Objective- The objective of both the methods viz. stepping stone method and modi [u-v] method is same i.e. to provide us an optimal solution(best possible solution) to the transportation problem. Either we use stepping stone or modi method, we are going to get the same optimal solution.
What is the difference?
In the stepping-stone method, we allocate +1 unit to each unoccupied cell and a closed loop is traced for each unoccupied cell. Net change in transportation cost T.C. (cell evaluations) are found for the loop. If all cell evaluations are ≥ 0 our optimal solution has reached. if not the most -ve cell evaluation value enters.
On the other hand, In modi[u-v] method cell evaluations of all the unoccupied cells are calculated using cij-(ui+vj). if cij-(ui+vj) ≥ 0 our optimal reaches. if not the most -ve cell evaluation enters and only one closed loop is traced for that particular cell. Thus it provides considerable time saving over the stepping-stone method.
P.S. Cell evaluations are same in both the cases.
Example- Download the following notes in which i have taken an example and solved the problem using stepping-stone method and modi[u-v] method. You can also see cell evaluations are same in both cases only approach is different to solve the transportation problem.
Click here to download notes
What is the difference?
In the stepping-stone method, we allocate +1 unit to each unoccupied cell and a closed loop is traced for each unoccupied cell. Net change in transportation cost T.C. (cell evaluations) are found for the loop. If all cell evaluations are ≥ 0 our optimal solution has reached. if not the most -ve cell evaluation value enters.
On the other hand, In modi[u-v] method cell evaluations of all the unoccupied cells are calculated using cij-(ui+vj). if cij-(ui+vj) ≥ 0 our optimal reaches. if not the most -ve cell evaluation enters and only one closed loop is traced for that particular cell. Thus it provides considerable time saving over the stepping-stone method.
P.S. Cell evaluations are same in both the cases.
Example- Download the following notes in which i have taken an example and solved the problem using stepping-stone method and modi[u-v] method. You can also see cell evaluations are same in both cases only approach is different to solve the transportation problem.
Click here to download notes
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