The Transportation Model

Shipping Costs

Each source-demand arc has a unit cost. The objective will use these exact costs, but the cost table itself is just pinned input data.

highlighted = computed this step

Cost Matrix

The unit costs are 2, 5, 4, and 1. Motivation: the objective multiplies each shipped amount by its arc cost, so every cell becomes a possible cost term.

cAX=2cAY=5cBX=4cBY=1c_{AX}=2\quad c_{AY}=5\quad c_{BX}=4\quad c_{BY}=1
Unit transportation costsEach unit-cost entry is pinned before the plan is optimized.unit costsXYA25B41

Arc View

The same costs can be read as a network. Interpretation: transportation is a special min-cost flow with sources, sinks, and shipment arcs.

arc labels are exact unit costs\text{arc labels are exact unit costs}
unit-cost graphc=2c=5c=4c=1A supply 3B supply 2X demand 2Y demand 3

Diagram note

Honesty note: this lesson only sets the costs; the next chapter solves the shipment plan. Pixel positions are rounded for layout; every number shown is exact.

costs are inputs, not solver output\text{costs are inputs, not solver output}
unit-cost graphc=2c=5c=4c=1A supply 3B supply 2X demand 2Y demand 3