The North West corner rule is a method for computing a basic feasible solution of a transportation problem, where the basic variables are selected from the North – West corner ( i.e., top left corner ).
The standard instructions for a transportation model are paraphrased below. Please read them carefully.
This trial routing method is often far from optimal.
The Amulya Milk Company has three plants located throughout a state with production capacity 50, 75 and 25 gallons. Each day the firm must furnish its four retail shops R1, R2, R3, & R4 with at least 20, 20 , 50, and 60 gallons respectively. The transportation costs (in Rs.) are given below.
The economic problem is to distribute the available product to different retail shops in such a way so that the total transportation cost is minimum
Starting from the North west corner, we allocate min (50, 20) to P1R1, i.e., 20 units to cell P1R1. The demand for the first column is satisfied. The allocation is shown in the following table.
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Now we move horizontally to the second column in the first row and allocate 20 units to cell P1R2. The demand for the second column is also satisfied.
Proceeding in this way, we observe that P1R3 = 10, P2R3 = 40, P2R4 = 35, P3R4 = 25. The resulting feasible solution is shown in the following table.
Here, number of retail shops(n) = 4, and
Number of plants (m) = 3
Number of basic variables = m + n – 1 = 3 + 4 – 1 = 6.
The total transportation cost is calculated by multiplying each xij in an occupied cell with the corresponding cij and adding as follows:
20 X 3 + 20 X 5 + 10 X 7 + 40 X 8 + 35 X 2 + 25 X 2 = 670