- Preparation:
- The Hungarian Algorithm
for the Transportation Problem
works on a bi-partite graph
where:
- total supply (from factory vertices) = total capacity (of warehouses)
If the two amounts are not equal:
- Add a
dummy vertex
whose supply/capacity is equal to the
excess
- Connect the dummy vertex to all vertices of the other set using high cost edges
- The Hungarian Algorithm
for the Transportation Problem
works on a bi-partite graph
where:
- Example:
- Supply, capacity and cost assignment:
Total supply = 7 + 6 + 8 = 21
Total capacity (demand) = 5 + 3 + 5 + 2 = 15Excess supply = 6
- Adding dummy vertex:
- Adding dummy edges of high cost:
Note:
- As long as the cost of dummy edge > max. cost of real edge, the algorithm will avoid using a dummy edge if a real edge is available
- Supply, capacity and cost assignment: