The transportation problem arises when there are number of sources of supply points and
The goods have to be supplied from the different supply sources to the demand centers each have a fixed unit cost of transport from each source. Depending on the volume and mix of transport allocated to each sources the cost will vary. However there exists a minimum cost. If the transportations are then allocated by these amounts in appropriate vehicle sizes it will also minimize the fuel costs by using appropriate vehicles and use its full capacity in the current situation of increasing fuel costs.
There are number of models to solve such problems. The easiest and most effective model is the Vogel model of minimizing the transportation costs. It has simple steps and it can be solved using s spread sheet or by an operational research software which uses such models to solve transportation problems where the number of sources and demand.
centers are very large.
Steps in Vogel model of transportation problem optimization
Step 1
Determine for each row and column the difference between the cost of each cell in the row and column
Step 2
Determine, which is the maximum penalty or difference and also determine the least cost
of this difference. If there is more than one minimum difference in row or column then allocation with a lower cell is preferred.
Step 3
Delete the column or row where the balance come to zero and delete the column or row.
Step 4
Recalculate the differences again and determine the maximum difference again and allocate the least amount to the lowest cost of the maximum difference if there exist more than one combination differences. Delete the zero columns or row. Repeat the same process until two cells are left over. Finish all allocation and check for arithmetic accuracy.
Step 5
Calculate the transportation cost and verify whether it can be further reduced by reallocations in different quantities and to different cells using the same process.
If the cost cannot be further reduced then this becomes the optimal solution.
If supply and demand is not equal then create a dummy cell and use the same process to minimize the total transportation cost.
This problem also can be solved by linear programming method using simplex method. However, this method is more complex then the above method and it won't be feasible method for all organizations depending on the financial capacity and technical skills needed to use this method. Transportation is a logistical problem for much organization especially for manufacturing and transport companies. This method is a useful tool in the decision making process of the allocation problem in these organizations.
As Vogel method gives the optimum solution is the first stage of the allocation itself and it has the minimum of reallocations to be dome to obtain the optimum solution compared to other methods such as lest cost method and North West method to solve transportation problem it is a useful model or method to solve such problems. As well, it can be easily computerized as it can be converted in to an algorithm. Transportation is an important area of operational research itself and transport is an important part of most businesses this model is very useful for many operations to improve their efficient allocation of resources and there fore minimize cost to be competitive in a dynamic and uncertain market place where cost pressures have to be effectively managed by improving the efficiency of operations and systems.
