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TRANSPORTATION MODELS

Perhaps the most widely used LP models are the transportation models. Oil companies commit huge resources to the implementation of such models. The classic example of a transportation problem involves the shipment of some homogeneous commodity from msources of supply or origins to npoints of
demand or destinations. By homogeneous is meant that there are no significant differences in the quality of the items provided by different sources of supply i.e., the product characteristics are essentially the same.

In the classic example, each origin can supply any of the destinations. And the demand at each destination may be supplied jointly from a combination of the origins or totally from one origin. Each origin usually has a specific capacity which represents the maximum number of units it can supply. Each destination has a specified demand which represents the number of units needed.

Given that each origin can supply units to each destination, some measure

x12+x22= 500

x13+ x23= 400

x14+ x24= 350

The complete formulation LP model is as follows.

Minimize Z=4x11 + 6x12+ 2.5x13+ 3 x14+ 5x21+2x22+ 3.5x23 +4.5x24

Subject to x11+ x12 + x13 + x14 ≥1000

X21 + x22+ x23 + x24 ≥ 800

x11+x21= 300

x12+x22= 500

x13+x23= 400

x14+ x24= 350

x11, x12, x13, x14,x21, x22, x23, x24 ≥0.