The Transportation Model

Supplies, Demands, and Balance

A transportation problem assigns limited supply to demand points. This lesson pins the balanced instance before any optimization happens.

highlighted = computed this step

Supplies

Source A has supply 3 and source B has supply 2. Motivation: a transportation model starts by naming what can be shipped before any route is priced.

sA=3sB=2s_A=3\quad s_B=2
Balanced transportation instanceThe supplies and demands are the pinned balanced instance.supply and demandAB or Ytotalsupply325demand235

Demands

Demand point X needs 2 and demand point Y needs 3. Why: every shipped unit must end at a demand point, so column totals are part of the model rather than decoration.

dX=2dY=3d_X=2\quad d_Y=3
Balanced transportation instanceThe supplies and demands are the pinned balanced instance.supply and demandAB or Ytotalsupply325demand235

Balanced Total

Total supply and total demand both equal 5. Interpretation: in a balanced instance, every unit can be assigned without surplus or shortage inside this exact model.

∑si=∑dj=5\sum s_i=\sum d_j=5
Balanced transportation instanceThe supplies and demands are the pinned balanced instance.supply and demandAB or Ytotalsupply325demand235

Diagram note

Honesty note: the table is the exact balanced instance that the solver will optimize. Pixel positions are rounded for layout; every number shown is exact.

balance is checked before optimizing\text{balance is checked before optimizing}
Balanced transportation instanceThe supplies and demands are the pinned balanced instance.supply and demandAB or Ytotalsupply325demand235