## Minimizing the Cost of Transportation

Read this article. The study employed a transportation model to find the minimum cost of transporting manufactured goods from factories to warehouses. As you read, think of some factors that can greatly increase transportation and logistics time.

### Data Analysis

The table 1 below, displays an individually associated cost of transporting a piece of bag from the individual supply centre (plant) to the various demand destinations, and also the demands from various destinations, as well as the supply capacity of the plants.

Table 1. Transportation Tableau of the Secondary Data Collected from BUA Cement Company

Conventionally, when we are dealing with transportation problem it is paramount to determine whether the problem in reference is balanced transportation problem or unbalanced transportation problem, which can be determined by evaluation the following scenarios (situations);

1. if TOTAL DEMAND = TOTAL SUPPLY, thus the problem is balanced

2. if TOTAL DEMAND ≠ TOTAL SUPPLY, thus the problem is unbalanced

However from the Table 1, the Total Demand=107,700 and Total Supply= 87,700. Therefore in this case we are having an unbalanced transportation problem, and in the transportation problem algorithms, it is basic assumption that the problem is balanced, and hence we need to balance the problem through the introduction of dummy variable (Dummy Plant).

And the supply from the dummy plant is going be given by the difference between the Total Demand and Total Supply (i.e 107700-87700=20000), thus 20000 units will assumed to be supplied by the Dummy Plant.

The Table 2 below displays the balanced version of the transportation problem where the Dummy Plant takes the remaining 20000 units to be supplied, with associated cost as zero (0), and from that Total Demand is equal to the Total supply, hence the problem is balanced, and therefore we can proceed to finding the IBFS (Initial Basic Feasible Solution).

Table 2. The Balanced Transportation Tableau

The Table 3 below represents the result obtained as initial basic feasible solution (IBFS) by applying the North-West Corner Method. North-West Corner Method is one of the simplest methods for finding the initial basic feasible solution. In which the allocation starts from the upper left area of the table. Transportation cost is computed by evaluating the objective function which is given by:

Min Z = SUM (Allocated units*Associated Cost)

Min Z = 2,336,000

Therefore, total transportation cost = 2,336,000.

Table 3. North-West Corner Method

The Table 4 below represents the result obtained as initial basic feasible solution (IBFS) by applying the Least Cost Method. Least Cost Method is more reliable in comparison to the northwest corner method because it takes into account the cost of transportation during the allocation. In which the Allocation starts from the cell with the lowest transportation cost.

Table 4. Least-Cost Method

Transportation cost is also computed by evaluating the objective function:

Min Z = SUM (Allocated units*Associated Cost)

Min Z = 4,160,900

Therefore, total transportation cost = 4,160,900.

The Table 5 below represents the result obtained as initial basic feasible solution (IBFS) by applying the Vogel Approximation Method (VAM). Vogel Approximation Method is advanced version of least square method and most scholars believe VAM to be the most reliable Method in comparison with northwest corner method and Least cost method, for the fact that it does not only takes into account the cost of transportation during the allocation but rather it also considers the supply and demand before allocation could be made.

Table 5. Vogel Approximation Method

Transportation cost is also computed by evaluating the objective function:

Min Z = SUM (Allocated units*Associated Cost)

Min Z = 2,331,800

Therefore, total transportation cost = 2,331,800.