TRANSPORTATION

Transportation

• The procedure followed is Minimization Procedure

• Problem is generally solved in Vogel’s Approximation Method(VAM)

• Steps for the problem is : -

1. Convert profit matrix into loss matrix.

2. Balance the problem.

3. Arrive at Row penalty and column penalty

Row penalty and column penalty is calculated at (2^nd least – 1^st least) in the corresponding row or column.

4. Select from the entire Row penalty and column penalty maximum number.

5. From the entire Row or Column minimum is selected.

6. Strike the row or column which gets eliminated.

7. Continue until the entire item in the table is strike.

8. Write separately Initial solution table.

9. Check for Degeneracy. Degeneracy occurs when all the elements in the initial solution is equal to (Row + column – 1)

10. If degeneracy occurs introduce efcilon – ‘e’. ‘e’ is introduced in least independent cell.

11. Form UV Matrix. It is formed by the element in the original solution corresponding to the element in the Initial solution.

12. Find unalloted elements in the UV Matrix

13. Find : Ij i.e., (Original Matrix element – Unalloted element found above)

14. Check for optimal solution ie. All items must be zero or positive.

15. If not reached select the maximum negative in Ij matrix.

16. Form a loop and reallocate the solution.
17. Repeat from step 9.

Notes: -

1. If there is zero in Ij matrix while arriving at optimal solution then there is another solution for the problem.

2. Dummy column can be introduced in profit or loss matrix.

3. If there is penalty/redundancy payment for unsatisfying demand etc. is given then fills the dummy row or column with that amount or fill it with zeros.
4. If there is constraint in the problem first satisfy the constraint and then solve.

5. various other methods for solving the problem is
   • Least cost method
   • North west corner rule

6. Generally VAM method is used