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Wednesday, May 6, 2020

U-V Method (MODI method) (Transportation problem)

U-V Method (MODI method) (Transportation problem):-



U-V method or the MODI method is the best method to optimize the Transportation problem.

MODI Method is always preferred for the optimization problem.

➤Algorithm to solve a Transportation problem by Modi method / U-V method :-


STEP 1. check whether m+n-1 = Number of Allocated cells, if yes go to the Step 3, if not go to the Step 2. 4

STEP 2. Convert the necessary number of allocated cells  into allocated cells to satisfy the above condition.

TO convert in an allocated cell here is the procedure :-
* Starting from the least of unallocated cell.
* Check the loop formation one by one.
* There should be no closed loop formation.
* Select that cell as a new allocated cell & assign "ε".

TO make a closed loop here is the procedure :-
* Draw the lines horizontally & vertically towards allocated cells.
* The turning point of the loop should be at the allocated cell.
* Finally the loop should completed at where we started.

STEP 3. Calculate the value of Ui & Vi  for all the allocated cells by using this formula-
Ui+Vi=Cij  .

STEP 4. Calculate penalties Pij for the unallocated cells by using this formula-
Pij= Ui+Vj-Cij  .

STEP 5. Check the optimality condition , all Pij≤0 ,
if yes ; Stop the procedure ;optimality condition is reached. Else go to the step 6.

STEP 6. Select the most positive value of Pij & consider that cell as a new allocation/ basic cell.

STEP 7. From that particular cell draw a closed loop by using horizontal &  vertical linespassing through some allocated cells.

STEP 8. Starting from the new allocated cell, alternatively assign +ve & -ve sign at the corner of the closed loop.

STEP 9. Select the minimum of the allocated value among the -ve signed cells.

STEP 10. Frame the new iteration by applying the steps:-

(a) Add & Subtract  that selected minimum value in all the +ve & -ve signed cells respectively.
(b) Copy the remaining cells as it is .
(c) Go to step 1.

For more information & Numerical practice you can download the Handouts by clicking Here.
else.
you can go to the web.- https://drive.google.com/file/d/1_gnNJOWl02K2D98CdcXZdvQC0nI2eQfC/view?usp=sharing



Thank you.

1 comment:

If you have any doubts let me know.