# Total Transport Cost Optimization

In Management operational research methods and quantitative analytical tools enable management to optimize cost by using mathematical models. The Vogel’s method uses simple method to optimise transport cost, where there are supply sources and there is deamnd centers for those supply sources and supplies are done simultaneously on a regualar basis and the trasport cost is fixed and do not depend on the amount of goods transported. In these situation, the transport cost method of using a matrix table and use of vogel’s method enable management to solve for an optimal solution to the transport cost minimization problem.

For example if there is supply constrants and deamnd constraints from different sources of supply centers and demand centers, then producing a table and applying the vogel’s method  using a transport model software using such method may be able solve, where the supply centers and demand centers are numerous. However, if the demand and supply centers are limited a spread sheet model may be sufficient using such a method as an add in  for the formula tool of the spread sheet. The mathematical analysis of such a nature enable managers to rationaly make a decsion on transportation cost problem to be solved and minimize transport cost for an organization as a whole.

The steps of vogel’s methods are as follows:

Step one

Create a table of rows and columns for supply and demand in matriax form including total demand and supply  constraints for the table.

Step 2

Calculate for all rows and colums, the difference in cost in rows and colums, identifying two least cost in the rows and columns

Step 3

Then identify the row or column, which has the maximum difference and allocate the maximum quantity to a cell in the row or column, which has the least cost. If there is a tie allocate maximum quantity to the choosen cell of your preference. Then delete the the column or row, which has been fully filled by the previous allocation.

Step 4

Recalculate the differences as in step 2 and do the allocation using step 3

Step 5

Repeat the allocation untill you allocate all supply to all the demand centers fully. Check whether the solution is optimal by varying the allocation differently and check whether the total cost can be further minimized.

The researchers have found that the vogel’s method gives the optimal solution in its initial solution 80% of the time. There fore, the vogels method of solving transportation logistics problem is a usefull tool to allocate transportation of goods from supply centers to demand centers under certain circumstances.

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