“Describe the North-West Corner rule for finding the initial basic feasible solution in the transportation problem.” The question has been taken from MB0032 MBA assignment of SMU. This question has been taken from Operation Research chapter of Sikkim Manipal University. We already have discussed about MODI method, Matrix Minimum Method and Integer Programming Problem in this series.

North West Corner Rule:

Step 1: The first assignment is made in the cell occupying the upper left hand (North West) corner of the transportation table. The maximum feasible amount is allocated there, that is X11 = min (a1, b1).

So that either the capacity of origin O1 is used up or the requirement at destination D1 is satisfied or both. This value of X11 is entered in the upper left hand corner (Small Square) of cell (1, 1) in the transportation table.

Step 2: If b1 > a1 the capacity of origin O, is exhausted but the requirement at destination D1 is still not satisfied, so that at least one more other variable in the first column will have to take on a positive value. Move down vertically to the second row and make the second allocation of magnitude X21 = min (a2, b1 – x21) in the cell (2, 1). This either exhausts the capacity of origin O2 or satisfies the remaining demand at destination D1.

If a1 > b1 the requirement at destination D1 is satisfied but the capacity of origin O1 is not completely exhausted. Move to the right horizontally to the second column and make the second allocation of magnitude X12 = min (a1 – x11, b2) in the cell (1, 2). This either exhausts the remaining capacity of origin O1 or satisfies the demand at destination D2.

If b1 = a1, the origin capacity of O1 is completely exhausted as well as the requirement at destination is completely satisfied. There is a tie for second allocation; an arbitrary tie breaking choice is made. Make the second allocation of magnitude X12 = min (a1 – a1, b2) = 0 in the cell (1, 2) or X21 = min (a2, b1 – b2) = 0 in the cell (2, 1).

Step 3: Start from the new north west corner of the transportation table satisfying destination requirements and exhausting the origin capacities one at a time, move down towards the lower right corner of the transportation table until all the rim requirements are satisfied.

North West Corner Rule:

Step 1: The first assignment is made in the cell occupying the upper left hand (North West) corner of the transportation table. The maximum feasible amount is allocated there, that is X11 = min (a1, b1).

So that either the capacity of origin O1 is used up or the requirement at destination D1 is satisfied or both. This value of X11 is entered in the upper left hand corner (Small Square) of cell (1, 1) in the transportation table.

Step 2: If b1 > a1 the capacity of origin O, is exhausted but the requirement at destination D1 is still not satisfied, so that at least one more other variable in the first column will have to take on a positive value. Move down vertically to the second row and make the second allocation of magnitude X21 = min (a2, b1 – x21) in the cell (2, 1). This either exhausts the capacity of origin O2 or satisfies the remaining demand at destination D1.

If a1 > b1 the requirement at destination D1 is satisfied but the capacity of origin O1 is not completely exhausted. Move to the right horizontally to the second column and make the second allocation of magnitude X12 = min (a1 – x11, b2) in the cell (1, 2). This either exhausts the remaining capacity of origin O1 or satisfies the demand at destination D2.

If b1 = a1, the origin capacity of O1 is completely exhausted as well as the requirement at destination is completely satisfied. There is a tie for second allocation; an arbitrary tie breaking choice is made. Make the second allocation of magnitude X12 = min (a1 – a1, b2) = 0 in the cell (1, 2) or X21 = min (a2, b1 – b2) = 0 in the cell (2, 1).

Step 3: Start from the new north west corner of the transportation table satisfying destination requirements and exhausting the origin capacities one at a time, move down towards the lower right corner of the transportation table until all the rim requirements are satisfied.

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