MINIMUM COST METHOD: CHARACTERISTICS, ADVANTAGES, DISADVANTAGES - DUDAS - 2025

The least cost method is a procedure used to obtain the initial feasible solution for a transportation problem. It is used when the priority is to reduce the costs of product distribution.

The least cost method seeks to achieve the lowest cost of transportation between several demand centers (the destinations) and several supply centers (the sources).

Source: pixabay.com

The production capacity or supply of each source, as well as the requirement or demand of each destination are known and fixed.

The cost of transporting a unit of the product from each source to each destination is also known.

The product must be transported from various sources to different destinations in such a way as to meet the demand of each destination and, at the same time, minimize the total cost of transportation.

Other methods can be used if the priority is time savings rather than cost savings.

characteristics

The optimal allocation of a product from various sources to different destinations is called a transportation problem.

- Transport models deal with the transport of a product manufactured in different plants or factories (supply sources) to various warehouses (demand destinations).

- The objective is to satisfy the requirements of the destinations within the production capacity limitations of the plants, at the minimum cost of transportation.

Steps of the least cost method

Step 1

The cell that contains the lowest shipping cost in the entire table is selected. That cell is assigned as many units as possible. This amount may be limited by supply and demand restrictions.

In the case that several cells have the lowest cost, the cell where the maximum allocation can be made will be selected.

Then we proceed to adjust the supply and demand that is in the affected row and column. It is adjusted by subtracting the amount assigned to the cell.

Step 2

The row or column in which the supply or demand has been exhausted (be it zero) is eliminated.

In case both values, supply and demand, are equal to zero, any row or column can be eliminated, arbitrarily.

Step 3

The previous steps are repeated with the next lowest cost and continue until all the available supply from the different sources or all the demand from the different destinations is satisfied.

Applications

- Minimize transportation costs from factories to warehouses or from warehouses to retail stores.

- Determine the minimum cost location of a new factory, warehouse or sales office.

- Determine the minimum cost production schedule that meets the demand of the company with production limitations.

Advantage

The least cost method is considered to produce more accurate and optimal results compared to that of the northwest corner.

This is because the Northwest corner method only places importance on the supply and availability requirement, with the upper left corner as the initial allocation, regardless of shipping cost.

On the other hand, the least cost method includes transportation costs while assignments are being made.

- Unlike the northwest corner method, this method provides an accurate solution, considering the cost of transportation when making the mapping.

- The least cost method is a very simple method to use.

- It is very simple and easy to calculate the optimal solution with this method.

- The least cost method is very easy to understand.

Disadvantages

- To obtain the optimal solution, certain rules must be followed. However, the least cost method does not follow them step by step.

- The minimum cost method does not follow any systematic rules when there is a tie in the minimum cost.

- The least cost method allows a selection through observation of the personnel, which could create misunderstandings to obtain the optimal solution.

- It does not have the ability to provide any kind of criteria to determine whether the solution obtained with this method is the most optimal or not.

- The quantities of the offers and demands are always the same, since they do not vary over time.

- It does not take into account other types of factors to assign, but only that of transport costs.

Example

The concept of the least cost method can be understood through the following problem:

In this table, the supply of each source A, B, C is 50, 40 and 60 units respectively. The demand of the three retailers X, Y, Z, is 20, 95 and 35 units respectively. For all routes the cost of transportation is given.

The minimum cost of transportation can be obtained by following the steps below:

The minimum cost in the table is 3, with a tie in cells BZ and CX. Generally, to obtain the best initial solution, the cost should be chosen where the largest amount can be allocated.

Therefore, 35 units will be assigned to cell BZ. This satisfies the demand of retailer Z, leaving 5 units in source B.

Explanation of the method

Again, the minimum cost is 3. Therefore, 20 units will be assigned to cell CX. This fulfills the demand of retailer X, leaving 40 units in source C.

The next minimum cost is 4. However, the demand for Z is already completed. We move on to the next minimum cost, which is 5. Also the demand for X has already been completed.

The next minimum cost is 6, with a tie between three cells. However, you cannot assign units to cells BX and CZ, because the demand from retailers X and Z is satisfied. Then 5 units are assigned to cell BY. This completes the supply of source B.

The next minimum cost is 8, assigning 50 units to cell AY, completing supply from source A.

The next minimum cost is 9. 40 units are assigned to cell CY, thus completing the demand and supply for all destinations and sources. The resulting final assignment is:

The total cost can be calculated by multiplying the assigned amounts by the costs in the corresponding cells: Total cost = 50 * 8 + 5 * 6 + 35 * 3 + 20 * 3 + 40 * 9 = 955.

References

1. Business Jargons (2019). Least Cost Method. Taken from: businessjargons.com.
2. Assignment Consultancy (2019). Least Cost Method Assignment Help. Taken from: assignmentconsultancy.com.
3. Business Management (2015). Transportation problem. Taken from: engineering-bachelors-degree.com.
4. Josefina Pacheco (2019). What is the Least Cost Method? Web and Companies. Taken from: webyempresas.com.
5. Atozmath (2019). Least cost method example. Taken from: cbom.atozmath.com.