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Home > Operation Research calculators > North-West corner method example
1. north-west corner method example ( Enter your problem )
( Enter your problem )
Algorithm and examples
  1. Introduction
  2. Algorithm & Example-1
  3. Example-2
  4. Unbalanced supply and demand example
 		Other related methods
  1. north-west corner method
  2. least cost method
  3. vogel's approximation method
  4. Row minima method
  5. Column minima method
  6. Russell's approximation method
  7. Heuristic method-1
  8. Heuristic method-2
  9. modi method (optimal solution)
  10. stepping stone method (optimal solution)
3. Example-2
(Previous example)		2. least cost method
(Next method)

4. Unbalanced supply and demand example


Unbalanced supply and demand
If the total supply is not equal to the total demand then the problem is called unbalanced transportation problem.

It's solution :
1. If the total supply is more than the total demand, then we add a new column, with transportation cost 0
2. If the total demand is more than the total supply, then we add a new row, with transportation cost 0
Example
Find Solution using North-West Corner method
D1D2D3Supply
S148876
S216241682
S38162477
Demand7210241


Solution:
TOTAL number of supply constraints : 3
TOTAL number of demand constraints : 3
Problem Table is
`D_1``D_2``D_3`Supply
`S_1`48876
`S_2`16241682
`S_3`8162477
Demand7210241


Here Total Demand = 215 is less than Total Supply = 235. So We add a dummy demand constraint with 0 unit cost and with allocation 20.
Now, The modified table is
`D_1``D_2``D_3``D_(dummy)`Supply
`S_1`488076
`S_2`162416082
`S_3`81624077
Demand721024120



The rim values for `S_1`=76 and `D_1`=72 are compared.

The smaller of the two i.e. min(76,72) = 72 is assigned to `S_1` `D_1`

This meets the complete demand of `D_1` and leaves 76 - 72=4 units with `S_1`

Table-1
`D_1``D_2``D_3``D_(dummy)`Supply
`S_1`4(72)8804
`S_2`162416082
`S_3`81624077
Demand01024120


Move horizontally,

The rim values for `S_1`=4 and `D_2`=102 are compared.

The smaller of the two i.e. min(4,102) = 4 is assigned to `S_1` `D_2`

This exhausts the capacity of `S_1` and leaves 102 - 4=98 units with `D_2`

Table-2
`D_1``D_2``D_3``D_(dummy)`Supply
`S_1`4(72)8(4)800
`S_2`162416082
`S_3`81624077
Demand0984120


Move vertically,

The rim values for `S_2`=82 and `D_2`=98 are compared.

The smaller of the two i.e. min(82,98) = 82 is assigned to `S_2` `D_2`

This exhausts the capacity of `S_2` and leaves 98 - 82=16 units with `D_2`

Table-3
`D_1``D_2``D_3``D_(dummy)`Supply
`S_1`4(72)8(4)800
`S_2`1624(82)1600
`S_3`81624077
Demand0164120


Move vertically,

The rim values for `S_3`=77 and `D_2`=16 are compared.

The smaller of the two i.e. min(77,16) = 16 is assigned to `S_3` `D_2`

This meets the complete demand of `D_2` and leaves 77 - 16=61 units with `S_3`

Table-4
`D_1``D_2``D_3``D_(dummy)`Supply
`S_1`4(72)8(4)800
`S_2`1624(82)1600
`S_3`816(16)24061
Demand004120


Move horizontally,

The rim values for `S_3`=61 and `D_3`=41 are compared.

The smaller of the two i.e. min(61,41) = 41 is assigned to `S_3` `D_3`

This meets the complete demand of `D_3` and leaves 61 - 41=20 units with `S_3`

Table-5
`D_1``D_2``D_3``D_(dummy)`Supply
`S_1`4(72)8(4)800
`S_2`1624(82)1600
`S_3`816(16)24(41)020
Demand00020


Move horizontally,

The rim values for `S_3`=20 and `D_(dummy)`=20 are compared.

The smaller of the two i.e. min(20,20) = 20 is assigned to `S_3` `D_(dummy)`

Table-6
`D_1``D_2``D_3``D_(dummy)`Supply
`S_1`4(72)8(4)800
`S_2`1624(82)1600
`S_3`816(16)24(41)0(20)0
Demand0000


Initial feasible solution is
`D_1``D_2``D_3``D_(dummy)`Supply
`S_1`4 (72)8 (4)8 0 76
`S_2`16 24 (82)16 0 82
`S_3`8 16 (16)24 (41)0 (20)77
Demand721024120


The minimum total transportation cost `=4 xx 72+8 xx 4+24 xx 82+16 xx 16+24 xx 41+0 xx 20=3528`

Here, the number of allocated cells = 6 is equal to m + n - 1 = 3 + 4 - 1 = 6
`:.` This solution is non-degenerate

This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then Submit Here


3. Example-2
(Previous example)		2. least cost method
(Next method)


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