Minimizing the Cost of Transportation

Optimality Test for Least Cost Method

We solved for Least cost method in Table 4 but here, we want to obtain the best (optimal) possible solution for the Least cost method.
The optimality test after third iteration still indicates that there is a need for optimization of the solution, and hence we proceeded to the fourth iteration as given in Table 9. Table 9 shows that the optimal solution (Basic Feasible Solution) is being reached and there were a noticeable drop in the total cost of distribution in comparison to the previous iterations for the least square method.

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

= 108000 + 70300 + 176400 + 72900 + 507000 + 386400 + 651000 + 0 + 0
=1,972,000

The result also shows that when using least cost method, the best allocation routine to follow would be that of Table 9 because optimum solution was reached in the fifth iteration. This allocation requires less cost compared to the other iterations.

Table 9. Fourth Iteration