How is Modi method used in transportation problem?
Now draw a loop starting from the new basic cell. Assign alternate plus and minus sign with new basic cell assigned as a plus sign. Select the minimum value from allocated values to the cell with a minus sign. Subtract this value from the cell with a minus sign and add to the cell with a plus sign.
How do you solve degeneracy in transportation problem?
Using Least Cost Cell Method we get the following solution. Optimization of the solution using U-V Method: Check whether m + n – 1 = total number of allocated cells. In this case m + n – 1 = 4 + 5 – 1 = 8 where as total number of allocated cells are 7, hence this is the case of degeneracy in transportation problem.
What is degeneracy in transportation?
If the basic feasible solution of a transportation problem with m origins and n destinations has fewer than m + n – 1 positive xij (occupied cells), the problem is said to be a degenerate transportation problem. Degeneracy can occur at two stages: At the initial solution.
What is U and V Modi method?
The modified distribution method, also known as MODI method or (u – v) method provides a minimum cost solution to the transportation problem. In the stepping stone method, we have to draw as many closed paths as equal to the unoccupied cells for their evaluation.
Why Modi method is applied?
The MODI (modified distribution) method allows us to compute improvement indices quickly for each unused square without drawing all of the closed paths. Because of this, it can often provide considerable time savings over other methods for solving transportation problems.
How do you solve degeneracy problems?
In order to resolve degeneracy, the conventional method is to allocate an infinitesimally small amount e to one of the independent cells i.e., 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 (i.e., to satisfy the condition N …
Can degeneracy occur in transportation problem?
In a transportation problem with m origins and n destinations, if a basic feasible solution has less than m + n – 1 allocations (occupied cells), the problem is said to be a degenerate transportation problem. Degeneracy can occur at two stages: At the initial solution. During the testing of the optimal solution.
Can degeneracy occur in a transportation problem?
What is basic solution in transportation problem?
A feasible solution to a transportation problem is said to be a basic solution if it contains no more than m+ n-1 non-negative allocations, where m is the number of rows and n is the number of columns of the transportation problem.
Is UV and Modi method same?
How is the transportation problem solved with Modi?
The MODI method for solving transportation problem allow us to compute the total minimum transportation cost based on demand and supply. You can find the minimum cost for ‘n’ number of rows and columns.
Is there a non-degenerate solution to the transportation problem?
To find initial Basic feasible solution. Using north- west corner method. The non-degenerate initial basic feasible solution is given is Table 1. Therefore there is no degeneracy. To test the optimality. We use MODI method, for this first we calculate µ i, v j & Δ ij.
How to calculate degeneracy in the transportation problem?
In this case m + n – 1 = 4 + 5 – 1 = 8 where as total number of allocated cells are 7, hence this is the case of degeneracy in transportation problem.
How to find a solution to the transportation problem?
One can also use NorthWest Corner Method or Vogel’s Approximation Method to find the initial basic feasible solution. Using Least Cost Cell Method we get the following solution. Check whether m + n – 1 = total number of allocated cells.
