10 units to this cell.

Continue the process, identifying the next lowest cost cell, until all supply and demand requirements are satisfied.

Advantages of Least Cost Method

Advantages of Least Cost Method

Optimization of Transportation Costs:

The primary advantage of the Least Cost Method is that it aims to minimize transportation costs by selecting cells with the lowest cost for allocations. This can result in more cost-effective solutions.

Flexibility:

The method allows for flexibility in choosing the initial cell with the lowest cost. This flexibility can be useful in situations where multiple cells have the same minimum cost.

Ease of Implementation:

Similar to the North-West Corner Method, the Least Cost Method is relatively easy to implement. It does not require complex computations, making it accessible for users with basic knowledge of transportation problems.

Intuitive:

The method is intuitive, involving a systematic approach to allocate goods based on cost considerations. This makes it user-friendly and suitable for educational purposes.

Basis for Further Optimization:

While the initial solution obtained through the Least Cost Method may not be optimal, it serves as a starting point for more advanced optimization techniques if needed.

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