Minimizing the Cost of Transportation

Optimality Test for Vogel Approximation Method

In the same way that an optimality test was carried out for the North-West corner method and least cost method we applied it on the Vogel Approximation method in order to determine the Basic Feasible Solution.

Third iteration from Table 10 shows that the optimal solution is being reached and there will be no need for further improvement again and the total cost of distribution was low in comparison to the previous iterations.

Where,

Min Z= 5(21600) + 19(3700) + 12(14700) + 81(900) + 26(19500) + 23(16800) + 62(10500) + 0(11900) + 0(8100)

= 108000 + 70300 + 176400 + 507000 + 72900 + 507000 + 386400 + 651000 + 0 + 0

=1,905,300

The result also shows that when using Vogel Approximation Method, the best allocation routine to follow would be that of Table 10 because optimum solution was reached in the third iteration. This allocation routine requires less cost compared to the other iterations.

Table 10. Third Iteration