## Transportation Models

The objective function is defined to minimize the cost of transportation, subject to demand and supply constraints.

Assume there are m supply points and n demand points in a problem. Let ci j denote the given unit cost of transportation from supply point i to demand (destination) point j. Let xi j denote the amount of product to be transported from supply point i to demand (destination) point j. The objective function can then be expressed as follows:

Minimize z,

z = i=m

This equation can be expanded and written as equations in which each row of the right-hand side of equation represents the cost of transportation from a supply point. For example, row 1 of the right-hand side of the equation represents the cost

point m.