MODI Method
  • MODI means Modified Distribution method
  • Suppose we have obtained an initial basic feasible solution to a given transportation problem by any one of the method i.e. (NWCM,LCM,VAM).
  • The next step is to test whether this solution is optimal or not for this purpose we used MODI method.
  • MODI method is also known as u v method.
For applying MODI method to any feasible solution of a Transportation problem.
The following two conditions must be satisfied.
(1) The solution consists of exactly (m+n-1) individual allocations. (where m means row & n means column)
(2) These allocations are in independent positions.

Non-Degenerate TP
  • In the given transportation problem, first allocation using any one method of NWCM, LCM & VAM.
  • Then after to check M + N -1 = Allocation (Where M means no of Row & N means no of Column) If both are equal then the given TP problem is NonDegenerate.
Degenerate TP or Degeneracy
  • In the given transportation problem, first allocation using any one method of NWCM, LCM & VAM.
  • Then after to check M + N -1 = Allocation (Where M means no of Row & N means no of Column) If both are not equal then the given TP problem is Degenerate TP or Degeneracy.
  • That means M + N -1 = Allocation, so it is not feasible solution or it create a degeneracy.
How to remove Degeneracy?
  • If M + N - 1 = Allocation (Where M means no of Row & N means no of Column)
  • To remove degeneracy in transportation problem, we allocate very small quantity “e” to unoccupied cell, so we get M +N-1 number of occupied cell this amount is denoted by greek letter e, now we apply optimality test now to check again M + N - 1 = Allocation
  • here, e for Epsilon, and the value of e is by default 0.
Different terms used in MODI method
• Non – Degenerate
• Degenerate or Degeneracy
• Epsilon (e)
• u & v value
• Occupied cell
• Unoccupied cell
• Looping

Transportation Problem -2

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