Classical transportation problem
The classical transportation problem is solved.
Symbols:
| b(i) |
capacity of supplier i |
| d(j) |
demand quantity of customer j |
| x(i,j) |
transportation quantity from i to j |
| ds(j) |
cost difference in column j (Vogel's approximation
method) |
| dz(i) |
cost difference in row i (Vogel's approximation method) |
| u(i) |
dual variable associated to row i (MODI method) |
| v(j) |
dual variable associated to column j (MODI method) |
An initial solution is computed with Vogel's
approximation method. Next the MODI method
is applied to find the optimum solution.
All number are required to be integer.
If neccessary, a dummy-supplier or a dummy-customer with associated transportation
costs 9999 is introduced.
Literature:
- Krajewski/Ritzman (1996), Supplement G
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