Operation Research 10th Aug

Transportation Problem
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Transportation problem is one of the subclasses of linear programming problems in which the objective is to transport various quantities of a single homogeneous commodity, that are initially stored, at various originsto different destinations in such a way that the transportation cost is the minimum.




ai-avaibility of ware houses Wi
bi-demand of particular destination

For Balanced

ai=bj

Look at this statement for better knowing:

X11 quantity is transported from warehouse W1 to Delhi for a transportation cost of C11.


I.B.F.S.- Initial Basic Feasible Solutions

In respect to I.B.F.S. the transportation cost is

Summation of X(ij) * C(ij)

Techniques
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1.North West Corner Method
2.Row Minimum Method
3.Coloumn Minimum Method
4.Matrix Minimum Method
5.Vogel's approximation Method

N-W corner method
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->check for the element in the extreme N-W side
->check for the demand and capacity in that part, and adjust them accordingly
->if in any row or coloumn becomes zero then cut that row or coloumn with a pencil
->go to step 1 again until all elements are done

Coloumn min. method
--------------------
->Check for the element with the lowest cost in the first coloumn
->Check for the demand and capacity in that part, and adjust them accordingly
->check if all the elements in the first coloumn is filled or cut then move to the next coloumn and go to step 1 until all elements are done

Row min. method
-----------------
->Check for the element with the lowest cost in the first row
->Check for the demand and capacity in that part, and adjust them accordingly
->check if all the elements in the first row is filled or cut then move to the next row and go to step 1 until all elements are done