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Home > Operation Research calculators > Vogel's approximation method example
3. vogel's approximation method example ( Enter your problem )
( Enter your problem )
Algorithm and examples
  1. Algorithm & Example-1
  2. Example-2
  3. Unbalanced supply and demand example
  4. Maximization Problem 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)
1. Algorithm & Example-1
(Previous example)		3. Unbalanced supply and demand example
(Next example)

2. Example-2


Find Solution using Voggel's Approximation method
D1D2D3D4Supply
S111131714250
S216181410300
S321241310400
Demand200225275250


Solution:
TOTAL number of supply constraints : 3
TOTAL number of demand constraints : 4
Problem Table is
`D_1``D_2``D_3``D_4`Supply
`S_1`11131714250
`S_2`16181410300
`S_3`21241310400
Demand200225275250


Table-1
`D_1``D_2``D_3``D_4`SupplyRow Penalty
`S_1`11131714250`2=13-11`
`S_2`16181410300`4=14-10`
`S_3`21241310400`3=13-10`
Demand200225275250
Column
Penalty		`5=16-11``5=18-13``1=14-13``0=10-10`


The maximum penalty, 5, occurs in column `D_1`.

The minimum `c_(ij)` in this column is `c_11` = 11.

The maximum allocation in this cell is min(250,200) = 200.
It satisfy demand of `D_1` and adjust the supply of `S_1` from 250 to 50 (250 - 200 = 50).

Table-2
`D_1``D_2``D_3``D_4`SupplyRow Penalty
`S_1`11(200)13171450`1=14-13`
`S_2`16181410300`4=14-10`
`S_3`21241310400`3=13-10`
Demand0225275250
Column
Penalty		--`5=18-13``1=14-13``0=10-10`


The maximum penalty, 5, occurs in column `D_2`.

The minimum `c_(ij)` in this column is `c_12` = 13.

The maximum allocation in this cell is min(50,225) = 50.
It satisfy supply of `S_1` and adjust the demand of `D_2` from 225 to 175 (225 - 50 = 175).

Table-3
`D_1``D_2``D_3``D_4`SupplyRow Penalty
`S_1`11(200)13(50)17140--
`S_2`16181410300`4=14-10`
`S_3`21241310400`3=13-10`
Demand0175275250
Column
Penalty		--`6=24-18``1=14-13``0=10-10`


The maximum penalty, 6, occurs in column `D_2`.

The minimum `c_(ij)` in this column is `c_22` = 18.

The maximum allocation in this cell is min(300,175) = 175.
It satisfy demand of `D_2` and adjust the supply of `S_2` from 300 to 125 (300 - 175 = 125).

Table-4
`D_1``D_2``D_3``D_4`SupplyRow Penalty
`S_1`11(200)13(50)17140--
`S_2`1618(175)1410125`4=14-10`
`S_3`21241310400`3=13-10`
Demand00275250
Column
Penalty		----`1=14-13``0=10-10`


The maximum penalty, 4, occurs in row `S_2`.

The minimum `c_(ij)` in this row is `c_24` = 10.

The maximum allocation in this cell is min(125,250) = 125.
It satisfy supply of `S_2` and adjust the demand of `D_4` from 250 to 125 (250 - 125 = 125).

Table-5
`D_1``D_2``D_3``D_4`SupplyRow Penalty
`S_1`11(200)13(50)17140--
`S_2`1618(175)1410(125)0--
`S_3`21241310400`3=13-10`
Demand00275125
Column
Penalty		----`13``10`


The maximum penalty, 13, occurs in column `D_3`.

The minimum `c_(ij)` in this column is `c_33` = 13.

The maximum allocation in this cell is min(400,275) = 275.
It satisfy demand of `D_3` and adjust the supply of `S_3` from 400 to 125 (400 - 275 = 125).

Table-6
`D_1``D_2``D_3``D_4`SupplyRow Penalty
`S_1`11(200)13(50)17140--
`S_2`1618(175)1410(125)0--
`S_3`212413(275)10125`10`
Demand000125
Column
Penalty		------`10`


The maximum penalty, 10, occurs in row `S_3`.

The minimum `c_(ij)` in this row is `c_34` = 10.

The maximum allocation in this cell is min(125,125) = 125.
It satisfy supply of `S_3` and demand of `D_4`.


Initial feasible solution is
`D_1``D_2``D_3``D_4`SupplyRow Penalty
`S_1`11(200)13(50)1714250 2 |  1 | -- | -- | -- | -- |
`S_2`1618(175)1410(125)300 4 |  4 |  4 |  4 | -- | -- |
`S_3`212413(275)10(125)400 3 |  3 |  3 |  3 |  3 | 10 |
Demand200225275250
Column
Penalty		5
--
--
--
--
--
5
5
6
--
--
--
1
1
1
1
13
--
0
0
0
0
10
10


The minimum total transportation cost `= 11 xx 200 + 13 xx 50 + 18 xx 175 + 10 xx 125 + 13 xx 275 + 10 xx 125 = 12075`

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


1. Algorithm & Example-1
(Previous example)		3. Unbalanced supply and demand example
(Next example)


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