In transportation problem, which method gives the best result: North-West, Row Minima, Column Minima, Least Cost or Vogel’s Approximation (VAM)?
These methods are for finding the initial solution. North-west is an easy way to find a solution and works efficiently most of the time. But there isn't any superority among these methods. Basically, it depends on the problem.
Dear parag
All the method provides Intial solution. But VAM method Convergence very fast than the other approaches. For example you see same approaches in numerical analysis like bisection method, Newton raphson method, other.
Vogel's method is also more complex, whence it is natural to expect it to do better.
North-West disregards the costs. It may happen that the initial feasible solution is the worst (the most expensive) one.
All of them just provide a feasible (not optimal) solution. NorthWest is just an uninformed rule-of-tumb. Row and Column Minima, Least Cost are equivalent concerning efficiency. VAM uses more information and theoretically it is expected to perform better on the average.
The North-West Corner Method usually provides the worst solution as it does not consider cost in the sense the solution found by NW is probably worse than those found by the other methods. It does not need to be the worst global solution which stands for the transportation plan with the highest possible cost.
None of the methods provide optimal solution but feasible or near optimal. VAM and MODI (Modified Distribution) outperform NWCM and other methods mentioned. Researchers are now looking for possible ways of solving transportation problems using global techniques or creative algorithms with robust solution and graphical interface.
VAM is the best solution method but degeneracy is a major issue in transportation problem. In a standard transportation problem with m sources of supply and n demand , any feasible solution requires allocations in m + n – 1 independent cells. If the number of allocations is shorter than m+n-1, then the solution is said to be degenerate. To remove it, allocate a small positive quantity e to one or more unoccupied cell that have lowest transportation costs, so as to make m + n – 1 allocations. Then optimal reult is derived uing combination of VAM and MODI method.
To add to @Sanghita Basu's answer: in case of degeneracy the small amount is to be added at a cell which is having the smallest cost and not making any loop with the other allocated cells... Now about Vogel's Approximation method it gives the best initial Basic Feasible Solution (which can be degenerate)... All the other methods are either equal or inferior to Vogel's... Moreover, degeneracy can happen in any method... Whenever any individual demand quantity is equal to the individual supply quantity then degeneracy is going to take place... BTW whatever one gets as the initial BFS, MODIji will lead to Optimality...
True. Degeneracy can happen in any method. But in maximum cases I have found that other methods produced inferior results than VAM. So I have not considered degeneracy problem for NW or LC method. I have applied MODI to VAM only for solving degeneracy problem. Anyways I should check some more problems to see whether the other methods can produce same results as VAM or not. Thank you for your suggestion. I will check it.
in transportation problem what are the most known optimization methods that improve result ?
We can quite safely say that the transportation problem is solved - we have very fast solvers for huge problems. If anyone wants a challenging problem I think it is better to turn to integer optimization - where we still need a lot of development.
https://youtu.be/78vWxwrFoFc
Apart from all the answers by tje stalwarts, a small effort by a novice.
Least cost, North West Corner and Vogel's Approximation give starting points, of which the Vogel's method usually performs better than others. MODI can then be used to find THE OPTIMAL solution(s).
What is the difference between MODI and the standard simplex method for this problem? What is the actual contribution? The initial feasible solution-finding tool (Phase-1) is classic since the 1950s, and the second stage is the standard simplex method - also classic. I fail to see any real contribution.
I have felt for some time that RG is a haven for workers who have not read the literature - instead of utilising the power of modern software and hardware that we all can find in the latest books and papers, you actually want to use heuristics that do not provide you with an optimal solution. Why???? It's a waste!
Vogel’s Approximation Method (VAM) usually provides better result in comparison to othet methods for finding initial basic feasible solution.
Vogel's Approximation Method gives better result with less iterations.
Among the traditional methods, VAM usually gives better initial basic feasible solution.
The VAM does not always give the better results. There are other methods to give better results than the VAM.
Vogal Approximation Method provides a good results for finding IBFS. For Optimal Solution use MODI Method.
The Transportation Problem NorthWest-Corner method can never find an optimal solution to a transportation problem.
