Vogel's Approximation Method of Allocation.
This method also takes costs into account in allocation. Five steps are involved in applying this heuristic:
Step 1: Determine the difference between the lowest two cells in all rows and columns, including dummies.
Step 2: Identify the row or column with the largest difference. Ties may be broken arbitrarily.
Step 3: Allocate as much as possible to the lowest-cost cell in the row or column with the highest difference. If two or more differences are equal, allocate as much as possible to the lowest-cost cell in these rows or columns.
Step 4: Stop the process if all row and column requirements are met. If not, go to the next step.
Step 5: Recalculate the differences between the two lowest cells remaining in all rows and columns. Any row and column with zero supply or demand should not be used in calculating further differences. Then go to Step 2.
The Vogel's approximation method (VAM) usually produces an optimal or near- optimal starting solution. One study found that VAM yields an optimum solution in 80 percent of the sample problems tested.
Example of VAM: