Factories having surpluses | Supply |
A | 400 |
B | 1500 |
C | 900 |
Total | 2800 |
Distributors having demands | Demand |
W | 700 |
X | 600 |
Y | 1000 |
Z | 500 |
Total | 2800 |
Costs | W | X | Y | Z |
A | 20 | 40 | 70 | 50 |
B | 100 | 60 | 90 | 80 |
C | 10 | 110 | 30 | 200 |
W | X | Y | Z | |
A | 2 | 4 | 7 | 5 |
B | 10 | 6 | 9 | 8 |
C | 1 | 11 | 3 | 12 |
W | X | Y | Z | ||
A | 400 | 400 | |||
B | 200 | 800 | 500 | 1500 | |
C | 700 | 200 | 900 | ||
700 | 600 | 1000 | 500 | 2800 |
W | X | Y | Z | ||
A | 16,000 | 16,000 | |||
B | 12,000 | 72,000 | 40,000 | 124,000 | |
C | 7,000 | 6,000 | 13,000 | ||
153,000 |
W | X | Y | Z | Sum | |
A | 40 | 0 | |||
B | 60 | 90 | 80 | ||
C | 10 | 30 | |||
Sum |
W | X | Y | Z | Sum | |
A | 40 | 0 | |||
B | 60 | 90 | 80 | ||
C | 10 | 30 | |||
Sum | 40 |
W | X | Y | Z | Sum | |
A | 40 | 0 | |||
B | 60 | 90 | 80 | 20 | |
C | 10 | 30 | |||
Sum | 40 |
W | X | Y | Z | Sum | |
A | 50 | 40 | 70 | 60 | 0 |
B | 70 | 60 | 90 | 80 | 20 |
C | 10 | 0 | 30 | 20 | -40 |
Sum | 50 | 40 | 70 | 60 |
- First, that the estimation costs are higher than the real costs. In this case the solution is not optimal and a readjustment is necessary.
- Second, the estimation costs are equal or smaller than the real costs. In this case, no readjustments are necessary since the assignment is optimal and therefore a solution has been found.
- First, transfers are done along a circuit from an unused cell and by altering vertical and horizontal stages and by only using occupied cells.
- Second, each transfer is the exact opposite value of the other.
- Third, the value of a transfer is determined by the maximum value that all cells could subtract while still respecting the supply and demand constraints. For instance, if
W | X | Y | Z | ||
A | (+400) | 400 (-400) |
400 | ||
B | 200 (+400) |
800 (-400) |
500 | 1500 | |
C | 700 (-400) |
200 (+400) |
900 | ||
700 | 600 | 1000 | 500 | 2800 |
W | X | Y | Z | ||
A | 400 | 400 | |||
B | 600 | 400 | 500 | 1500 | |
C | 300 | 600 | 900 | ||
700 | 600 | 1000 | 500 | 2800 |
W | X | Y | Z | ||
A | 8,000 | 8,000 | |||
B | 36,000 | 36,000 | 40,000 | 112,000 | |
C | 3,000 | 18,000 | 21,000 | ||
141,000 |
W | X | Y | Z | Sum | |
A | 20 | 10 | 40 | 30 | 0 |
B | 70 | 60 | 90 | 80 | 50 |
C | 10 | 0 | 30 | 20 | -10 |
Sum | 20 | 10 | 40 | 30 |