Ch$.6$ The Transportation Model

Items are allocated from sources to destinations at a minimum cost.

In a balanced transportation model, the constraints have equalities.

Example: How many tons of wheat should be transported from each

grain elevator to each mill on a monthly basis in order to minimize

the total cost of transportation?

Grain Elevator Supply Mill Demand

$1.$ Kansas City $150$ A$.$ Chicago $200$

$2.$ Omaha $175$ B$.$ St$.$ Louis $100$

$3.$ Des Moines $275$ C$.$ Cincinnati $300$

Total $600$ tons $600$ tons

Transport Cost from Grain Elevator to Mill $($$$/$ton$)$

Grain Elevator A$.$ Chicago B$.$ St$.$ Louis C$.$ Cincinnati

$1.$ Kansas City

$2.$ Omaha

$3.$ Des Moines

$ $6$

$7$

$4$

$ $8$

$11$

$5$

$ $10$

$11$

$12$

xij $=$ tons of wheat

from each grain elevator, i$,$ i $=1,2,3$

to each mill j$,$ j $=$ A$,$ B$,$ C

Minimize Z $=$

subject to:

$=$

$==$ Decision variables in cells: