Transportation Problem - 4 - Least Cost Method (LCM) - 1
Operations Research - OR
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Obtaining Initial Solution of a Transportation Problem by the Least Cost Method (LCM):
Northwest Corner method does not utilize shipping costs, so it can yield an initial 'bfs' that has a very high shipping cost. Then determining an optimal solution may require several pivots.
To begin the Least cost method, first find the cell with the smallest shipping cost. Then assign / allocate (xij) to that cell at its largest possible value, min {si, dj}. Allocation always means "demand or supply, whichever is lower".
As in the NWC method, cross out row i or column j and reduce the supply or demand of the non-crossed-out of row or column by the value of xij.
Continue the same process for the remaining empty cells (instead of assigning upper left corner, the empty cell with the minimum cost is assigned).
Example:
Determine an initial basic feasible solution to the following transportation problem using LCM, if the objective is to minimize the transportation cost:
Source Destination
D1 D2 D3 D4 Supply
S1 1 2 1 4 30
S2 3 3 2 1 50
S3 4 2 5 9 20
D 20 40 30 10 100
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