First Watch Initial Basic Feasible Solution by Vogel's Approximation Method (VAM)
• Initial basic feasible...
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#MODIMETHOD #TRANSPORTATIONPROBLEM
Transportation Algorithm for Minimization Problem (MODI Method)
Step 1
Construct the transportation table entering the origin capacities (supply) ai
, the destination
requirement (demand) bj
and the cost cij.
Step 2
Find an initial basic feasible solution by Vogel’s method or by any of the given method.
Step 3
Test for optimality:
1. If number of positive independent allocations xij = m+n-1
Then IBFS is non-degenerate and optimality test can be performed.
2. If number of positive independent allocations xij less than m+n-1
Then IBFS is degenerate and optimality test cannot be performed. And first we
have to convert degenerate solution into non degenerate.
Step 4
Apply MODI Method
1. Set up cost matrix for allocated (occupied) cell only.
2. Enter the set of number ui for row and vj
for column such that for occupied cell
cij = ui
+ vj
.
3. Set any ui
or vj
= 0 which have maximum allocation to calculate the values of ui
, vj.
4. Compute ui
+ vj for unoccupied cells.
5. Compute the opportunity cost
dij = cij - ( ui
+ vj
) for unoccupied cells.
Step 5
Apply optimality test by examining the sign of each dij
1. If all dij greater than or equal to 0, the current initial basic feasible solution is optimal.
2. If at least one dij less than 0, the current initial basic feasible solution is not optimal and we have to improve the solution.
Step 6
Iterative towards an optimal solution:
1. Identify the most negative cell in dij matrix and called this cell as identified cell.
(The most negative value is the rate by which total transportation cost is reduced if
one unit is transported to this cell)
2. Write IBFS again which needs to be improved.
3.Marked (√) the identified cell and make a closed loop starting and ending in the
identified cell. All the corner of the loop should be on occupied cell except identified
cell.
4. Mark the identified cell as +ive and other corner of the loop with -ive, +ive, ive sign
alternatively.
5. Find minimum allocated value on the loop where we have -ive sign.
6. Add these minimum allocations in the loop where we have +ive sign and subtract
where we have-ive sign. ( by these most negative cell gets an allocation and
minimum allocated cell with -ive sign gets zero allocation)
7. By doing all the above steps we get second basic feasible solution.
Step 7
Now, return to step 4 and repeat the process until an optimal solution is obtained.
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Please watch: "UNBALANCED ASSIGNMENT PROBLEM IN OPERATION RESEARCH | USING HUNGARIAN METHOD | Lecture 03"
• Unbalanced Assignment ...
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Негізгі бет MODI - UV METHOD ( Optimal Solution) IN TRANSPORTATION PROBLEM
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