Question

Use the Northwest Corner Rule to develop an initial solution to th transportation problem shown below. Present your answer in the following format. A to 1 = Qty X, B to 2 = Qty Y, etc

WHS 1 WHS 2 WHS 3 Capacity

Factory A 400

Factory B   300

Factory C 500

Demand 300 500 400

Answer 1

As per Northwest Corner Rule, we will follow below approach

Step1:Identify the cell at North-West corner of the transportation matrix.

Step 2: Allocate as many units as possible to that cell without exceeding supply or demand. Then remove out the row or column that is exhausted by this assignment

Step 3: Reduce the amount of corresponding supply or demand which is more by allocated amount.

Step 4: Again identify the North-West corner cell of reduced transportation matrix.

Step 5:Repeat Step 2 and Step 3 until all the requirements are satisfied.

	WHS 1	WHS 2	WHS 3	Capacity
Factory A				400
Factory B				300
Factory C				500
Demands	300	500	400

Start with north west corner for WHS 1 and Factory A capacity for allocation.

	WHS 1		WHS 2		WHS 3		Capacity
Factory A	300						400
								Factory B							300
Factory C							500
								Demands	300		500		400

Then remove WHS 1 since demand is completed. 100 capacity from factory A is still left.

We move to next north west corner WHS 2 and factory A to start and then allocate as shown.

	WHS 2		WHS 3		Capacity
Factory A	100				100
						Factory B	300				300
Factory C	100				500
						Demands	500		400

In the step we cater for WHS 3 as shown

	WHS 3		Capacity
Factory C	400		400
				Demands	400

Hence the optimal solution is

A to 1 = Qty 300

A to 2 = Qty 100,

B to 2 = Qty 300

C to 2 = Qty 100

C to 3 = Qty 400

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