Vogel's Approximation Method (VAM) is a technique used in operations research to find an initial basic feasible solution for the transportation problem. It aims to minimize the total transportation cost by focusing on penalties or differences between the lowest costs in rows and columns.

Vogel's Approximation Method Sequence

The Vogel's Approximation Method involves a specific sequence of steps to allocate units and minimize costs. Here's a breakdown:

1. Step 1: Calculate Penalties (C)

   First, you need to calculate the difference between the two lowest costs in each row and each column. This difference represents the 'penalty' for not using the lowest cost cell in that row or column. This corresponds to option C: Find difference between the two unallocated least cost cells from each row and each column.

2. Step 2: Select Largest Penalty (B)

   Next, identify the row or column that has the largest penalty (the highest difference calculated in Step 1). This step targets the area where the cost disadvantage is greatest if the lowest cost is not chosen. This corresponds to option B: Select largest difference of rows/columns.

3. Step 3: Allocate to Lowest Cost Cell (A)

   Within the row or column identified in Step 2 (the one with the highest penalty), find the cell with the very lowest cost. Allocate as many units as possible to this cell, limited by the supply available in that row and the demand required by that column. This corresponds to option A: Assign largest quantity as per rim requirements to the cell in the row/column with smallest cost.

4. Step 4: Update and Eliminate (D)

   After making an allocation, update the supply and demand figures. If a row's supply is completely exhausted or a column's demand is fully met, eliminate that row or column from further consideration. If both are satisfied simultaneously, you can eliminate either. This corresponds to option D: Eliminate the row/column that has been satisfied.

5. Step 5: Check Rim Requirements (E)

   Continue repeating steps 1 through 4 until all supplies are exhausted and all demands are met. The final step is to ensure that all the original rim requirements (supply and demand constraints) have been satisfied. This corresponds to option E: Check all rim requirement conditions are met.

Correct Sequence Summary

Therefore, the correct sequence for applying Vogel's Approximation Method is C, B, A, D, E.

This sequence ensures that the method prioritizes minimizing costs by addressing the most significant cost differences first, making it an effective heuristic for finding a good initial solution to the transportation problem.