Transportation Problems | Vogel's approximation method

Introduction

This tutorial provides a comprehensive guide on solving transportation problems using Vogel's approximation method. This method is particularly useful in logistics and supply chain management, as it helps determine the most cost-effective way to transport goods from multiple suppliers to multiple consumers. By following the steps outlined below, you will learn how to apply Vogel's approximation method effectively.

Step 1: Set Up the Transportation Table

• Begin by identifying the supply and demand for each source and destination.
• Create a transportation table with the following:
  • Rows representing the suppliers.
  • Columns representing the consumers.
  • Each cell representing the cost of transporting goods from a supplier to a consumer.
• Fill in the supply and demand values at the ends of the rows and columns, respectively.

Step 2: Calculate Penalties

• For each row and column, calculate the penalties:
  • Row Penalty: Subtract the lowest cost from the second lowest cost in the row.
  • Column Penalty: Subtract the lowest cost from the second lowest cost in the column.
• If there is only one cost in a row or column, assign a penalty of zero.

Step 3: Identify the Maximum Penalty

• Look for the highest penalty value among all rows and columns.
• This indicates where you should allocate resources first for cost efficiency.

Step 4: Allocate Supply to the Least Costly Option

• In the row or column with the maximum penalty, find the least cost cell.
• Allocate as much supply as possible to that cell without exceeding the supply or demand.
• Adjust the supply and demand:
  • If supply is exhausted, cross out the supplier's row.
  • If demand is met, cross out the consumer's column.

Step 5: Update the Table and Recalculate Penalties

• After making an allocation, update your transportation table:
  • Remove any rows or columns that have been fully satisfied.
• Recalculate the penalties for the remaining rows and columns.

Step 6: Repeat Until All Supply and Demand are Met

• Continue the process of finding the highest penalty, allocating supplies, and updating the table until all supplies and demands are fulfilled.
• Ensure that every allocation meets the constraints of supply and demand.

Conclusion

Vogel's approximation method is a systematic approach to solving transportation problems that minimizes costs while meeting supply and demand constraints. By following the steps outlined above, you can effectively apply this method to any transportation problem. For further optimization, consider exploring methods like the stepping stone or MODI methods after obtaining an initial feasible solution with Vogel's approximation.