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Transportation Problem : Find Optimal Solution

Find the optimal solution for the following problem:

TO
FROM Chicago Atlanta supply
St louis 40 63 250
Richmond 70 30 400
demand 300 350 650

Solution This solution is FREE courtesy of BrainMass!

solution:

Using the north west corner rule the initial basic feasible solution is

TO
CHICAOG ATLANTA
FROM
ST LOUIS 250
RICHMOND 50 350

TOTAL COST = 250 *40 + 50 *70 + 30 * 350

= 24000

optimal solution:

we have cij = ui+vj

ui = cij - vj
vj = cij - ui
randomly assign 0 to any one ui and then complete the table for assigned values

ui
40 - 0
70 30 30
vj 40 0

also

dij =cij - ( ui + vj) for non assigned values

ui
- 63 0
- - 30

vj 40 0

dij table:

- 63
- -

since the value is positive, the solution is optimal

TO
CHICAOG ATLANTA
FROM
ST LOUIS 250
RICHMOND 50 350

Total cost = 24000

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