Northwest Corner Rule Examples: Transportation Problem

In the previous section, we used northwest corder rule to solve a transportation problem. In this section, we provide another example. Let's concentrate on the following example:

Northwest Corner Rule: Example 2

Luminous lamps has three factories - F₁, F₂, and F₃ with production capacity 30, 50, and 20 units per week respectively. These units are to be shipped to four warehouses W₁, W₂, W₃, and W₄ with requirement of 20, 40, 30, and 10 units per week respectively. The transportation costs (in Rs.) per unit between factories and warehouses are given below.

Find an initial basic feasible solution of the given transportation problem using northwest corner rule

Solution.

Starting from the North west corner, we allocate 20 units to F₁W₁. The demand for the first column is completely satisfied.

Table 1

Use Horizontal Scrollbar to View Full Table Calculation.

Factory	Warehouse				Supply
	W1	W2	W3	W4
F1		2	1	4	30 10
F2	3	3	2	1	50
F3	4	2	5	9	20
Demand	20	40	30	10

Proceeding in this way, we observe that F₁W₂ = 10, F₂W₂ = 30, F₂W₃ = 20, F₃W₃ = 10, F₃W₄ = 10. An initial basic feasible solution is exhibited below.

Final Table

Factory	Warehouse				Supply
	W1	W2	W3	W4
F1			1	4	30
F2	3			1	50
F3	4	2			20
Demand	20	40	30	10

Number of basic variables = m + n – 1 = 3 + 4 – 1 = 6.

Initial basic feasible solution

20 X 1 + 10 X 2 + 30 X 3 + 20 X 2 + 10 X 5 + 10 X 9 = 310.