transportation problems – the north-west corner method a manufacturer has 70 products at depot a,...

Transportation problems – The north-west corner method

A manufacturer has 70 products at depot A, 30 at depot B and 40 at depot C. He has orders for 50 products from retailer 1, 75 from retailer 2 and 15 from retailer 3.

The costs, in £10, of moving each item from a depot to a retailer are given in the table below.

To1 2 3

From

A 4 3 5

B 7 5 6

C 5 2 3

50534

7 5 6

5 2 3

1 2 3

A

B

C

From

ToSupply

Demand

70

30

40

50 75 15 140


Set out the given information in a transportation tableau.

Start with depot A which has a total supply of 70, and send as many of these as possible to retailer 1.

50 items can be sent to retailer 1.

This is the total demand for retailer 1, so cells B1 and C1 will be left empty.

20


Set out the given information in a table.

There are still 20 items left in depot A.

All of these can be sent to retailer 2.

The supply from depot A has now been used, so cell A3 will be left empty.

50534

7 5 6

5 2 3

1 2 3

A

B

C

From

ToSupply

Demand

70

30

40

50 75 15 140

30



Now consider depot B which has 30 items.

Retailer 2 still needs 55 items, so all 30 items from depot B can be sent to retailer 2.

The supply from depot B has now been used, so cell B3 will be left empty.

50 20534

7 5 6

5 2 3

1 2 3

A

B

C

From

ToSupply

Demand

70

30

40

50 75 15 140

25



Now consider depot C which has 40 items.

Retailer 2 still needs 25 items, so 25 items from depot C can be sent to retailer 2. This satisfies the total demand from retailer 2.

50 20

30

534

7 5 6

5 2 3

1 2 3

A

B

C

From

ToSupply

Demand

70

30

40

50 75 15 140

15



Depot C still has 15 items left.

Retailer 3 needs 15 items, so 15 items from depot C can be sent to retailer 3. This satisfies the total demand from retailer 3.

50 20

30

25

534

7 5 6

5 2 3

1 2 3

A

B

C

From

ToSupply

Demand

70

30

40

50 75 15 140



The total cost of transportation in £10 is:

(50×4) + (20×3) + (30×5) + (25×2) + (15×3) = 505

so the total cost of transportation is £5050.

Factory 1 sends 50 units to destination 1 and 20 units to destination 2.Factory 2 sends 30 units to destination 2.

Factory 3 sends 25 units to destination 2 and 15 units to destination 3.

50 20

30

25 15

534

7 5 6

5 2 3

1 2 3

A

B

C

From

ToSupply

Demand

70

30

40

50 75 15 140

transportation problems – the north-west corner method a manufacturer has 70 products at depot a,...

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