Definition- Modi[u-v] or Modified distribution method is used to check optimality of the initial basic feasible solution determined by using any of the ibfs(initial basic feasible solution) methods viz. North-west corner rule, Least cost method and vogel's approximation method.
Procedure:
Step 1- Calculate ibfs(initial basic feasible solution).
Step 2- Check optimality conditions i.e. feasible solution has exactly m+n-1 number of allocations and all these allocations are at independent positions(it doesn't form a loop).
Step 3- Apply Modi method if above conditions satisfies. Calculate ui+vj=cij for occupied cells. Take u1=0 {u values along row and v values along column}.
Step 4- Calculate cij-(ui+vj) for unoccupied cells.
Step 5- If all values of cij-(ui+vj) ≥ 0 {Optimal solution}
Most -ve value enters (if not)
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Procedure:
Step 1- Calculate ibfs(initial basic feasible solution).
Step 2- Check optimality conditions i.e. feasible solution has exactly m+n-1 number of allocations and all these allocations are at independent positions(it doesn't form a loop).
Step 3- Apply Modi method if above conditions satisfies. Calculate ui+vj=cij for occupied cells. Take u1=0 {u values along row and v values along column}.
Step 4- Calculate cij-(ui+vj) for unoccupied cells.
Step 5- If all values of cij-(ui+vj) ≥ 0 {Optimal solution}
Most -ve value enters (if not)
Click here to download notes
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